An Improved Method To Determine Horizontal Well Productivity At Steady State

Project and Seminar Material for Science and Engineering

An Improved Method To Determine Horizontal Well Productivity At Steady State


As the petroleum industry continues to experience advances and progress in drilling techniques, the use of horizontal well in field development has been increasing very rapidly throughout the oil industry. It becomes therefore important to adequately determine the performance of horizontal wells.

The existing methods available to determine horizontal well productivity at steady state requires complex mathematical analysis and are difficult to develop. In the course of this work, a new method was developed using simple analytical methods. Results obtained by this new method were compared to that gotten from already established methods of Borisov (1964), Giger (1984) and Joshi (1988).

The major objective of this work is to present a simple and effective means to estimate the performance of horizontal wells. An excel sheet was also created in the course of this project to calculate and compare productivity index gotten from the various method. The spread sheet also enable me carry out sensitivity analysis of the results gotten by varying key parameters.

Table Of Contents

  • Title Page
  • Certification
  • Dedication
  • Table Of Content
  • List Of Tables
  • List Of Figures
  • Acknowledgement
  • Abstract
  • Nomenclature

Chapter One

  • 1.1 Introduction
  • 1.2 Background Of Study
  • 1.2.1 Applications Of Horizontal Wells
  • 1.2.2 Advantages Of Horizontal Wells
  • 1.2.3 Disadvantages Of Horizontal Wells
  • 1.2.4 Inflow Performance Relationship
  • 1.3 Problem Statement
  • 1.4 Research Objective
  • 1.5 Research Question
  • 1.6 Justification Of This Study
  • 1.7 Scope Of Study

Chapter Two

  • 2.1 Literature Review
  • 2.2 Productivity Index
  • 2.3 Horizontal Well Productivity
  • 2.3.1 Borisov’s Model
  • 2.3.2 Giger’s Model
  • 2.3.3 Joshi’s Model
  • 2.3.4 Renard And Dupuy Model
  • 2.3.5 Elgaghad, Osisanya And Tiab Model
  • 2.3.6 Babu And Odeh (Pseudo-Steady State) Model

Chapter Three

  • 3.1 Model Description
  • 3.2 Individual Layer And Boundary Characterization

Chapter Four

  • 4.1 Analysis Of Result
  • 4.2 Percentage Deviation Of Results
  • 4.3 Discussion

Chapter Five

  • 5.1 Conclusion
  • 5.2 Recommendation
  • References
  • Appendix

List Of Tables

  • Table 4- SEQ Table \* ARABIC 1; Comparison of Productivity index Result
  • Table 1A; Variation of Productivity Index with Changing Well Length
  • Table 1B; Comparison of Vertical and Horizontal Well Productivity at Various Reservoir Thickness

List Of Figures

  • Figure1-1; A schematic of a vertical well drilled perpendicular to the bedding plane, and a horizontal well drilled parallel to the bedding plane.
  • Figure 1-2; Horizontal well following thin bed formation.
  • Figure 1-3; use of horizontal well to minimize Water and/or Gas coning
  • Figure 1-4; Intersection of Fractures
  • Figure SEQ Figure \* ARABIC 1-1; Division of 3D horizontal well problem into 2D problems
  • Figure 2-2; Transformation of Eclipse into Unit Circle
  • Figure 2-3; Babu and Odeh Physical Model
  • Figure 3-1; Reservoir Model with fully penetrating well
  • Figure 3-2; Model Boundaries conditions
  • Figure 3-3; Flow Geometry in the Reservoir
  • Figure 4-1; Plot of Productivity Index against Well Length
  • Figure 4-2; Plots of Productivity Index against Reservoir Thickness
  • Figure 4-3; The effect of Reservoir Thickness on Productivity Ratio


  • A, drainage area of horizontal well, ft2
  • a, reservoir width
  • a = half major axis of drainage ellipse, ft
  • Bo, oil formation volume factor, rb/STB
  • b, extension of drainage volume of horizontal well in y-direction,ft
  • C, unit conversion factor
  • CH, geometric factor in Babu and Odeh’s model
  • D, wellbore diameter
  • h, reservoir thickness, ft
  • Iani, permeability anisotropy, dimensionless
  • J, productivity index, STB/day/psi
  • k, effective permeability, md
  • kH, horizontal permeability, md
  • kV, vertical permeability, md
  • L, horizontal wellbore length, ft
  • L1/2, half length of horizontal wellbore, ft
  • p, reservoir pressure, psi
  • pe, reservoir pressure at boundary, psi
  • pi, initial pressure, psi
  • pwf, bottomholeflowing pressure, psi
  • qo, oil production rate, STB/day
  • re, radius of outer boundary of the reservoir, ft
  • rw, wellbore radius, ft
  • s, skin factor, dimensionless
  • sR, partial penetration skin factor, dimensionless
  • Greek symbol
  • ε, relative pipe roughness
  • Φ, flow potential
  • ϕ, porosity
  • θ,wellbore inclination
  • µ, viscosity
  • ρ, density

Chapter One

1.1 Introduction

The major purpose of a horizontal well is to enhance reservoir contact and thereby enhance well productivity. A horizontal well is drilled parallel to the reservoir bedding plane. In other words, a vertical well is drilled perpendicular to the bedding plane (see fig1.1).

Figure 1.1 A Schematic of a Vertical Well Drilled Perpendicularly to the Bedding Plane, and a Horizontal Well Drilled to the Bedding Plan

Figure 1-1 A Schematic of a Vertical Well Drilled Perpendicularly to the Bedding Plane, and a Horizontal Well Drilled to the Bedding Plan

If the reservoir bedding plane is vertical, then a conventional vertical well will be drilled parallel to the bedding plane and in the theoretical sense it would be horizontal well. The objective here is to intersect multiple pay zones Horizontal wells have become popular for producing oil and gas reservoirs in many regions around the world. The objectives of horizontal wells include increasing oil and gas production, turning a non-commercial oil or gas reservoir into a commercial reservoir and controlling severe coning problems.

Due to the fact that horizontal wells can enhance reservoir recovery, they should be taken into consideration when planning a field development. While horizontal wells are generally more expensive to drill than vertical wells, they often reduce the total number of wells required in a reservoir development. As an increasing number of horizontal gas wells are drilled, the need for a quick and reliable method to estimate the pressure-rate behavior of these wells is important to optimize well performance and make operational decisions. A reliable and simple analytical and empirical relationship will provide engineers a technique to assess the performance of horizontal wells prior to undertaking extensive and often time-consuming simulation studies to model the well behavior.

Inflow performance relationship (IPR) is a pressure-rate relationships used to predict performance of oil and gas wells. There is a linear relationship when the reservoir is producing at pressure above bubble point pressure i.e. when Pwf is greater or equal to bubble point pressure. A curve is obtained at Pwf less than bubble point pressure. The linear form of an IPR represents the Productivity Index (PI) which is the inverse of the slope of the IPR. Horizontal oil well IPR also depends on the flow condition that is whether it is transient, steady or pseudo-steady state flow, which is determined by reservoir boundary condition. As the use of horizontal and multilateral wells is increasing in modern exploitation strategies, inflow performance relationships for horizontal wells are needed. The objective of this work is to develop analytical equation and IPRs for horizontal oil wells in steady state conditions that are easy to apply.

1.2 Background Of Study

Horizontal wells are high-angle wells (with an inclination of generally greater than 85ᵒ) drilled to enhance reservoir performance by placing a long wellbore section within the reservoir. There was relatively little horizontal drilling activity before 1985. A variety of configurations of drilled wells have come to be characterized as horizontal wells or drainholes. Drainholes are short length wellbores drilled pre-existing vertical wells in order to enhance production. These extend between 100 and 500 ft. in either direction. Horizontal wells on the other hand, involve the drilling of new wells and are usually 1000ft or more in length.

The use of horizontal wells to increase the area of contacted reservoir dates back to the early 1940’s. Feasibility of creating such architecture to drain a reservoir better, has been proven for a long time but the economic viability of such a process did not establish itself until recent years. This has been largely due to titanic advances in drilling, surveying and interpretation technologies.

The following are fields around the world that have been successfully drilled and are producing through horizontal wells:

  • Austin Chalk Formation Texas
  • Spraberry Tread West Texas
  • Pearsall Field South Texas
  • Okoro Oilfield Niger Delta, Nigeria

1.2.1 Applications Of Horizontal Well

Horizontal wells are mostly applied in the following areas;

1. To Exploit Thin Oil and Gas Zone Reservoirs: A horizontal wells reflects an increased area of contact of the well with the reservoir when compare to vertical wells in a thin pay zone. As a result of this increased area of contact, there is an increase in production from horizontal wells.

Figure 1.2 Horizontal well following thin bed formation

Figure 1-2: Horizontal well following thin bed formation

2. Reduction of Coning: A horizontal well is expected to have a reduced pressure drawdown when compared to a vertical well for a similar production level. This reduced drawdown pressure is expected to delay the onset of water (gas) breakthrough. Oil recovery is expected to be high except in cases where the well intersects fractures or zones of high permeability which could result in early water (gas) breakthrough.

Figure 1.3 use of horizontal well to minimize Water and or Gas coning

Figure 1-3: use of horizontal well to minimize Water and/or Gas coning

3. To intersect fracture in a naturally fractured reservoir in order to drain them effectively.

Figure 1-4 Intersection of Fractures

Figure 1-4: Intersection of Fractures

4. In Enhance Oil Recovery (EOR) applications, especially in thermal EOR. Horizontal well provides a large reservoir contact area and therefore enhances injectivity of an injection well. It also helps to increase the sweep efficiency.

1.2.2 Advantages Of Horizontal Wells

  1. Improved sweep efficiency in pattern flood situations.
  2. Reduction in coning. Lower drawdown for the same flow rate as vertical wells, causes stable interface movement delaying the breakthrough of unwanted fluids.
  3. Reduced fluid velocities around wellbore thereby reducing the occurrence of turbulent flow.
  4. Fewer number of wells is required for field development.
  5. Better access to isolated zones and exploiting gravity drainage mechanism effectively.
  6. Drilling relief wells for blow out prevention.
  7. Accessing untapped portion of a reservoir under constrained drilling conditions (offshore platforms).

1.2.3 Disadvantages Of Horizontal Wells

  1. It is not suitable for thick reservoirs.
  2. Completion and Stimulation technology has not been perfected yet.
  3. If natural fractures connect the aquifer or gas cap, the breakthrough of unwanted fluids can be accelerated.
  4. Not suitable in low vertical permeability situations.
  5. Higher cost of drilling per well.
  6. Hole problems encountered while drilling can be a serious drawback.

1.2.4 Inflow Performance Relationship (IPR)

The relation between production rate (q) and flowing wellbore pressure (pwf) over the practical range of production conditions, this relation is commonly known as inflow performance relationship (IPR). Productivity index is a measure of the ability of a well to produce. It is the ratio of the liquid flow rate to the pressure drawdown defined as below:

J = Qo/Pi-Pwf  —– 1.1

Productivity index is also denoted by J. It is a reliable indication of the well productive capacity only if the well is producing during pseudo steady state flow regime. Hence, it is important to allow the well to flow at constant flow rate for a sufficiently long period of time to reach the pseudosteady state. For performance analysis of oil wells, engineers often assume that flow rate is directly proportional to pressure drawdown, with productivity index J as the proportionality constant. The resulting IPR is a straight line passing through the origin and is only applicable to undersaturated oils. The effect of two phase flow on the shape of IPR curve was first observed in 1920s and 1930s during field testing with a curved rather than straight line IPR [1]. In this case, the productivity index is not constant and decreases with increasing drawdown. Several empirical methods have been proposed in the literature.

1.3 Problem Statement

With the increasing use of horizontal well in oil field development, it is important to develop simple and easy to apply method to determine the well performance and future performance prediction using the inflow performance relationship. The various method available for single phrase steady state inflow performance relationship for horizontal well required complex calculation and mathematics, making the process difficult to understand and replicate. This work seeks to develop a simple analytical method for horizontal well performance relationship.

1.4 Research Objective

The general objective of this research is to develop a simple method to estimate horizontal oil well productivity. The specific objectives include;

  1. To develop a simple method to estimate horizontal oil well productivity.
  2. To compare the new method to existing established method

Once develop the new equation will be apply to a single phrase reservoir model to determine horizontal well productivity.

1.5 Research Question

How do the reservoir flow geometry and reservoir properties affect the productivity of a horizontal oil well?

1.6 Justification Of The Study

Horizontal wells are drilled for the basic reason of producing more oil and gas than vertical well. When an engineer is in the process of deciding whether to drill a horizontal or vertical well, one of the first things he looks at is the ratio of horizontal productivity to vertical productivity. It becomes necessary to develop simple analytical method to determine the productivity of horizontal wells.

1.7 Scope Of Study

It is very important in petroleum engineering to formulate the relation between production rate (q) and flowing wellbore pressure (pwf) over the practical range of production conditions. As more and more horizontal wells are drilled all over the world, methods for evaluation and analysis of performance of these well becomes important to justify the cost incurred in drilling horizontal wells. Horizontal oil well productivity determination is a very important aspect in oil field development plan.

Chapter Five

5.1 Conclusion

In conclusion, this project work have been able to establish that horizontal well productivity can be determine using simple analytical method as oppose to the other conventional methods that required complex mathematics and transformation of elliptical drainage problems.

This new analytical model is easy to develop and apply. This method saves time and gives closely related results and those obtain by Borisov (1964), Giger (1984) and Joshi (1988) method. It is also noticed that as the length of the well increases towards that of reservoir, my new method gives almost the same result as that of Joshi (1988) and Borisov (1964). With this method horizontal well performance can be easily determine within the limit of application. This will enable the reservoir engineer to make inform decision on whether to use vertical or horizontal well for the field development.

5.2 Recommendation

As more horizontal well are drilled around the world daily, it becomes necessary to carry further research and development in describing horizontal well productivity and the factors that affect it. Existing model should be reviewed in the light of actual field production performance of horizontal well. There should be modification of existing method to accurately determine horizontal well productivity after matching with actual field data. The influence of wellbore hydraulics, frictional losses and well eccentricity on the productivity of horizontal should also be considered.

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