Production well optimization and modelling is very important in the efficient management of oil and gas production from a well. A major factor contributing to this process is the accurate estimations of the flowing bottom-hole pressure at the formation as it helps in various petroleum production engineering analysis. Some of this analysis includes studies on Vertical Lift Performance (VLP) and Inflow Performance. The effective determination of bottom-hole pressure has been a major concern in the industry due to several reasons as it can either be measured or estimated. In the case of measurement, a pressure gauge is needed down-hole, this is very accurate but expensive and time-consuming. For this reason, this project will focus on flowing bottom-hole pressure estimation from wellhead pressure and data as it is generally cost-effective and it can be easily determined within a short period of time. This will be achieved through the modification of Guo’s (2001) method of simultaneous flow of gas, oil, water and sand particles (4-phase flow) in borehole tubing. Guo’s model will be modified and will only consider the frictional pressure gradient term in the general energy equation and account for only vertical multiphase flow. The result of this work obtained with the use of mat lab when applied to the simulation of two-phase flow in vertical oil wells and high Gas-Oil ratio wells are relatively accurate. However, low Gas-Oil ratio wells fall short of the model estimation of pressure.






TABLE OF CONTENTS ………………………………………………………………….. vi




CHAPTER ONE …………………………………………………………………………… 1

1.0    INTRODUCTION    1

1.1     Background of Study    1

1.1.1    What is Bottom Hole Flowing Pressure …………………………………….. 2

1.1.2    Typical Flow Regimes ………………………………………………………... 3\l "

1.2.3    Vertical multiphase flow    4

1.2    Statement of Problem    7

1.3    Aim & Objectives    8

1.4    Significances of Study    9

1.5    Scope of the Project     9




3.0    METHODOLOGY    16

3.1    Model Derivation and Development    16

3.2    Model Assumptions    16

3.3    Model Modification    17

3.3.1    Modification of mixture specific weight, ρm    17

3.3.2    Modification of mixture velocity, Vm    21

3.4    Solution Method    27



4.1    Raw Data Analysis    28

4.2    Result Analysis    29

4.2.1    High GOR well    30

4.2.2    Low GOR well    31

4.2.3    Low GOR producing water well    32

4.2.4    High GOR producing water well    33

4.2.5    Heavy oil well    34



5.1    Conclusion    35

5.2    Recommendation    35




Figure1.1: Flow Patterns in Vertical Flow ……………………………………………………6

Figure1.1.3: Flow Regime in Vertical Flow as a Function of the Superficial Velocities of Gas and Liquid Flow …………..7

Figure 4.2.1: Approximate Pressure Profile for High GOR well …………………………..30

Figure 4.2.2: Approximate Pressure Profile for Low GOR well …………………………..31

 Figure 4.2.3: Approximate Pressure Profile for Low GOR (Producing water) well …….32

Figure 4.2.4: Approximate Pressure Profile for High GOR (Producing water) well ……33

Figure 4.2.5: Approximate Pressure Profile for Heavy oil well …………………………34


Table 4.1: Well Head Pressure, Flow Rates and Fluid Gravity Data for Five Different wells………..28

Table 4.2: Summary of estimated flowing bottom-hole pressures compared with the measured values for the five producing vertical oil wells……………………………………………………………….29


A: Pipe cross-sectional area, sq.ft

di:Tubing inner diameter, ft.

dh: Incremental depth, ft.

dP: Pressure differential, lb/ft3

ɛ: Pipe wall roughness factor, dimensionless

ƒ: Dimensional Moody frictional factor (Nikuradse’s correlation)

g: Acceleration due to gravity, ft/s2

gc: gravitational constant, lb-force

K: Universal positive constant with a value dependent on units employed

Ps: Atmospheric pressure, psia

P: Pressure, lb/ft3

Pwh: Wellhead pressure, psia

Qs: Volumetric flow rate of solid, ft3/day

Qo: Volumetric flow rate of oil, bbl/day

Qw: Volumetric flow rate of water, bbl/day

Qgs: Volumetric flow rate of gas at standard conditions, ft3/day

Q: Volumetric flow rate of mixture, ft3/sec

qs: Volumetric flow rate of solids, ft3/sec

ql: Volumetric flow rate of liquids, ft3/sec

qg: Volumetric flow rate of gas, ft3/sec

Ts:Surface Temperature, 0R

T: Bottom-hole temperature, 0R

Vm:Mixture fluid velocity, ft/sec

V: Volume of flowing fluid, ft3

W: weight flow rate of mixture, lb/sec

Ws: Weight flow rate of solids, lb/sec

Wl: Weight flow rate of liquids, lb/sec

Wg: Weight flow rate of gas, lb/sec

ρm: Mixture specific weight, lb/ft3

ρw: Density of water, lb/ft3

ρo: Density of oil, lb/ft3

γs: Specific gravity of Solid with respect to water, dimensionless

γo: Specific gravity of Oil with respect to water, dimensionless

γw: Specific gravity of water, dimensionless

γg: Specific gravity of gas with respect to air, dimensionless




     Interpretation of data from Well test analysis have been based on the implicit assumption that the reservoir is a homogeneous single layer. However, the real petroleum reservoir, is a composition of layers with unique interlayer characteristics. The individual layers are usually separated from each other by an interface which could be either permeable or impermeable. Pressure behavior in this kind of vertically heterogeneous system is not necessarily like that of a single layered system and seldom reveals more than the average properties of the entire system. It is against this backdrop that this study became necessary.  Well completion in such systems would be more instructive, enabling better reservoir and production engineering practice if detailed layer information is available at it prime. The petroleum industry is however interested in accurately calculating the pressure losses that occur for multiphase flow in the tubing and pipelines. Accurate predictions of pressure losses in pipes would enable proper design. Also, pressure determination in a production system in the petroleum industry is very important as it helps in the effective production of oil and gas from the reservoir but of all, the most important is the determination of flowing bottom-hole pressure as its knowledge helps in the determination of so many parameters needed for efficient production and also to avert early depletion of the reservoir. Its knowledge can also be used to prevent formation damage which could be caused by early sand production in the reservoir. Surface pressures often can be converted to bottom-hole values if adequate information is available about the wellbore system.


The pressure at the bottom of a working oil, water, or gas well (the Great Soviet Encyclopedia, 1979). The pressure measured in a well at or near the depth of the producing formation. For well-test purposes, it is often desirable to refer the pressure to a datum level chosen at a reference depth by calculating the pressure that would occur if the pressure measurement were made at the datum level rather than at the actual depth of the gauge

(Schlumberger oilfield glossary). A knowledge of this pressure is fundamental in determining the most efficient methods of recovery and the most efficient lifting procedure, yet there is less information about these pressures than about any other part of the general problem of producing oil (Millikan and Sidwell, 1930). As earlier said, the bottom-hole pressure can be determined from surface pressures like the well head pressure if adequate information is available about the production system which can be easily gotten from well testing operations (Economides, 1979). Since the well head pressure and parameters are easily gotten from pressure transient analysis whose success depends on the accurate measurement or estimation of bottom-hole pressure (Omohimoria and Ayodele, 2013), it is therefore desirable and necessary to obtain the bottom-hole pressure from these data. This will be carried out in order to further highlight the advantages which is associated with having adequate knowledge about the bottom-hole pressure of a reservoir.


 At certain position and time in the reservoir, different flow behaviours are usually encountered in the reservoir. This gives rise to different flow regimes. Flow regimes are usually classified according to the rate of change of pressure with respect to time and position


During steady-state flow, the pressure does not change with time. This is observed for example when a constant pressure effect, such as resulting from a gas cap or some types of water drive, ensures a pressure maintenance in the producing formation. Pressure usually will changes from one point to the other in the reservoir algebraically,


Pseudo steady state

The pseudo steady-state regime characterizes a closed system response. With a constant rate production, the drop of pressure becomes constant for each unit of time.

Image……………………….. 1.2

Where k is a constant.  In practice, this can be reached more easily than the steady state.

 Transient state

Transient responses are observed before constant pressure or closed boundary effects are reached. The pressure variation with time is a function of the well geometry and the reservoir properties, such as permeability and heterogeneity. It can be expressed mathematically as,

Image………………………….. 1.3


Usually, well test interpretation focuses on the transient pressure response. Near wellbore conditions are seen first and later, when the drainage area expands, the pressure response is characteristic of the reservoir properties until boundary effects are seen at late time (then the flow regime changes to pseudo steady or steady state). The applications of the steady-state flow to describe the flow behavior of several types of fluid in different reservoir geometries are presented below. These include:

• Linear flow of incompressible fluids

• Linear flow of slightly compressible fluids

• Linear flow of compressible fluids

 • Radial flow of incompressible fluids

 • Radial flow of slightly compressible fluids

 • Radial flow of compressible fluids

 • Multiphase flow

1.1.3 VerticalMultiphase flow

Much has been written in the literature regarding the multiphase flow of fluids in the pipe. This problem is much more complex than the single-phase flow problem because there is the simultaneous flow of both liquids (oil or condensate and water) and vapour (gas). The mechanical energy equation Image is the basis for methods to estimate the pressure drop under multiphase flow; however, the problem is in determining the appropriate velocity, friction factor, and density to be used for the multiphase mixture in the calculation. In addition, the problem is further complicated as the velocities, fluid properties, and the fraction of vapour to liquid change as the fluid flows to the surface due to pressure changes.

Many researchers have proposed methods to estimate pressure drops in multiphase flow. Each method is based on a combination of theoretical, experimental, and field observations, which has led some researchers to relate the pressure-drop calculations to flow patterns. Flow patterns or flow regimes relate to the distribution of each fluid phase inside the pipe. This implies that a pressure calculation is dependent on the predicted flow pattern. There are four flow patterns in the simplest classification of flow regimes:

⦁    Bubble flow

⦁    Slug/Plug flow

⦁    Churn flow

⦁    Annular-mist flow

Bubble: (Fig...) This type of flow was noted to occur at very low gas velocities.  This type of flow is characterized by bubbles of gas moving along the upper part of the pipe at approximately the same velocity as the liquid.

Slug/Plug flow: (Fig…) In this type of flow, the flow of liquid is basically restricted due to the number of gases that evolve from the liquid phase and collage to form slug-like gas pockets. Like the bubbly flow, the liquid phase is the continuous phase but in this case, the gas phase overrides the liquid phase.

Churn flow /Semi-annular: (Fig...) It is characterized by secondary currents set up by the velocity gradients in the liquid causing the liquids to climb the tube walls and, aided by waves, to coalesce at the top.  The amount of liquid in the bottom of the tube was greater than at the top and walls, hence the name semi-annular.

Annular: (Fig...) This type of flow is characterized by liquid flowing in a thin film around the entire inside face of the pipe, the gas flowing at a high velocity as a central core.  The liquid is flowing in a continuous annular ring, hence the name annular flow.


Figure 1.1: Flow patterns in Vertical Flow


Figure 1.1.3 above (Taitel, Bornea and Duckler, 1980) shows the various flow regimes that could be expected in vertical flow as a function of the superficial velocities of gas and liquid flow


A calculation method for predicting Bottom Hole Pressure (BHP) based on easily obtainable wellhead parameter has been the preferred method in the oil and gas industry. But the predictive capability of the existing correlations is a thing of concern to the oil industry operators. This is due to the inability of the existing models and correlations to account for the presence of sand particles in the flow stream; also, the requirement for the well to be shut-in for BHP predictions is counterproductive.


The aim of the project is to determine the flowing bottom-hole pressure of a vertical well from surface pressure and well parameters. This will be done by the modification of the general energy equation considering only the frictional pressure term. The modified equation (derived model) will be validated with well data that will be gotten from a company.

The objectives of determining the flowing bottom-hole pressure of a well from wellhead pressure and wellhead data include the following:

⦁    Efficient interpretation of the behaviour of the underground system.

⦁    Determination of BHP helps in the provision of important information for efficient production, avert early depletion and early sand production in the reservoir.

⦁    Determination of the most efficient methods of recovery and the most efficient lifting procedures.

⦁    Determination of pressure losses in pipes and tubing for proper design of Artificial Lift Systems - Gas Lift, ESP’s etc.

⦁    Production Optimization - Identification of production bottlenecks, Gaslift optimization, and completion designs.


This study providesa better and economic guide on how flowing bottom-hole pressure can be estimated from well head pressure and well head data and also considers time. In order words, the estimation method delivers results quickly without much expenses, unlike directly measuring the BHP with down-hole pressure gauges which is much more expensive.


The main focus of this research is limited to the estimation of flowing bottom-hole pressure (BHP) for a vertical well from well head pressure (Surface pressure) and well head data which will be obtained from a company. It will show how pressure can be determined mathematically from the available data through modelling using MATLAB. It should be noted that this study is a modification of Guo’s systematic model for flowing bottom-hole pressure predictions.



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