The study will examine pump capacity determination for two-phase vertical fluid flow. It will determine the Hydraulic Horse Power Requirement needed to maintain production of reservoir fluid within economic limit.

It is important to accurately predict the pressure drop accross a production system. This has been a difficult task in the oil and gas industry as the production system in real life is not homogenous (single phase) as assumed in most theories. The reason for this is that the two-phase flow is complex and difficult to analyze. Ideally, gas moves at a much higher velocity than the liquid. As a result, the down hole flowing pressure of the liquid-gas mixture is greater than the corresponding pressure corrected for down hole temperature and pressure and this could be calculated from the produced gas-liquid ratio.

Multiphase flow is a complex problem occurring in most industries. In the oil and gas industry, the ability to predict the holdup of each phase is of considerable importance. Therefore, in order to design and operate oil production systems in an optimized manner, it is necessary to accurately predict the behavior of two-phase flow of oil and gas in tubing.

Engineers performing multiphase-flow design calculations for wellbores are clearly faced with the question; which correlation or model should be used? Many companies  have employ the two-phase flowdiscused in this study, several of these models are incorporated in the literature.

No existing comprehensive model properly accounts for all the effects of produced gas-liquid ratio in larger diameter tubing. Although excellent models such as Duns and Ros (1963), Orkiszewski (1967) and Beggs and Brill (1973) are available to predict flow patterns at all tubing sizes.


Title Page………………..i




Table of content……...…v




1.0 Background of Study    3

Statement Of The Problem    5

Objectives    6

Scope of The Work    6


Review of Literature    7

Multiphase Flow Concept    7

2.2    Two-Phase Flow Terms    9

2.2.1 Flow Regime.    9

2.2.2 Liquid holdup    11

Void Fraction    13

2.3     Reservoir Fluid Properties    13

2.3.1    Solution Gas-Oil Ratio, Rs    14

2.3.2    Viscosity, Image    16

2.3.3    Formation Volume Factor, FVF    19

2.3.4    Density, Image    22

2.3.5    Fluid Flow Rate, Q.    23


Methodology    26

3.1 Empirical Correlations    26

3.1.1 Orkiszewski’s Correlation (1967)    27

3.1.2 Beggs and Brill Correlation (1973)    31

3.1.3 Duns and Ros Correlation    33

3.1.4 Hagedorn and Brown Correlation    39

3.2 Algorithm for application of the Empirical Correlations    42

3.2.1 Duns and Ros Correlation (1963)    42

3.2.2 Hagedorn and Brown Correlation (1964)    47

Orkiszewski’s correlation    49

Beggs and Brill’s Correlation (1973)    51


4.1 Results and Discussion    52

4.2 Preliminary Calculation Results    55



5.1 CONCLUSION    58


References    59

Appendix A    62

Input Data For Analysis    62

Appendix B    63

Nomenclature    63



1.0 Background of Study

In the production system, Pressure drop has been a major issue in the field. These pressure drops could be experienced as a result of valves and fittings

installed, due to friction along pipe sections or in lifting fluid up to a certain level.

As these pressure drops are identified, and the economic flow rate of a reservoir fluid is known, pumps may be employed to reduce the effect of pressure drop and maintain a given fluid flow rate for good economic recovery. These pump applications are usually analysed to determine an optimum Hydraulic pump requirement for a given fluid system and pipe diameter. It can form one of the basic aspect to be considered during well completion in selecting production tubing diameter.

In general, a pump is a device used to transport liquids, gases, and slurries. However,the term pump is usually used to refer to liquid handling equipment. The purpose of the pump is to provide a certain pressure at certain flowrate of a process stream. The pressure requirement is dictated by the process andpiping involved, while the flow rate is controlled by the required capacity in thedownhole units.

At least one out of every 10 barrels of oillifted in the world’s oil and gas operations are produced using an ElectricSubmersible Pump (ESP). Typical installationsproduce liquids in the 2,000 to 20,000 bpd range,making the ESP an effective and economical meansof lifting large volumes of fluids from great depthsunder a variety of well conditions.

There are several types of pumps used for liquid handling. However, these can bedivided into two general forms: positive displacement pumps (including reciprocatingpiston pump and the rotary gear pump), and centrifugal pumps. The selection of thepump type depends on many factor including the flow rate, the pressure, the nature ofthe liquid, power supply, and operating type (continuous or intermittent).

The power requirement for a mechanical system, like pumps and compressors, isgiven by the general mechanical balance equation:

            P = -mWs = m                                 1.1

All terms in this equation take their normal meaning with m being the mass flow rate,and α a coefficient used to take into account the velocity profile inside the pipe (forlaminar α = 0.5, while for turbulent α = 1). The required work (or power) given by Pis the total work that needs to be delivered to the fluid. This work will be drawn froma motor (operated with electricity or engines). The conversion between the motor andpump power is not complete and an efficiency is defined to describe the powerconversion. The efficiency is given by:


The input power can be measured from the source. For example, if the pump is

operated with electricity, the input power will be I×V (current times voltage). Theoutlet power can be determined using Equation (1.1).

1. Static head (Δzterm): the height to which the fluid will be pumped.

2. Pressure head ( term): the pressure to which the fluid will be delivered (ina pressurized vessel for example). The pressure units must be converted to lengthunits using relation.

3. System or dynamic head (F term): the energy lost due to friction in pipes, valves,fittings, etc.

1.1.         Statement Of The Problem

It is important to accurately predict the pressure drop accross a production system. This has been a difficult task in the oil and gas industry as the production system in real life is not homogenous (single phase) as assumed in most theories. The reason for this is that the two-phase flow is complex and difficult to analyze. Ideally, gas moves at a much higher velocity than the liquid. As a result, the down hole flowing pressure of the liquid-gas mixture is greater than the corresponding pressure corrected for down hole temperature and pressure and this could be calculated from the produced gas-liquid ratio.

This pressure drop in a flowing (production) system could be identified using different existing correlations. Some of these correlations are empirical, mechanistic or numerical. Hagedorn and Brown is the most widely used correlation for vertical wells (Schoham, 2006). In planning well completion the tubing diameter that will give less pressure drop hence much liquid production can be selected by the use of multiphase correlation.

It is also very necessary to plan for pumps in tubing size selection should need arise on future production for pumping of the reservoir fluid to optimize production.

1.2.         Objectives

Determine the Hydraulic Horse Power Requirement needed to maintain production of reservoir fluid within economic limit.

The above objective can be achieved by using two-phase pressure drop correlations to determine pressure drop in selected production tubing used in the Niger Delta.

1.3.         Scope of The Work

The determination of pressure drop using the selected two-phase correlations using production tubings used most often in the Niger Delta.


Review of Literature

Multiphase Flow Concept

The use of multiphase flow- pressure drop correlation is a vital consideration for the development of production system vertical components. Hagedorn& Brown, Duns &Ros, Aziz &Govier developed the most widely used correlations for vertical multiphase flow in the oil and gas industry. In the vertical component of production system, the flow of fluids may probably pass through the annulus between the casing and the production tubing. Therefore, it is necessary to predict the pressure drop in the annulus. Recently, Lage (2000) developed a mechanistic model for upward two-phase flow in vertical and concentric annulus. This model was composed of a procedure for flow pattern prediction and a set of independent mechanistic models for calculating gas friction and pressure drop in each of flow patterns.

The production and transportation of multiphase gas-liquid-solid in the petroleum industry is a common trend, the solid phase is due to the production of sand along with reservoir fluids. Multiphase fluid flow is considered a transient phenomenon since the flow pattern changes, from dispersed bubble to slug, plug, annular and stratified flow patterns as shown schematically in Figure 2.1 and 2.2 depending on the topography, fluid properties, pipe size, flow rates and corresponding pressure drop (Bello et al. 2011). Slug and churn flow are sometimes combined into a flow pattern called intermittent flow. It is common to introduce a transition between slug flow and annular flow that incorporates churn flow. Taitel et al., 1980 & Duns and Ros, 1963 named annular flow as mist or annular-mist flow.  

The increase in pressure drop is due to the addition of a gaseous phase to an oil-water flow and induces disturbances and instabilities caused by gas bubbles, plugs and slugs especially for the most core annular flow patterns that are favorable. (Sotgia 2006) gave an expression for pressure drop reduction factor in a three phase oil-water-gas flow. 




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