Journal of EngineeringVolume 13 September2006 Number 3

WELL PERFORMANCE ANALYSIS BASED ON FLOW

CALCULATIONS AND IPR

Dr. Mohammed S. Al-Jawad Dhefaf J. S. Ottba

University of Baghdad University of Baghdad College of Engineering College of Engineering

Petroleum Department Petroleum Department

ABSTRACT

A study has been done to analyze the total production system by developing a computer model. Every

component of the production system has been programmed individually and then linked in the composite

production system computer program. These components are; reservoir component, vertical component,

surface choke component and finally horizontal component.

Each of the previous components are developed using various equations or models to determine the

pressure loss thorough that component. In the current study the Wiggins method has been used to

calculate the IPR curves. The vertical and horizontal components are developed using the unified

mechanistic model of Gomez. Lage mechanistic model has been used to calculate the pressure losses

through annulus. Perkins mechanistic model is used to calculate the pressure loss through surface chokes.

A filed example problem is presented to analyze the production system. This example has been used

to determine the optimum system design which maximizes production rate for a set of condition.

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M.S. Al-Jawad and WELL PERFORMANCE ANALYSIS BASED D. J. S. Ottba ON FLOW CALCULATIONS AND IPR

823

KEYWORDS

Well performance analysis, Production system analysis, IPR, Vertical multi-phase flow,

Horizontal multi-phase flow, Choked flow.

INTRODUCTION

The objective of production system analysis can be summarized as:

- Predict the optimum flow rate for specific reservoir condition.

- Predict the pressure drop in vertical tubing and annulus, and horizontal lines.

- Predict the pressure drop through surface well head chokes.

- Determine the well head pressure and bottom hole pressure for specific well.

- Determine the proper size of tubing, flow line and surface well head chokes.

A basic requirement for well analysis is the ability to define the entire inflow performance

relationship (IPR) of the well. Accurate well test data must be obtained and the proper IPR applied for

successful analysis. Models for other well components can be used in addition to complete the predicted

well performance.

Figure (1) shows the components that make up a detailed flowing well system. Beginning with the

reservoir and proceeding to the separator, the components are: reservoir component, tubing string

component (pipe and annulus), surface choke component, flow line component.

The Inflow performance relationship (IPR) of wells is an essential part of the information which is

required in production well analysis. Several methods have been proposed in the literature to predict the

IPR curves of a well. Brown (1984), presented a solution to calculate three-phase flow IPR curves. His

method based on the combination of Vogels equation for the oil IPR and a constant productivity index

for water. Wiggins (1994),developed a generalized equation to predict inflow performance. He used a simulator results to generate IPR curves. His method assumes that each phase can be treated separately.

Browns method differs from generalized three-phase IPR method of Wiggins because it coupled the

water and oil rates.

The use of multiphase flow- pressure drop correlation is very important for developing the vertical

and horizontal components of production system. The correlation that are most widely used for vertical

multiphase flow were developed by Hagedorn & Brown, Duns & Ros, Aziz & Govier. In the vertical

component of production system, the fluids can flow through the annulus between the casing and the

production tubing. Therefore, it is necessary to be able 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.

For the multiphase flow through horizontal flow line there are the correlations of Dukler et al. (1964),

Eaton et al. (1967), Beggs and Brill (1973), Makherjee and Brill (1985). Gomez et al. (1999) presented a

unified mechanistic model for the prediction of flow pattern, liquid holdup and pressure drop in wellbores

and pipelines. This model is applicable to the entire range of inclination angles, from horizontal to

upward vertical flow.

Surface choke component is represented by the critical and subcritical flow through chokes. Many

correlations for multiphase flow across choke were presented. Fourtunati (1972) presented a first work to

be applicable to both critical and sub-critical flow. Ashford and Pierce (1974) developed an equation for

sub-critical flow through restrictions. Finally, Perkins (1990) presented a mechanistic model for the

multiphase flow through chokes. His flow equations are valid for both critical and subcritical flow.

Journal of EngineeringVolume 13 September2006 Number 3

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WELL PERFORMANCE ANALYSIS

Well performance analysis is a combination of various components of oil or gas wells in order to

predict flow rates and to optimize the various components in the system.

RESERVOIR COMPONENT

The first component is the reservoir component, which represents by the flow through the porous

media and given rise to the concept of inflow performance relationship (IPR). The IPR of an oil well

relates the gross liquid well bore production rate to the bottom hole production pressure. Wiggins

developed a generalized equation to predict inflow performance relationship (IPR) for three-phase flow.

The generalize IPR equations are: 2

48.052.01

max,

=

rp

wfp

rp

wfp

OQ

OQ

.1

and,

.2

2

28.072.01max,

=

rp

wfp

rp

wfp

wQ

wQ

r

p = average reservoir pressure.

wf

p = flowing bottom-hole pressure.

O

Q = oil production rate.

max,O

Q = maximum oil production rate.

wQ = water production rate.

max,wQ = maximum water production rate.

VERTICAL COMPONENT

The vertical component is described by the vertical multi-phase flow in the tubing string, which is

divided into two categories: (a) multi-phase through vertical pipes, (b) multi-phase flow through annuli.

In mechanistic model approach, the important variables of multiphase flow are incorporated and then

coupled with appropriate laboratory and field data. The characteristic of the existing flow pattern is taken

into consideration. The prediction of flow pattern represents the first step of developing mechanistic

models. The other step is the development of a pressure drop model for each flow pattern to calculate the

liquid holdup and pressure drop.

Many empirical correlations and mechanistic models that have been developed over the years are

evaluated in this work. The Duns & Ros, Hagedorn & Brown, Aziz & Govier empirical correlations were

compared with unified Gomez mechanistic model for vertical flow in pipes and with Lage

mechanistic

model for vertical flow in annuli. A) Multi-phase through vertical pipes (Gomez's Unified Mechanistic Model)

This model has been developed to predict flow pattern, liquid hold up and pressure drop in well bores

and pipelines. It is applicable to the whole range of inclination angles from horizontal to upward vertical

flow. Therefore, this model can be applied to determine pressure drop in both vertical pipes and

horizontal flow lines, with no need to switch among different models. The unified model consists of a

unified flow patterns prediction model and separate models for determine pressure drop for the existing

M.S. Al-Jawad and WELL PERFORMANCE ANALYSIS BASED D. J. S. Ottba ON FLOW CALCULATIONS AND IPR

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flow patterns. The flow patterns prediction model is based on the Barnea model, which is applicable for

entire range of inclination angles. Gomezs model presents the transition mechanism for each individual

boundary. The transition criteria for each flow pattern is given in the form either equations or map.

Figure 2 represents the generalized flow pattern map. The transition criteria for this model, include the

stratified to non-stratified, slug to dispersed bubble, annular to slug and bubble to slug flow.

The criterion for stratified to non-stratified transition is given by the following condition:

( )

11

12

2

2

GG

LG

LdAA

dAv

hF .... 3

Where F is a dimensionless group,

cos)( dg

vF SG

GL

G

= .... 4

The transition from slug to dispersed bubble occurs at high liquid flow rates, where the turbulent forces overcome the interfacial tension forces lead to dispersing the gas phase into small bubble size which can be

determined from:

4.026.05.0

max

2725.015.4

+

=

d

vf

v

vd mm

Lm

SG

.................5

Two critical bubble diameters are considered. First is the critical diameter, below which bubbles do

not deform due to agglomeration or coalescence, and this is given by:

( )

5.0

4.02

=

GL

CDd

.6

The other critical diameter is defined as the critical bubble size below which bubbles migrate to the

upper part of the pipe and is presented by:

( )

cos8

32

g

vfd

GL

mmLCB

= 7

Therefore, the transition to dispersed bubble flow will occur when (CD

dd