1

THE EFFECT OF BASO4 SCALE ON THE PRODUCITVITY INDEX

OF A HORIZONTAL WELL

BY

OLORUNSHOLA ADELEKE AYOKARI

MATRIC NUMBER: 04CN01668

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT

FOR THE AWARD OF BACHELOR’S DEGREE IN PETROLEUM

ENGINEERING DEPARTMENT OF COVENANT UNIVERSITY OTA.

SUBMITTED TO THE DEPARTMENT OF PETROLEUM

ENGINEERING

COLLEGE OF SCIENCE & TECHNOLOGY

COVENANT UNIVERSITY OTA.

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CERTIFICATION

I hereby certify that OLORUNSHOLA ADELEKE AYOKARI, a student of the

department of Petroleum Engineering, Covenant University, ogun state, dully carried out this

project: ‘THE EFFECTS OF BASO4 SCALE ON THE PRODUCITVITY INDEX OF A

HORIZONTAL WELL’ under my supervision.

Supervisor Head of department, petroleum engineering

Engr A. Fadairo Prof. C.T AKO

................................... .......................................

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DEDICATION

This project is dedicated to God with whom all things are possible and without whom i am

nothing. Also, to my family, for their total love, care as well as support during the testing

times of this project.

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ACKNOWLEDGEMENT

My sincere gratitude goes to God for his provision in times of need during this project.

I would love to appreciate my parents for their full support as well as my supervisor, Engr.

Fadairo for his time, attention and unconditional guidance during the course of this project

execution.

To Engr. Craig, Dr. Anawe, Engr. makinde, Engr. Adeyemi, Engr. Adebayo and Mr.

Daramola for guiding me through the completion of this project, I really appreciate you all.

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TABLE OF CONTENTS

Title Page………………………………………………………………………….. 1

Certification…………………………………………………………………………2

Dedication…………………………………………………………………………..3

Acknowledgements………………………………………………………………… 4

Table of Contents…………………………………………………………………....5

Abstract……………………………………………………………………………....6

Chapter One:

Introduction……………………………………………………….............................7-22

Chapter Two: Literature Review……………………………………………………23-28

Chapter Three: Methodology……………………………………………………….29-35

Chapter Four: Analysis of Results………………………………………………….36-44

Chapter Five: Conclusions and Recommendations………………………………....45

Nomenclature………………………………………………………………………45-47

References………………………………………………………………………….47-52

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ABSTRACT

The great flow efficiency experienced in horizontal well has currently become a popular

alternative for the development of hydrocarbon in any reservoir setting around the world. It

has also proven to be excellent candidate for thin reservoir by its ability to create a drainage

pattern that is quite different from that of vertical well.

Several analytical models have been reported for estimating the productivity index of

horizontal wells. Almost all these analytical predictive models assumed infinitely conductive

or uniform flow along the entire long horizontal well length. The infinite conductivity

assumption is tolerable when the horizontal portion of the well is very small compare to

entire reservoir volume. Otherwise all possible pressure losses in the long horizontal portion

of the wellbore should be taken into consideration.

An improved predictive model has been developed for estimating productivity index of

horizontal well. Results show that the discrepancies in the result of the previous models and

experimental results were not only due to effect of friction pressure losses as opined by Cho

and shah but may also be due to all prominent pressure losses experienced by the flowing

fluid in a conduct as well as due to the deposition of scale which affect the productivity index

value. This project includes the effect of scale deposition on the productivity index as well as

the production rates. This was done by introducing the Skin parameter into the flow equation

of a horizontal well.

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CHAPTER ONE

INTRODUCTION

Scale is the inorganic mineral deposited from brine (salt solution). Precipitation of scale can

occur in the formation pores near the wellbore, thereby reducing formation porosity and

permeability and impairing fluid flow in the formation and in so doing affecting the

productivity index of a well. Deposition of sulfate scales such as (BaSo4) can become a

major problem during water-flooding, if the injected water and formation water are

incompatible and are capable of forming insoluble salts when they are mixed together.

Mixing of incompatible waters takes place in the water-contacted portion of the reservoir

during flooding. When seawater containing sulfate ions comes into contact with formation

water containing barium ions, barium sulphate (BaS04) salt will be precipitated. This

phenomenon can occur around the well bore during water flooding in a horizontal well.

DEFINITION

Scale is any crystalline deposit (salt) resulting from the precipitation of mineral compounds

present in water. Oilfield scales typically consist of one or more types of inorganic deposit

along with other debris (organic precipitates, sand, corrosion products, etc.)

8

Fig 1.0.1: typical examples of scale formation.

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CAUSES OF SCALE FORMATION

The major cause of scale formation around the wellbore is the mixing of mixing of

incompatible water which takes place in the water-contacted portion of the reservoir during

flooding. When seawater containing sulfate ions comes into contact with formation water

containing barium ions, barium sulfate salt will be precipitated. This phenomenon occurs

around the well bore during water flooding.

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EFFECTS OF SCALE DEPOSITION

The effects of scale formation or deposition can be summarized below:

FORMATION DAMAGE: Formation damage is a generic terminology referring to the

impairment of the permeability of petroleum bearing formations by various adverse

processes. Formation damage is an undesirable operational and economic problem that can

occur during the various phases of oil and gas recovery from subsurface reservoirs including

production, drilling, hydraulic fracturing, and work over operations). Formation damage is

caused by physio-chemical, chemical, biological, hydrodynamic, and thermal interactions of

porous formation, particles, and fluids and mechanical deformation of formation under stress

and fluid shear. These processes are triggered during the drilling, production, work over, and

hydraulic fracturing operations.

The deposition of scale can cause formation damage by leading to impairment of the

permeability and porosity reduction of the formation there by affecting the well inflow

performance as well as reducing the well productivity. Hence the need for modelling the

prediction of the effects of scale deposition on the productivity index of a well is important.

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Fig 2.0: example of formation by scale deposition

Other effects can be includes:

blockages in perforations or gravel pack

restrict/block flow lines

safety valve & choke failure

pump wear

corrosion underneath deposits

Some scales are radioactive (NORM).

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Fig 3.0: common oil field scales and some of their physical properties.

MECHANISMS OF SCALE FORMATION

Carbonate scales precipitate due to ΔP (and/or ΔT)

wellbore & production facilities

Sulphate scales form due to mixing of incompatible brines

injected (SO4) & formation (Ba, Sr and/or Ca)

near wellbore area, wellbore & production facilities

Concentration of salts due to dehydration

wellbore & production facilities

Ca2+ (aq) + 2HCO-3(aq) = CaCO3(s) + CO2(aq) + H2O(l)

Ba2+ (aq) (Sr2+or Ca2+) + SO42-

(aq) = BaSO4(s) (SrSO4 or CaSO4)

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FACTORS THAT INFLUENCE SCALE FORMATION

There are several reasons why scales form. The amount and location are influenced by

several factors. Some of these factors are discussed briefly below:

Super-saturation

This is the most important factor with respect to minerals precipitation. A supersaturated

solution contains more ions than it can hold thermodynamically; indicating that sooner or

later a salt will precipitate. The degree of super-saturation therefore denotes the possibility of

salt precipitation. However, the degree of super-saturation is not an indication of the amount

of salt that can precipitate.

Reaction Kinetic

The kinetic of a reaction will determine how far the reaction proceeds in order to bring a

system to thermodynamic equilibrium. The reaction kinetics is influenced by several factors

with temperature being the most important. The precipitation rate for different salts varies.

While supersaturated NaCl solution will precipitate spontaneously if it is supersaturated. On

the other hand supersaturated CaCO3 or FeCO3 solutions may remain stable for several hours

or days and at high temperature without the salt precipitating. While the degree of super-

saturation determines if a salt will precipitate or not, the kinetic indicates how fast the

precipitation will take place. It is therefore necessary to include reaction kinetics

consideration in developing a model that predicts scaling tendency.

Change in Pressure and Temperature

In the reservoir, the brine is in chemical equilibrium with its surroundings at the prevailing

temperature and pressure. As the brine is produced, equilibrium is disturbed as the brine

moves to a zone of lower temperature and pressure. A pressure drop will decrease the

14

solubility of CaCO3 in water thereby increasing the saturation ratio for CaCO3 while a

temperature drop will have the opposite influence24

. The net effect of a drop in temperature

and pressure on the solubility of CaCO3 in water depends on the temperature change relative

to the pressure change. Pressure drop is a major cause of scale formation in producing wells,

and in production tubing. Pressure drops also increase CO2 gas partial pressure and increase

the scale deposition of calcium carbonate.

Effect of pH and CO2/H2S Partial Pressure

This is an important phenomenon in the aqueous chemistry of sulphate scale and

carbonates/sulphides scale. While the sulphates are more or less independent of pH, the pH is

strongly dependent on the solubility of carbonates/sulphides. The prediction of

carbonates/sulphides scale is therefore more complicated than the prediction of sulphates

scale because of the necessity to calculate both pH and the concentration of all the

carbonate/sulphides species. One of the main reasons for CaCO3 scale being precipitated

during oil recovery is the increase in pH increase due to loss of CO2 from the aqueous phase

as the pressure drops24

.

Mixing of Incompatible Waters

Two waters are incompatible if they interact chemically and precipitate minerals when they

are mixed. A typical example of incompatible waters is sea water with high concentration of

SO42-

and low concentration of Ca2+

,Ba2+

,Sr2+

and formations waters with very low

concentration of SO42-

but high concentration of Ca2+

, Ba2+

and Sr2+

. Mixing these waters may

therefore cause precipitation of CaSO4, BaSO4and/or SrSO4. Seawater is frequently injected

into the reservoir for pressure maintenance and during water flooding.

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Effects of other Compounds

The presence of other compounds will influence the saturation index for the precipitating

salts in various ways. Presence of organic acids will directly influence the pH and thereby the

potential for carbonate/ sulphide precipitation. It is also well known that the ionic strength

influences the salt solubility. For example, the solubility of SrSO4 in 2.5M NaCl is

approximately 7 times larger than the solubility in pure water. The reason for this change in

solubility is the change in activity coefficients as the ionic strength is increased.

In this project work the effects of BaS04 scale deposition on the productivity index of a

horizontal well would be considered.

In doing this the basis of the knowledge of productivity index is of paramount importance.

WHAT IS PRODUCTIVITY INDEX (P.I)?

Productivity index can be said to be a measure of the ability of a well to produce. Defined by

the symbol J, the productivity index is the ratio of the total liquid flow rate to the pressure

drawdown.

It defines the relationship between the surface production rate and the pressure drop

(Drawdown) across the reservoir. Expressed mathematically, it is given as:

For Steady State flow of incompressible fluid

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Skin Damage for Horizontal Wells

For a given skin damage the stimulation treatment to remove near-wellbore damage would

have less effect on the productivity of a horizontal well than on the productivity of a vertical

well. Therefore, before deciding to stimulate a horizontal well, it is important to estimate the

pressure loss in the skin zone and compare it with the overall pressure drop from the reservoir

to the wellbore pressure. This comparison can be used to determine a need for horizontal

well stimulation.

In many reservoirs, especially in low-permeability reservoirs, after drilling vertical wells, the

vertical wells will be cemented and perforated. Prior to production, these wells will be

stimulated using propped or un-propped fractures. In these types of reservoirs, vertical well

drilling probably causes severe damage, but it is overcome by fracture stimulation. If a

horizontal well is drilled in such a reservoir, the damage due to horizontal wells will be larger

than that in the vertical well. This is because horizontal drilling takes a longer time than

vertical drilling, resulting in a conical - shape damage zone.

This damage zone can significantly reduce productivity of a horizontal well. Based on the

expected damage value, a proper stimulation and near wellbore formation, cleanup procedure

needs to be critically reviewed, a well completed as an open hole or with a slotted liner may

be difficult to clean and special cleanup procedures may have to be devised. Swabbing the

well is one alternative, but it can be time-consuming and may be inefficient to clean up long

horizontal wells. Another option, where severe damage is expected, is to consider cementing

17

and perforating horizontal wells. Small stimulation treatments in the perforated zones can be

designed to overcome near-wellbore damage.

Drilling related damage in a high permeability reservoir is smaller than that in a low-

permeability reservoir. For the similar skin damage value, the influence of damage on

horizontal well productivity is not as detrimental as in a vertical well. Thus horizontal wells

can sustain more damage than vertical wells without a significant loss of well productivity

Influence of Areal Anisotropy

In naturally fractured reservoirs, the permeability along the fracture trend is larger than in a

direction perpendicular to fractures. In these cases, a vertical well would drain more length

along the fracture trend. The following equations can be used to estimate each side of a

drainage area in an areally anisotropic reservoir. Assuming a single phase, steady -state flow

through porous formation, and the following equation can be written,

Xk

p

X yk

p

yx y( ) ( ) 0

Assuming constant values of kx and ky in x and y directions respectively.

The above equation can be rewritten as

kp

Xk

p

yx y

2

2

2

20

Multiplying and dividing through-out by k kx y the above equation becomes,

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k kk p

k x

k p

k yx y

x

y

y

x

2

2

2

20

this equation can be transformed into,

k kp

x

p

yx y

2

2

2

20

Where

y y k kx y/

Thus an areally anisotropic reservoir would be the equivalent of a reservoir with an effective

horizontal permeability of k kx y and the length along the high-permeability side is

k ky x/ multiplied by the length along a low permeability side. Thus, if permeability along

the fracture trend is 16 times larger than the perpendicular to it, then the drainage length

along the fracture is four times larger than the length perpendicular to the fracture. In such

areally anisotropy reservoirs, it is difficult to drain larger reservoir length in the low

permeability direction using vertical wells. Thus horizontal wells are highly beneficial in

areally anisotropic reservoirs.

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Formation damage in horizontal well

The concept of skin factor was developed to account for loss in productivity due to a near

wellbore formation damage. The near wellbore damage causes an extra pressure drop near

the wellbore resulting in loss of pressure drawdown. The pressure drop in the skin region is

proportional to the flow rate per unit well length. For vertical wells, pressure drop due to

positive skin factor pskin is proportional to qv/h. For horizontal wells, pressure drop due to

positive skin factor is proportional to qh/L. Thus, because of lower flow rate per unit well

length, long horizontal wells exhibit a smaller loss of well productivity due to drilling

damage than a vertical well.

Sparlin and Hagen derived the following equation to calculate flow rate from a damaged

horizontal well. If d represents thickness of the damaged zone around the horizontal well,

then the average vertical permeability, kavg-vert and the average horizontal permeability, kavg-

horz are calculated as shown below.

kk k h r

k r d r k h r davg vert

s w

w w ws

ln / ( )

ln(( ) / ) ln( / ( ))

2

2 2 .....a

kk k r r

k r d r k r r davg hortz

s e w

w w s e w

ln( / )

ln(( ) / ) ln( / ( )) ........b

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q

q

c h L h r

k k c k k h L h r

d

h

w

avg horiz avg vert w

ln( ) ( / ) ln[ / ( )]

( / ) ln( ) ( / )( / ) ln[ / ( )]

2

2.....c

where,

ks = damage zone permeability

d = damage zone thickness

qd = flow rate of a damaged horizontal well

qh = flow rate of an undamaged horizontal well

c = [reh+(reh2 - (L/2)

2)0.5

]/[L/2]

Note that equations (a) and (b) are for isotropic reservoirs only, thus k simply represents

reservoir permeability. Equation c represents a loss in production for a horizontal well due to

near wellbore damage.

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Limitations of Horizontal Wells

One major advantage of the horizontal well is a large reservoir contact area and the

disadvantage is that only one pay zone can be drained per horizontal well. However,

horizontal wells can be used to drain multiple layers. This can be accomplished by two

methods (1) drill a ‘staircase’ type well where long horizontal portions are drilled in more

than one layer and (2) cement the well and stimulate it by using propped fractures. The

vertical fractures perpendicular to the wells could intersect more than one pay zone and

thereby drain multiple zones. The other disadvantage of horizontal well is their cost.

Typically, it costs about 1.4 to 3 times more than a vertical well depending upon drilling

methods and completion techniques employed. Hence for economic success, producible

reserves from a horizontal well not only have to be proportionately larger, but they should

also be produced in a shorter time span than a vertical well.

Horizontal Well Applications

1. In naturally fractured reservoirs, horizontal wells have been used to intersect fractures and

drain them and the reservoir effectively.

2. In reservoirs with water and gas coning problems, horizontal wells have been used to

minimise coning problems and enhance oil production.

3. In gas production, horizontal wells can be used in low permeability as well as in high-

permeability reservoirs. In low permeability reservoirs, horizontal wells can improve

drainage area per well and reduce the number of wells that are required to drain the reservoir.

In high permeability reservoirs, where near - wellbore gas velocities are high in vertical

wells, horizontal wells can be used to reduce near wellbore velocity.

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OBJECTIVES OF THE PROJECT

The objectives of the project is to estimate the effect of Baso4 scale on the productivity index

of a horizontal through the introduction of the skin factor into the flow equation of a

horizontal well which is an indication of the measure of damage caused by the scale

deposition. Also, to enable effective planning and treatment of the scale deposited when the

productivity index is affected by deposition of the scale.

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CHAPTER 2

LITERATURE REVIEW

Scale and its deposition is considered to be one of the most difficult problems encountered

during the exploitation of the oil reservoir. Miscible and immiscible flooding operations

exhibit suitable environments for such precipitation and deposition. In some cases asphaltene

precipitation can occur during natural depletion and oil transportation and, more commonly

during well stimulation activities.

Recent investigations indicate that in permeability damage of a well (horizontal) by scale

deposition is more likely to be severe near the wellbore hence affecting the productivity index

as well as the inflow performance of the well.

Yuan et al and Atkinson et al (1990), developed models for predicting sulphates scale

formation caused by commingling of chemically incompatible water as well as temperature

and pressure changes. The models which are based on the Pitzer’s equation have been

adjudged to be reliable in calculating sulphates solubility over a wide range of concentrations

and temperatures. The simultaneous co-precipitation of BaSO4, SrSO4 and CaSO4 which is a

common phenomenon in scale formation is considered by the models.

Todd and Yuan (1991), conducted a laboratory investigation using the North Sea reservoir

brines that produced barium and strontium sulphate scales. This experiment was based

mainly on the effect of super-saturation on permeability. Crystals depositing along and

growing perpendicular to the pore surface caused most of the reduction in core permeability.

They observed that doubling the super-saturation ratios of both barium and strontium

sulphate increased the quantity of scale that was formed inside the pores and a change in the

permeability of the crystals. The shortcomings of a good number of the early models that

have been developed on the problem in question were found to have neglected the effects of

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pressure changes on scales formation and also setting other physical factors that would have

affected the modeled wellbore at nominal values and also making them uniform among most

values which ended up rendering heat change ( i.e. heat loss or gain at different points and

periods ) to be set at zero. Moreover, a view of only one mineral precipitation and saturation

was considered without accounting for the effects of possible formation of other available

minerals in the same solution to form scales can also be seen as a major setback.

Frank et al (1991), presented a formation damage model that described the effects of rock and

fluid interaction processes, clay swelling, dissolution and precipitation reactions and fine

migration. The model is based on chemical reactions involving dissolution, precipitation and

ion exchange in which the precipitates contribute to plugging of pore throat. The results

show that the Extended UNIQUAC model, with the added pressure parameters, is able to

represent binary (NaCl–H2O, CaCO3–H2O, BaCO3–H2O, SrCO3–H2O, MgCO3–H2O,

Mg(OH)2–H2O and CO2–H2O), ternary (CaCO3–CO2–H2O, BaCO3–CO2–H2O, SrCO3–CO2–

H2O, MgCO3–CO2–H2O, CO2–NaCl–H2O and CO2–Na2SO4–H2O), and quaternary (CO2–

NaCl–Na2SO4–H2O) solubility data within the experimental accuracy in the range of

temperatures and pressures considered in the study, i.e. from 0 to 250 °C, and from 1 to

1000 bar, respectively.

Nancy et al (1998), described an equilibrium models for the prediction of carbonate and silica

scale formation, CO2 break out and H2S gas exchange in geothermal brine systems to high

concentration and temperature. These equilibrium descriptions are based on a minimization

of the free energy of the system with solute activities described by the semi-empirical

equations of Pitzer (1973; 1987). The carbonate model is parameterized by appropriate

osmotic, electromotive force and solubility data (T ≤ 250ºC) available in binary and ternary

solutions in the seawater Na–K–H–Ca–Cl–SO4–H2O system. The silica model is

25

parameterized by solubility data to 320ºC in the Na–Mg–Cl–SO4–SiO2–H2O system. The H2S

model is parameterized by solubility data in the H2S–NaCl–H2O system to 320ºC. The

respective temperatures which these models were parameterized through were seen to have

been kept at particular levels without considering what the effects of varying temperature

would be on the models, thereby rendering the outcome of the model to be extremely

theoretical.

In 2001, Hyun Cho, et al presented a paper on the effect of long horizontal wells on

productivity index associated with the effects of friction pressure losses of a liquid

hydrocarbon in the wellbore under inflow conditions, called as specific productivity index to

distinguish the conventional productivity index. This study also demonstrates the influence of

wellbore damage near the horizontal wellbore on the specific productivity index of long

horizontal wells.

Dikken discussed the effects of friction pressure losses of the high flow rate in the long horizontal

wellbore. A volume balance across the boundary of the well then leads to a differential equation that

can be solved for the profile of flow rate along the wellbore. He solved this problem analytically for

an infinite horizontal well length and numerically for a finite horizontal well length.

Novy generalized Dikken’s work by developing equations that covered both single-phase oil

and gas flow. In the case of gas flow the non-Darcy flow term is included in the analysis. The

simplified flow model was developed as a boundary-value problem and solved by

assumptions of single phase and steady state condition. The results have provided engineers

with the criteria for the selection of reasonable horizontal well length as the point at which

friction reduces productivity by 10 % or more.

26

Landman proposed further improvements over Dikken’s model by using the productivity

index to be changed along the wellbore. A methodology is developed to calculate an

optimum perforation density along the well that gives constant specific inflow along the well.

Renard and Duppy provided a basis for comparing the flow efficiencies, the ratio of a well’s

actual productivity index to ideal productivity index of vertical and horizontal wells. They

derived analytical expressions by assuming steady state flow of an incompressible fluid in a

homogeneous anistropic formation.

Recently, Cho and Shah developed a semi-analytical well model, which analyzes

quantitatively the effects of friction losses of liquid hydrocarbon flow on productivity index

under inflow conditions. They describe the flow in the reservoir with a specific productivity

index, which is constant within the unit length. However, this model does not consider

formation damage around wellbore.

Zhang et al (2001), modeled the kinetics of carbonate scaling (application for the prediction

of down-hole carbonate scaling) based on thermodynamics principles to indicate the tendency

for scaling from solution and kinetic models to predict the rate of scaling and thus the time

required to cause blockage. The application of such models could contribute to field scale

management and in the development of more effective treatments of carbonate scale during

oilfield production.

Moghadasi et al (2004), presented an experimental and theoretical study of formation damage

(permeability reduction) due to scale formation in porous media resulting from water

27

injection. They considered the injection of two incompatible solutions of calcium and

sulphate/carbonate to form calcium sulphate and calcium carbonate within the porous

medium. From the process, they observed that the characteristics of precipitate such as; large

degrees of super-saturation, presence of impurities, change in temperature and the rate of

mixing influenced the quality and the morphology of precipitates which all together affected

the extent of formation damage in the formation.

De Montigny et al suggested that, as horizontal well length increases, the influence of

formation damage on total pressure drop becomes negligible, resulting in an additional

advantage over vertical wells.

However, Sparlin and Hagen indicated that the damage zone may affect productivity more in

horizontal wells, and that skin damage sometimes can prevent horizontal well projects from

succeeding. These two opposing interpretations of the horizontal well productivity, as Renard

and Duppy noted, come from a lack of well-defined reservoir and well characteristics to

quantify the effect of formation damage on the productivity index for horizontal wells.

Fadairo, S. Omole, O et al described the effects of oilfield scale on mobility ratio. This paper

presents an analytical model based on existing thermodynamic models for predicting brine

mobility, hydrocarbon mobility and mobility ratio of water flooded reservoir with possible

incidence of scale precipitation and accumulation. The key operational and reservoir/brine

parameters which influence the mobility ratio such as salt concentration in the brine,

produced water rate, pressure drawdown, reservoir temperature were identified using this

model.

28

Results of the study shows that the mobility ratio of a water flooded reservoir remains

constant until water breakthrough and achieves an increasing local maximum at 10% pore

volume injected water as the flow rate of produced water increases with a significant jump

beyond the critical flow rate observed at mobility ratio of 1. Similar results corroborating

above were obtained with variation in skin factor.

This model therefore can be used to diagnose, evaluate and simulate mobility ratio and skin

factor in a water flood scheme enabling production engineers plan an economically efficient

water flood scheme.

29

CHAPTER 3

METHODOLOGY

WELLBORE PRESSURE PROFILE

Undamaged Formation

Giger and Joshi presented the pressure profile created by 3D steady-state flow to a horizontal

well located inside an ellipsoidal drainage. Once the pressure distribution is known, Darcy’s

law can be used to calculate oil production rate. The pressure distribution caused by steady-

state flow to the horizontal well is approximated by sub-dividing the 3D flow problem into

two 2D, as Joshi simplified. This will approximate friction pressure loss problem into two

categories: (1) oil flow into a horizontal well in a horizontal plane and (2) oil flow into a

horizontal well in a vertical plane.

XY

f

YZ

HF

XYZ

Fe

XYZ

He

D

P

D

PP

D

PP

D

pP

2223

(1)

In this first zone (2D-xy), flow is studied in horizontal plane as if it were a vertical fracture of

the same length as the horizontal fracture of the well. The pressure drop in this 2Dxy flow has

been determined by Giger and Joshi from potential-fluid-flow theory as specified in Eq.2:

)(cosh2

10

'

XhK

BQPP

h

Fe

..............................................2

30

Where, X is a parameter, which depends on shape and dimensions of area drained by well.

When drainage is ellipsoidal type, X will be 2a/L. If X ≥ 1, more popular solution of the

pressure drop in horizontal plane11 is given in equation 3:

1

22ln

2

2

0

'

L

a

L

a

hK

BQPP

h

Fe

.................................3

The additional pressure drop term (2D-yz), , in the vicinity of the well is derived by

Giger and given as:

wh

HFr

h

LK

BQPP

2ln

2

0

''

...........................................4

The approximate solution for the pressure drop of both inflows by combining eqs.2 and3

becomes:

wh

HFFer

h

L

hX

hK

BQPPPP

2lncosh

2

10

''

.......5

As established by Muskat, the reduction of one-phase flow problem in an anisotropic porous

medium to flow in “an equivalent isotropic medium” uses the transformation dictated by

dimensional analysis. In this transformation, the well becomes elliptical and its radius, wr has

to be changed to wr (1+ β)/ 2β to have the same section. Several solutions are available in the

literature. After reflecting anisotropy of formation, Eq. 5 becomes:

31

7.................................2

1,

2lncosh

2

'

'

10

''

ww

wh

He

rrwhere

r

h

L

hX

hK

BQPP

................6

Damaged Formation

The potential for severe formation damage around horizontal wells exists due to the increased

time of formation exposure to the drilling fluids as compared to the time that a vertical well is

exposed to the drilling fluids. Solids used for increasing the fluids hydrostatic allow drillers

to drill overbalanced, with the excess pressure over the formation pressure preventing

formation fluid influx. The formation damage is occurred by this solid invasion into the

formation. When the drill bit exposes the virgin formation to drilling fluid, pore bridging is

accomplished by mud solids (mainly barite) that migrate into those pore spaces very close to

the rock surface, forming internal mud cake or filter cake. In this spurt invasion phase, mud

enters the formation quite freely, although the overall motion still satisfies Darcy’s law for

low Reynolds number flows. Formation damage around a horizontal wellbore will be very

detrimental to productivity because the reservoir fluids must converge radically to the

borehole. This formation damage may offset the increased productivity expected from

horizontal wells. In vertical wells, acid breakdown treatments or small fracture treatments can

be used to remove the effect of skin damage and provide stimulation. In horizontal boreholes,

removing skin damage may be quite difficult. The logistics of pumping either acid or

multistage fracture treatments is quite difficult and is expensive because large treatment

volumes are required for long horizontal wells. Formation damage around a horizontal

wellbore will be very detrimental to productivity because the reservoir fluids must converge

32

radically to the borehole. The filtrate invasion, or called as mechanical skin damage, directly

affect permeability of the formation near the horizontal wellbore. Adair and Gruber present

the average vertical and horizontal permeability reflecting invaded damage as given in

Equations (8) and (9).

s

es

w

se

w

ees

H

r

rk

r

rk

r

rKK

KAVG

lnln

ln

.............................8

s

wss

w

se

w

wses

V

r

rrk

r

rk

r

rrKK

KAVG

2lnln

2ln

.........................9

The invaded damage zone that extends to sr around the horizontal wellbore affects only

pressure near the well. This is an additional pressure drop due to the reduction of

permeability in the invaded damage zone. Horizontal [ HS ] and vertical skin factors [ VS ] are

related as:

V

w

s

s

H SL

h

r

r

K

K

L

hS

ln1 .......................10

33

The pressure drop '

He PP for isotropic formation in the vicinity of the well caused by

convergence of streamlines toward this horizontal well is given as:

wsssh

Her

h

r

h

LK

BQ

r

h

L

h

L

a

hK

BQPP

2ln

2ln

22ln

22

0

'

0

''

.........11

Equation 11 can be simplified by using the definition of horizontal and vertical skin factors

specified in equation 10

H

wh

He Sr

h

L

h

L

a

hK

BQPP

2ln

22

0

''

...........................12

By using the same transformation applied to equation 5, equation 12 can be accounted for the

formation anisotropy and given as:

14........................).........exp(2

1,

2)(cosh

2

21

2)(cosh

2

'

'

10

'

10

''

Vwwe

weh

V

wh

He

Srrwhere

r

h

L

hX

hK

BQ

SL

h

r

h

L

hX

hK

BQPP

...........13

34

SPECIFIC PRODUCTIVITY INDEX

Fluid Flow Restriction

The production rate based on drawdown pressure of horizontal well is derived by assuming

steady-state flow of an incompressible fluid in an anisotropic formation. The steady state

equations developed by Economides et al. (22) are used for describing the flow in the

reservoir. Despite the fact that the solution is for steady-state and for only one set of

boundary conditions, relative comparison is considered valid, and can be extended to general

reservoir exploitation studies. The following assumptions are made in this study.

(1) Flow inside the well is single phase and steady-state.

(2) The complete horizontal section is open to production (Open-hole production or slotted

liner).

(3) Radial flow near the tip of the well is ignored.

(4) Horizontal well runs parallel to a constant pressure boundary.

The inflow performance of the well in terms of the productivity index per unit length of

producing horizontal section and the drawdown at each position along the section provides

the following equation.

)]()[()( xPPxJxq wess (15)

where, Pe is the constant pressure at the outer boundary condition, and Pw(x) is the pressure

varying along the wellbore due to frictional pressure loss. Figure 1 shows the simple

horizontal flow model. Js(x) is the specific productivity index per unit length of the wellbore.

It depends on geometry of well, formation characteristics (permeability) and flow patterns

(spherical or radial flow). It is assumed that the specified productivity index per unit length of

the wellbore is constant.

35

In the above model, the major modification is the introduction of the horizontal permeability

(Kh) due to scale deposition which in this case is BaS04

Hence, the horizontal permeability Kh is given by:

[ {

} ]

(16)

Where F is the model parameter

36

CHAPTER 4

ANALYSIS AND RESULTS

The result is a validation of the results obtained by Hyun Cho et al in their analysis of the

prediction of specific productivity index in a long horizontal well which did not include

permeability impairment due to scale deposition (BaS04).

Pore volume of seawater injected (%) BaS04 Precipitated (g/m^3)

0

0

10

71

20

65

30

58

40

48

50

42

60

32

70

28

80

18

90

10

100 0

Table 1: amount of BaSo4 precipitated as a function of pore volume

Pay thickness (h)

26m

Initial permeability

0.5922E-13 (60md)

Initial porosity

0.05

Reservoir pressure

33600kpa

Bottomhole pressure

22060kpa

37

Reservoir temperature 353K(80c)

Brine formation volume factor

1.7

Brine viscosity

0.0007Pa-S

Hydrocarbon formation volume factor

1.2

Hydrocarbon viscosity

0.003

Connate water saturation

0.2

ANALYSIS OF RESULTS

AT B = 2.828

Pore

Volume J Ratio

0 1

10 0.88089

20 0.88953

30 0.9003

40 0.91669

50 0.92693

60 0.94445

At B= 3.1622

Pore

Volume J Ratio

0 1

10 0.87431

20 0.88336

30 0.89466

40 0.91188

50 0.92267

60 0.94115

38

At B= 2.9277

Pore Volume J Ratio

0 1

10 0.87885

20 0.88762

30 0.89856

40 0.9152

50 0.92561

60 0.94343

FIG 1.0: Effects of varying anisotropy factor B at a constant horizontal length on the

productivity index at different pore volume injected.

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

0 20 40 60 80

prod index vs pv atB=2.828 at constantlength(4000ft)

prod index vs Pv atB=2.9277 at a constanthorizontallength(4000ft)

prod index vs pv atB=3.1622

39

DATA FOR THE SECOND PLOT

At a drawdown of 1637.74psi

Pore Volume Q (Prod. Rate)

0 85704.8

10 75321.6

20 76073.6

30 77010.61

40 78437.17

50 79329.59

60 80856.63

At a drawdown of 2000psi

Pore Volume Q (Prod. Rate)

0 104662.3

10 91982.36

20 92900.7

30 94044.98

40 95787.08

50 96876.9

60 98741.71

40

A drawdown of 2500psi

Pore Volume Q (Prod. Rate)

0 130827.8

10 114978

20 116125.9

30 117556.2

40 119733.9

50 121096.1

60 123427.1

Fig 2-the effects of pressure draw on the production rate at Kh=60md and Kv=7md

60000

70000

80000

90000

100000

110000

120000

130000

140000

0 20 40 60 80

prod rates vs porevolume atdp=1637.74psi

prod rates vs porevolume at dp=2000psi

prod rates vs porevolume at dp=2500psi

41

DATAS FOR PLOT 3 AND 4

AT B = 2.9277

Horizontal

Length Q (Prod. Rate) J Ratio

1000 20866.48 1

2000 33606.65 1.61056

3000 52718.8 2.52648

4000 77010.61 3.69064

5000 106730.4 5.11492

6000 139767.1 6.69816

7000 177759.3 8.51889

AT B = 3.536

Horizontal Length Q (Prod. Rate) J Ratio

1000 31902.48 1

2000 51150.96 1.60335

3000 80062.45 2.5096

4000 116237.9 3.64354

5000 160060.9 5.01719

6000 208220.3 6.52678

7000 263481.4 8.25896

42

AT B = 4.183

Horizontal Length Q (Prod. Rate) J Ratio

1000 41041.35 1

2000 65542.37 1.59698

3000 102385 2.49468

4000 147842.8 3.60229

5000 202437.1 4.93252

6000 261845.7 6.38005

7000 329908 8.03843

FIG 3: The effect of varying horizontal length on the production rate at varying anisotropy

factor.

0

50000

100000

150000

200000

250000

300000

350000

0 2000 4000 6000 8000

Prod rate vs Horizontal lengthat B=2.9277

prod rate vs horizontal lengthat B=3.536

prod rate vs horizontal lengthat B=4.183

43

Fig 4: The effects of varying anisotropy at different horizontal length on the productivity

index.

0

1

2

3

4

5

6

7

8

9

0 2000 4000 6000 8000

prod index vshorizontal lenght atB=2.9277

prod index vshorizontal length at B=3.536

prod index vshorizontal length atB=4.183

44

RESULTS AND DISCUSSIONS

From figure 1 the effect of varying reservoir anisotropy factor B at a constant horizontal

length indicates that the productivity index decreases with increasing B Factor in a situation

where the source of formation damage is not stated but in comparison with the result obtained

by HYUN CHO et al, the results indicates that as scale is precipitated at different pore

volume and at changing concentration the productivity index increases after 0% pore volume

as the concentration of scale decreases.

From figure 2 the effects of pressure draw down at varying skin due to the scale deposition at

a constant horizontal length indicates that the lower the pressure drawdown the lower the

production rate which is an indication of the fact that due to scale deposition, the production

rate increases with decreasing concentration of scale.

Figure 3, indicates that the production rate increases with increasing horizontal lengths and

also increases with increasing anisotropy factor which is an indication of the fact that the

concentration of the scale decreases with increasing horizontal length. In comparison it

means the production rate increases with decreasing scale concentration.

From figure 4, there is an indication that productivity index/ratio increases with increasing

horizontal length but it does not increase with increasing parameter of anisotropy and this is

due to the presence of scale deposited.

45

CHAPTER 5

CONCLUSION AND RECOMMENDATION

Neglect frictional losses of hydrocarbon flow in long horizontal wellbore from the point of

inflow to the heel point, the estimation of production rate will be significantly overestimated.

This may affect the final project economics seriously.

Minimizing formation damage during drilling and completion increases production rate as

well as overall cost effectiveness of a project. This may reduce the well construction cost by

reduction in extra well length, which will not contribute to the production.

NOMENCLATURE

a = half major axis of drainage ellipse, ft

Bo = Formation volume factor

D = Inner diameter of wellbore, ft

fgc = Conversion factor, 32.17lbm-ft/lbf-s2

h = formation thickness, ft

Js = Areal productivity Index (PI), stb/day/psi

Js(x) = Productivity index per unit length, sbl/d/pasi/ft

K = Isotropic formation permeability, md

Ke = Effective reservoir permeability, md

Kh = Horizontal permeability, md

KHavg = Average horizontal permeability, md

Kv = Vertical permeability, md

KVavg = Average vertical permeability, md

L = Horizontal well length, ft

46

NRe = Reynolds number, dimensionless

Pe = External boundary pressure, psi

PF = Intermediate arbitrary pressure in wellbore, psi

Pf = Friction pressure loss, psi

PH' = Pressure at the heel without friction loss, psi

PH = Pressure at the heel with friction loss, psi

Pw = Pressure in the wellbore

Q = Oil production rate with friction loss, stb/day

Q' = Oil production rate without friction loss, stb/day

qs = Inflow into the well unit length, rbl/ft

qw = Flow rate in the wellbore, rbl/day

RF = Recovery factor

RS = Flow resistance of the well, Dimensionless

re = Radius of drainage area, ft

rs = Radius of a invaded zone around wellbore, ft

rw = Wellbore radius, ft

rwe = Effective wellbore radius, ft

r’we = Effective wellbore radius in anisotropic, ft

SH = Horizontal skin factor, dimensionless

Sv = Vertical skin factor, dimensionless

t = Production lasting time, year

Vx = Superficial oil velocity, ft/sec

x = Distance along the well coordinator, ft

X = Drainage configuration parameter

ϐ= Anisotropy ( Kh / Kv ), dimensionless

47

Po = Drawdown at the heel of the well, psi

ρ= Oil density, lbm/cuft

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