benson oghenovo ugbenyen

8/16/2019 Benson Oghenovo Ugbenyen

1/147

N pproach to stimulation candidate selection

and optimization

A

Research Thesis

Presented to the Department of Petroleum Engineering,

African University of Science and Technology,

Abuja

in Partial Fulfillment of the Requirements for the Award of Master of

Science (MSc)

in

Petroleum Engineering

By

BENSON OGHENOVO UGBENYEN

Abuja, Nigeria November, 2010


2/147

An Approach to Stimulation Candidate Selection and Optimization

By

Benson Oghenovo Ugbenyen

RECOMMENDED: ________________________________

________________________________

________________________________

________________________________

APPROVED: ________________________________Supervisor : Prof. (Emeritus) David O. Ogbe

________________________________

________________________________

________________________________

Date


3/147

iii | An Approach to Stimulation Candidate Selection and Optimization

ABSTRACT

Well stimulation consists of several methods used for enhancing the natural producing ability of

the r eservoir when p roduction rate declines. A de tailed l iterature r eview of s ome of t he well

published stimulation models are di scussed in this research. This d iscussion was preceded wi th

an introduction t o f ormation damage concepts and an o verview o f well stimulation m ethods.

Production decline curve analysis is combined with economic discounting concepts to develop a

model that can be used for optimizing stimulation decisions. The model i s presented in t he form

of a no n-linear programming pr oblem subject t o t he constraints imposed by t he p roduction

facilities, reservoir productivity and the stimulation budget approved by management. Production

data from four stimulation candidate wells, o ffshore Niger Delta was used to validate the model

developed by s etting up a maximization problem. Solution to the problem was ob tained using

non-linear o ptimization software. The r esult o btained was v erified u sing Wolfram R esearch’s

Mathematica 7.0 . The results s how that the o ptimization m odel c an be c ombined w ith

stimulation t reatment modules, de veloped from i ndustry w ide models, t o q uantify s timulation

benefits. C andidate w ells w ere t hen r anked ba sed on stimulation c ost, p ayout t ime a nd

stimulation b enefit. Hence, th e m odel i s valid f or stimulation ca ndidate s election; and i s

therefore recommended for use in optimizing stimulation decisions.


4/147

iv | An Approach to Stimulation Candidate Selection and Optimization

DEDICATION

This research is dedicated to my Lord Jesus Christ who has been, and will ever be the best role

model anyone could find. And also, to the good people of the Niger Delta.


5/147

v | An Approach to Stimulation Candidate Selection and Optimization

ACKNOWLEDGEMENT

I wi sh t o sincerely a ppreciate G od Almighty for H is l ove, c are a nd wonderful works t hat a remade m anifest i n m y life each da y. Also, m y s incere thanks g o to my supervisor, P r of.(Emeritus) David O. Ogbe for guiding me to success in this work, Dr. Samuel Osisanya and Prof.

Peters Ekwere f or s erving in m y thesis committee, and m y m other, M rs. G race Ugbenyen f or being there always for me.

The following persons, among others, who contributed in no small measure to the success of thiswork deserved to be acknowledged.

My f r iends: Lymmy B ukie O gbidi, Akpana Paul, R aymond Agav, H a bibatu Ahmed, a n dChristopher Mudi who paid m e several v isits a t AUST t o c heer me u p. T he members o f H opeHall Parish, Redeemed Christian Church of God, Galadimawa, Abuja, who have always been awarm family to me. Nature will not forgive me if I fail to thank Miss Esther Akinyede who waskind to provide me with a laptop to continue this work when lightning storm damaged my laptop

on 14th

July 2010 a t Julius Nyerere Hall, AUST, Abuja, and I got no help from t he Universityeven t hough I pl eaded f or assistance. I w ill n ot f ail to m ention Mr. Alfred Emakpose whoassisted me in no small measure to keep things straight when the odds were against me. Finally, Iwould like to thank my wonderful new friends, who would be mad at me if I fail to mention theirnames; Hatem, Adel, Amar, Fauzan and Andrew, who are here with me as I write these lines atThe Beaches Hotel, Prestatyn, North Wales, where I neglected some of my schedule to put most

parts of this work together.


6/147

vi | An Approach to Stimulation Candidate Selection and Optimization

TABLE OF CONTENTS

ABSTRACT……………………………………….………….....iii

DEDICATION…………………………………….…………....iv

ACKNOWLEDGEMENT…………………………….………...v

TABLE OF CONTENT………………………………………...vi

LIST OF FIGURES……………………………….………….....x

LIST OF TABLES………………………………………………xi

CHAPTER ONE: INTRODUCTION

1.1 The Near Wellbore Condition…………………………………….……………….…....1

1.1.1 The Composite Skin Effect…………………………………………….…….....11.2 Well Stimulation: Definition and Objectives………………………………….….……..1

1.2.1 Well Stimulation Objectives………………………………………………….…1

1.3 Well Stimulation Methods…………………………………………………….………...2

1.3.1 Matrix Stimulation……………………………………………………………....2

1.3.1.1 Matrix Acidizing Fluid Selection and Treatment Additives ……………....3

1.3.1.2 Benefits and Limitations of Matrix Acidizing Processes………………......4

1.3.2 Fracture Acidizing…………………………………………………….…….......4

1.3.3 Hydraulic Fracturing…………………………………………………….……....6

1.3.4 Recompletion……………………………………………………………….…...7

1.4 Gravel Packing………………………………………...……………………………...…7

1.5 Stimulation Economics and Candidate Selection……………………………….……....8

1.6 Objective and Procedure of the Study…………..………………………………………8

1.7 Limitation of the Study……………………..………………………………………...…9

CHAPTER TWO: LITERATURE REVIEW

2.1 Review of Formation Damage Mechanism…………………………………….….........10

2.1.1 Definition…………………………………………………………….……….…10

2.1.2 Causes of Formation Damage……………………………………………….….10

2.1.3 Quantifying Formation Damage………………………………………..……….11

2.1.3.1 Skin Factor……………………………………………………….……...…11


7/147

vii | An Approach to Stimulation Candidate Selection and Optimization

2.1.3.2 Depth of Damage……………………………………………………….…13

2.1.3.3 Damage Ratio………………………………………………………….…..14

2.1.3.4 Flow Efficiency…………………………………………………………....16

2.1.3.5 Permeability Variation Index………………………………………….…..16

2.1.4 Economic Impact of Formation Damage on Reservoir Productivity

………………………...…………….….17

2.2 Matrix Acidizing Models………………………………………………..………….…..17

2.2.1 Sandstone Acidizing Models……………………………………………….…..18

2.2.2 Carbonate Acidizing Models……………………………………………….…..22

2.3 Acid Fracturing Models……………………………………………………………..….26

2.4 Hydraulic Fracturing Models……………………………………………..……….……28

2.5 Literatures on Stimulation candidate Selection…………………………………….…...30

CHAPTER THREE: METHODOLOGY

3.1 Well Screening Technique……………………………………………..…………….…33

3.2 Design of Stimulation Treatment Models………………………………………….…...34

3.2.1 Matrix Acidizing Design Model…………………….……………………….…38

3.2.1.1 Summary……………………………………………………………….….38

3.2.2 Recompletion Design Model……………………………………………….…..38

3.2.3 Gravel-Pack Design Model……………………………………………….….…403.3 Development of a Model for Optimizing Stimulation Decisions………………….…..44

3.3.1 Optimization Model Assumptions…………………………………………..….45

3.3.2 Stimulation Productivity Ratio…………………………………………….…...46

3.3.3 The Present-value Discount Factor……………………….……………….…....46

3.3.4 Defining the Objective Function, Q D

3.4 Optimization Model Constraints…………………………...……….…………….……50

…………………………………….…….46

3.4.1

Constraint 1: Break-even Requirement……………………...…………….……513.4.2 Constraint 2: Remaining Reserve Limitation…………………………….…….51

3.4.3 Constraint 3: Flow String capacity……………………………………….…….52

3.4.4 Constraint 4: Budget Allocation………………………………………….…….53

3.4.5 Constraint 5: Maximum Formation Productivity ratio……...…………….……53

3.4.6 Constraint 6: Productivity Improvement………………………………….……54


8/147

viii | An Approach to Stimulation Candidate Selection and Optimization

3.5 Stimulation Cost and Productivity Ratio Relationship………………………….……..54

3.6 Summary of the Optimization Model………………………………….………….……55

3.7 Solution to the Optimization Model………………………………………………..…..56

CHAPTER FOUR: MODEL VALIDATION, RESULTS AND DISCUSSION

4.1 Sensitivity Analysis…………………………………………………...…………….….58

4.1.1 Effect of Price of Oil…………………………………………….……………...58

4.1.2 Effect of Discount Rate……………………………………………….…….….58

4.1.3 Effect of Decline Rate……………………………………………………….…58

4.1.4 Effect of Pre-Stimulation Production rate…………………......………….........63

4.1.5 Effect of Abandonment Rate……………..……………………………………63

4.1.6 Effect of Stimulation Time……………………………………………….…….664.2 Model Validation: Case Study 1 ……………………...……………………….….…...66

4.2.1 Formulation of the Bestfield Model…………………………………….……....66

4.2.2 Solution of the Well BU 3 Model…………………………………………..…...72

4.2.3 Discussion of the Well BU 3 Model Result……………………………….……73

4.2.4 Application of the Model Result in Candidate Selection…………………..…..74

4.2.5 Effect of Price of Oil on Well BU 3 Model Result……………………….…….74

4.3 Model Validation: Case Study 2………………………………………………….……774.3.1 Formulation of Well BU 5 Model……………………………………….……...77

4.3.2 Solution of the Well BU 5 Model……………………………………….………80

4.3.3 Discussion of the Well BU 5 Model Result…….………………………..……...81

4.3.4 Effect of Oil Price on Well BU 5 Model Result………………………………...82

4.3.5 Using Case Study 2 Model Result in Candidate Selection……………..………82

CHAPTER FIVE: CONCLUSION AND RECOMMENDATION

5.1 Conclusion…………………………………………………………………………...…845.2 Recommendation…………………………………………………………………….…85

REFERENCES…………………………………………………………………………….…….87

NOMENCLATURE………………………………………………………………………….….95

APPENDIX A: A SIMPLE WELL SCREENING FLOW CHART…………………………...98


9/147

ix | An Approach to Stimulation Candidate Selection and Optimization

APPENDIX B: STIMULATION COST AND PERFORMANCE………………………….....99

APPENDIX C: SOLVER RESULTS………………………………………………………….100

APPENDIX D: WHAT’S BEST 10.0 RESULTS……………………………………………...115

APPENDIX E: MATHEMATICA 7.0 RESULTS……………………………………………..120

APPENDIX F: DERIVATION OF THE OBJECTIVE FUNCTION FOR OTHER

DECLINE CASES……………………………………………………….…..124


10/147

x | An Approach to Stimulation Candidate Selection and Optimization

LIST OF FIGURES

3.1 Production Decline Profile for a Stimulated Well.………………… ……………….…454.1 Effect of oil price on the objective function ………….…………………………….….60

4.2 Effect of discount rate on the objective function …………………..……………….….61

4.3 Effect of decline rate on the objective function ……………………………………..…62

4.4 Effect of pre-stimulation production rate on the objective function……………….…...64

4.5 Effect of abandonment rate on the objective function ………………...………….........65

4.6 Effect of stimulation time……………………………………….………………….…...67

4.7 Cost Versus Productivity Ratio Plot for Well BU 3 …..……………………………...…71

4.8 Effect of oil price on Well BU 3 model result……………………………………….…..76

4.9 Cost Versus Productivity Ratio Plot for Well BU 5 ……………………………….……79

4.10 Effect of oil price on Well BU5 model result………………………………………….83


11/147

xi | An Approach to Stimulation Candidate Selection and Optimization

LIST OF TABLES

Table 4.1 : Input Data for Sensitivity Analysis…………….………..59

Table 4.2 : Bestfield Model Data……………………………….…….68

Table 4.3: Bestfield Model Summary………………………………..75

Table 4.4: Well BU 5 Model Data…………………………………...78


12/147

1 | An Approach to Stimulation Candidate Selection and Optimization

Chapter One

Introduction

1.1 The Near Wellbore Condition

Permeability reduction i n t he r egion near t he wellbore in a producing zo ne i s r eferred t o a s

“damage”. The damaged region i s c alled s kin z one w hile the term “skin e ffect” refers t o a

dimensionless parameter used to quantify the extent of damage. Reduction in permeability in the

near-wellbore region results in lower productivity due to increased pressure drop, hence damage

is not desirable.

1.1.1 The Composite Skin Effect

The skin effect can be obtained from a well test. It m easures t he extent of damage in the near-

wellbore zone. The total skin effect obtained from the well test is a composite parameter which

consists of s kin c omponents d ue to mechanical c auses – a di sturbance of t he fluid f low

streamline n ormal t o t he w ell, o r formation damage - alteration o f t he natural r eservoir

permeability. It i s very important to be able to identify the formation damage component of the

skin s ince t his c an b e r educed by b etter operational practices, or possibly, b e r emoved or

bypassed by stimulation treatments. Formation damage can result from many different operations

such a s dr illing, cementing, perforating, completion/gravel pa cking, production, i njection,

workover, stimulation, etc.

1.2 Well Stimulation: Definition and Objectives

Well stimulation is a way of increasing well productivity by removing (or bypassing) formation

damage in t he near-wellbore r egion or by superimposing a highly conductive structure onto the

formation.

1.2.1 Well Stimulation Objectives

The objectives of w ell s timulation can be di vided into technical ob jectives and e conomic

objectives.


13/147


• Technical Objectives

Remove, reduce or b ypass t he f ormation damage, reduce sand production and cl eaning-

up the perforations.

• Economic Objectives

Increase flow rate and optimize production from the reservoir.

1.3 Well Stimulation Methods

Several stimulation t echniques e xist bu t t he commonly u sed methods i nclude matrix a cidizing,

fracture a cidizing, fracpack , ex treme o verbalance operations and hy draulic fracturing. These

methods h elp t o optimally increase well or reservoir productive c apacity by providing a net

increase in the productivity index. This increase in productivity index can then be used either to

increase t he p roduction r ate o r t o d ecrease the dr awdown pressure differential. Increase i n

production rate will eventually increase productivity. A decrease in drawdown can help prevent

sand production and water or gas coning and/or shift the phase equilibrium in the near-wellbore

region t owards s maller f ractions of condensate. Some of the m ost c ommon s timulation

techniques are discussed in the following sections.

1.3.1 Matrix Stimulation

Matrix stimulation is injecting an acid/solvent into the formation at below the fracturing pressure

of t he formation to d issolve/disperse materials th at im pair well production i n sandstone

reservoirs or to create new, unimpaired flow channels in carbonate reservoirs. Mineral acids are

most c ommonly us ed in matrix s timulation hence t his t echnique is f requently ca lled ma trix

acidizing. Matrix acidizing is a near-wellbore treatment, with all of the acid reacting within a few

to perhaps as much as 10 ft of the wellbore in carbonates. Matrix acidizing lower permeability

limit is 10mD for oil wells and 1mD for gas wells.

In sandstone, only a small f raction o f the m atrix i s soluble hence r elatively s low r eacting acid

dissolves the permeability-damaging minerals. Carbonate formations are different in that a large

fraction of the matrix is soluble (usually > 50%), hence acid will react rapidly with flow channels

and pores and creates new flow paths by dissolving the formation rock.


14/147


As a rule of thumb, matrix acidizing is applied only in situations where a well has a large skin

effect t hat cannot b e attributed t o mechanical, o peration o r surface p roblems. The r emoval of

damage by matrix a cidizing r equires t hat t he t ype ( or c ause) a nd location of t he damage be

identified before its removal is attempted. The damage identification process involves:

• Examining t he well records to identify operations t hat might ha ve r esulted in formation

damage

• Carrying out specific laboratory testing, such as a reservoir core flushing, to determine if

the identified operations did indeed lead to core damage for the particular combination of

the fluids in question and the reservoir formation

• Examining t he da maged core with sophisticated a nalytical techniques s uch a s t he

scanning electron microscope to confirm the damage type and the damage location and

hence develop ideas on how to remove it.

1.3.1.1. Matrix Acidizing Fluid Selection and Treatment Additives

The t ype of a cid u sed for a s timulation j ob i s a function of t he da mage t ype. Generally, a cid

selection guidelines are based on t emperature, mineralogy and petrophysics. The most common

acids u sed a re h ydrochloric a cid ( HCl) a nd a m ixture o f hydrochloric a nd h ydrofluoric a cids

(HF/HCl) usually known a s mud acid. HCl is suitable f or li mestone, d olomite, formation w ith

iron m aterials a nd C aSO 4

Additives help make acid treatments more e ffective. They are mixed with the treating fluids to

modify a pr operty of t he fluid (e.g., co rrosion, precipitation, emulsification, s ludging, scaling, f ines

migration, clay swelling tendency, surface tension, flow per layer, friction pressure). The treating fluid

is d esigned t o e ffectively r emove or b ypass t he damage, whereas a dditives a re u sed t o prevent

excessive c orrosion, p revent s ludging and e mulsions, pr event iron pr ecipitation, improve

cleanup, improve coverage of the zone and prevent precipitation of reaction products. Additives

. H F i s mostly us ed i n s andstone, c lay, f eldspar, s and (spent on

material, not quartz or sand), and it is not used in carbonate formations. Acid mixtures such as

acetic-hydrochloric a nd formic-hydrochloric a cids a re u sed i n high temperature ca rbonate

formation w hile t he formic-hydrofluoric a cid mixture i s us eful i n high t emperature sandstone

formation.


15/147


are a lso u sed i n preflushes a nd overflushes t o stabilize clays a nd di sperse pa raffins a nd

asphaltenes. Types of a dditives include: acid corrosion inhibitors, aromatic solvents, Iron stabilizers,

surfactants, mutual s olvents, diverters, scale i nhibitors, clay stabilizers, aluminum stabilizer, retarders,

nitrogen and alcohols.

1.3.1.2. Benefits and Limitations of Matrix Acidizing Processes

Matrix a cidizing is usually very economically a ttractive (low c ost), because r elatively s mall

treatments may improve the well performance considerably.

Some pr oblems a ssociated with matrix a cidizing a re: difficulty to i dentify the type of damage,

multiple damages with completing remedies, detrimental by-products of stimulation, frequently,

ineffective o r p artially e ffective treatments. It involves complex chemical a nd t ransport

phenomena t hat, w hile effective i n r emoving one k ind o f damage, may cr eate a nother o ne.

HCL/HF blends can create early damage in formations, however the lower the HF concentration

in t he b lend t he l ess chance there i s for damage creation. Acid placement and damage removal

from l aminated f ormations where some perforations penetrate very h igh-permeability la yers is

especially problematic.

Successful m atrix treatments r equire correct c hoice of fluid t o a ttack damage an d u niform

placement o f the s elected treating f luid. Improper f luid pl acement i ncreases reservoir

heterogeneity. Misapplied stimulation t reatments a re costly and ineffective, o ften creating more

problems than they solve.

It is important to note that not all damage can be removed by matrix acidizing. Whenever there

are insoluble scales (e.g. BaSO4) or acid sensitive sandstones, other stimulation methods (such

as acid fracturing to bypass scales) are considered.

1.3.2 Fracture Acidizing

In this method of acidizing, acid is injected into the formation at a rate high enough to generate

the pressure required t o fracture t he formation. T he r apid i njection produces a buildup i n the


16/147


wellbore pressure until it is large enough to overcome compressive earth stresses and the rock’s

tensile strength. At this p ressure, t he r ock fails, a llowing a c rack ( fracture) t o be formed.

Continued fluid injection increases the fracture length and width. The injected acid differentially

etches t he formation fracture faces as it r eacts, r esulting i n t he formation of h ighly c onductive

etched channels that remain open after the fracture closes. Two procedures are commonly used.

Acid alone is injected, or a fluid (called a pad) that will create a long, wide fracture is injected

and followed by an a cid. A conventional fracture acidizing t reatment involves pumping an acid

system after fracturing. It may be preceded by a nonacid preflush and usually is overflushed with

a nonacid fluid.

Acid s olubility of th e f ormation is a key f actor i nfluencing w hether f racture acidizing or

proppant treatments should be employed. If the formation is less than 75% acid soluble, proppanttreatments should be used. For acid solubilities between 75 and 85%, special lab work can help

define w hich approach should be u sed. Above 85% acid solubility, fracture acidizing would b e

the most effective approach.

Treatment v olumes for fracture a cidizing a re much l arger t han for matrix acidizing t reatments,

being as high as 1,000 to 2,000 gal/ft of perforated interval.

As a ge neral guideline, fracture a cidizing i s used on formations with >80% hydrochloric a cid

solubility. Low-permeability carbonates (>20 md) are the best candidates for these t reatments.

Fluid loss to the matrix and natural fractures can also be better controlled in lower permeability

formations.

The su ccess of t he acid f racturing treatment depends on two ch aracteristics o f t he etched

fracture: effective fracture length (which is a function of the rate of acid consumption, acid fluid

loss ( wormhole formation) a nd acid convection a long t he fracture) a nd e ffective fracture

conductivity (a function of the etched pattern, vo lume of r ock di ssolved, r oughness of etched

surface, rock strength and closure stress). The acidized fracture length and fracture conductivity

are therefore controlled largely by the treatment design and formation strength.


17/147


1.3.3 Hydraulic Fracturing

Hydraulic Fracturing consists of pumping a vi scous fluid at a sufficiently high pressure (greater

than the formation fracture pressure) into the completion interval so that a two winged, hydraulic

fracture is formed. This fracture is then filled with a high conductivity, proppant which holds thefracture open (maintains a high conductivity path to the wellbore) after the treatment is finished.

Propped hydraulic fracturing is aimed at raising the well productivity by increasing the effective

wellbore radius f or w ells c ompleted i n low p ermeability c arbonate or clastic f ormations.

Hydraulic fracturing i s t o improve productivity i n low-permeability f ormations, or to pe netrate

near-wellbore damage or for sand control in higher permeability formations.

Hydraulic fracturing i s a mechanical process hence it i s only necessary to know that formation

damage is present when designing such a treatment. When a well is hydraulically fractured, most

pre-treatment skin e ffects such a s f ormation da mage, perforation skins a nd s kins d ue t o

completion and partial penetrations are bypassed and have no e ffect on the post-treatment w ell

performance. Phase-and r ate-dependent s kins effects a re either eliminated or contributes i n the

calculation of the fracture skin effects. Generally pre-treatment skin effects are not added to post-

fracture skin effects.

Hydraulic fracturing differs from fracture acidizing in that hydraulic fracturing fluids usually arenot c hemically r eactive, a nd a proppant i s placed i n the f racture t o keep the f racture open and

provide conductivity.

The Inflow Performance of a F racture Stimulated well i s controlled by a quantity known as t he

dimensionless fracture conductivity which depends on the fracture permeability conductive

fracture w idth, f ormation permeability and the conductive fracture single wing length. The

fracture c onductivity i s i ncreased by an i ncreased fracture width, a n i ncreased proppant

permeability ( large, more spherical p roppant grains ha ve higher permeability), and minimizing

the permeability damage to the proppant pack from the fracturing fluid.

Propped hy draulic f racture w ell s timulation s hould onl y be c onsidered when the: well i s

connected to adequate produceable reserves; reservoir pressure is h igh enough to maintain flow


18/147


when producing t hese r eserves ( or i t i s economically ju stifiable to i nstall a rtificial li ft);

production s ystem can pr ocess t he e xtra pr oduction; professional, experienced p ersonnel are

available for t reatment de sign, e xecution a nd supervision t ogether with h igh quality pu mping,

mixing and blending equipment.

1.3.4 Recompletion

For wells with certain t ypes of da mage such a s pa rtially or t otally p lugged p erforations,

insufficient perforation density o r low depth of perforation, it may b e sufficient t o r ecommend

recompletion technique. Hence the idea of r ecompletion is to increase the perforation density or

to increase the depth of perforations. The overall aim of this method is to increase production by

bypassing t he da mage. R ecompletion i s a lso u sed effectively in reducing w ater p roduction. I n

this approach t he w ell i s re-perforated at a new hi gher zone w hile t he pe rforations i n the water

zone are plugged off.

1.4 Gravel Packing

Gravel packing is used in weak formations that have been producing sand or have the tendency

of producing s and. The gravel m ixed in a ba se f luid is pu mped as sl urry to f ill all p erforation

tunnels and t he s creen/casing a nnulus. Productivity a nd l ife of t he gravel pack depends on

packing t he perforations w ith gr avel. If not pa cked, f ormation f ines c an invade t he tunnels

impairing productivity and also reducing the area open to flow. Re-completions in low pressure

reservoirs w here formation s and ha s be en pr oduced, can accept l arge volumes o f additional

gravel.

1.5 Stimulation Economics and Candidate Selection

The evaluation of t he economics of stimulation treatment must consider many factors including:

treatment cost, initial increase in production rate, additional reserve that may be produced beforethe well reaches i ts economic l imit, rate of pr oduction d ecline b efore and a fter s timulation, and

reservoir and mechanical problems that could cause the treatment to be unsuccessful.

Selection of the optimum size of a stimulation treatment is based primarily on economics. The

most commonly used m easure of e conomic e ffectiveness is t he n et present v alue (NPV). The


19/147


NPV is the difference between the present value of all receipts and costs, both current and future,

generated a s a r esult of t he stimulation treatment. Future r eceipts and costs a re converted i nto

present value u sing a discount rate and taking i nto account the year in which they will appear.

Another measure of t he economic e ffectiveness i s t he payout period (PO); t hat is, t he t ime i t

takes for the cumulative present value of the net well revenue to equal the treatment costs. Other

indicators i nclude i nternal rate of return (IRR), profit-to-investment ratio (PIR) and growth rate

of return (GRR). The NPV (as well as other indicators) is sensitive to the discount rate and to the

predicted future hydrocarbon pr ices. A s with a lmost a ny other e ngineering a ctivities, costs

increase almost linearly with the size of the stimulation treatment but (after a certain point) the

revenues increase only marginally or may even decrease. This suggests that there is an optimum

size of t he t reatment t hat will maximize t he N PV. Hence it i s i mportant to select stimulation

candidate wells that have potentials for maximum benefit.

Candidate Selection (Recognition) is the process of identifying and selecting wells for treatment

which have the capacity for higher production and better economic return. Hence in stimulation

candidate w ell s election, t he well stimulation treatment yielding the hi ghest di scounted rate o f

return is the treatment which, in principle, should be carried out first.

1.6 Objective and Procedure of the Study

The goal o f t his r esearch i s to present a model for i dentifying s timulation candidates,

recommending stimulation treatment option and optimizing the stimulation process selected. The

model i s a lso u sed to rank stimulation candidates based on economics. Hence this research will

attempt to answer the question: “given the need to stimulate several wells in a field, how do we

rank the wells based on s timulation benefit and what stimulation approach to use in order to get

the highest economic returns?” To answer these questions, a merit function is developed based

on production decline curve analysis and economic discounting concepts. In combination with agood stimulation treatment module, the model can be used for ranking stimulation candidates.

The research procedure begins i n chapter one with an introduction to the concept of skin factor

and w ell s timulation methods. S everal lit eratures o n f ormation da mage a nd s timulation models


20/147


are r eviewed in chapter t wo. Chapter t hree c ontains a w ell s creening m odule, design o f s ome

selected stimulation modules and an optimization model which consists of an objective function

with constraint. The optimization model combines the concept of production decline curves with

economic d iscounting. The m odel developed i n chapter three is va lidated in chapter f our using

actual field data from the Niger Delta.

1.7 Limitation of the Study

This research is intended for stimulation candidate selection in the Niger Delta. Matrix acidizing

technique is the main stimulation technique that has been used up to date in the Niger Delta due

to t he g ood permeability of t he N iger D elta formation. Hence only matrix acidizing t echnique,

recompletion and gravel packing are considered in the methodology presented in chapter three of

this research. Acid fracturing and hydraulic fracturing are not considered.


21/147

10 | An Approach to Stimulation Candidate Sele ction and Optimization

Chapter Two

Literature Review

In or der t o properly select s timulation candidate w ells, it i s n ecessary t o first ha ve a n in-depth

understanding of t he c oncepts of f ormation d amage and well s timulation. A lot of researches

conducted on formation damage and w ell s timulation methods can be found in literatures. We ll

stimulation i s c onsidered a m ajor key to proper r eservoir m anagement, he nce several authors

made valid contributions.

2.1 Review of Formation Damage Mechanism

2.1.1 Definition

Civan 1 defined formation d amage a s a generic t erminology r eferring t o t he i mpairment o f t he

permeability of petroleum bearing formations by various adverse processes. I t is an undesirable

operational a nd e conomic problem t hat c an o ccur du ring t he va rious p hases of oi l a nd ga s

recovery f rom s ubsurface r eservoirs including d rilling, production, hydraulic f racturing, and

workover operations. Bennion 2 viewed formation damage as any process that causes a reduction

in the natural inherent productivity of an o il and gas pr oducing formation, or a r eduction i n the

injectivity o f a water or gas injection well. Bennion also pointed out that the formation damage

issue is often overlooked because of ignorance and apathy. In many cases, the operators are not

seriously c oncerned with f ormation d amage because of t he b elief t hat i t can be circumvented

later o n, simply by a cidizing a nd/or h ydraulic fracturing. But Porter 3 and M ungan 4

argued t hat

because formation damage i s usually nonreversible, it i s better to avoid formation damage rather

than deal with it later on using expensive and complicated procedures.

2.1.2 Causes of Formation DamageAmaefule et al. 5

classified the various factors causing formation damage as following:

• Invasion of f oreign f luids, s uch as w ater and c hemicals used for i mproved

recovery, drilling mud invasion, and workover fluids;


22/147


• Invasion o f foreign particles and mobilization of indigenous particles, such a s

sand, mud fines, bacteria, and debris;

• Operation conditions s uch a s w ell flow r ates a nd wellbore pr essures a nd

temperatures;

• Properties of the formation fluids and porous matrix.

Amaefule et al. 5

further grouped these factors in two categories:

• Alteration of formation properties by various processes, including permeability reduction,

wettability a lteration, lithology c hange, r elease of mineral p articles, pr ecipitation of

reaction-by products, and organic and inorganic scales formation

• Alteration of fluid properties by various processes, including viscosity alteration by

emulsion block and effective mobility change.

2.1.3 Quantifying Formation Damage

Terms used in quantifying formation damage as presented by various authors include:

2.1.3.1

Van Everdingen and Hurst

Skin Factor6 defined skin effect or skin factor as a mathematically dimensionless

number which r eflects t he altered permeability d ue to damage , at a d istance r d , causing asteady-state pressure difference. A relationship between the skin effect, s , reduced permeability,

R and altered zone radius, r d

may be expressed as:

= −1 ……………………………………….....…….2.1Equation 2.1 is known as Hawkins 7

formula. From the equation it can be deduced that If <

the well is damaged and > 0; conversely, if > , then < 0 and the well is stimulated. For = 0,

the near-wellbore permeability is equal to the original reservoir permeability.

Generally, certain well logs may enable calculation of the damaged radius, r d , whereas pressure

transient analysis may provide the skin effect, s , and reservoir permeability, k . Equation 2.1 may

then be used to calculate the value of the altered permeability .


23/147


In the absence of production log data, Frick and Economides 8

postulated t hat, an elliptical cone

is a more plausible shape of damage distribution along a horizontal well. They developed a skin

effect expression, analogous to the Hawkins formula:

= −1 1+1 43 ,2 2 + , + 1 …….….…..2.2where is the equivalent skin effect, is t he i ndex of a nisotropy a nd , is the

horizontal axis of the maximum ellipse, normal to the well trajectory. The maximum penetration

of d amage is n ear t he vertical section of t he well. T hey stated t hat the shape of t he el liptical

cross-section will depend greatly on t he i ndex of a nisotropy. The i ndex of anisotropy is

defined as:

= ……………………………………………….……..2.3with being the horizontal permeability and is the vertical permeability.

Piot and Lietard 9 expressed the total skin of a well as a sum of the pseudoskin of flow lines from

the f ormation face to t he pi peline and the true skin due to f ormation damage. Economides and

Nolte 10

The total skin effect may be written as:

shown t hat t he t otal skin effect i s a composite of a number of factors, most of which

usually cannot be altered by conventional matrix treatments.

= + + + + ∑ …………………...............2.4The last term in the right-hand side of Eq. 2.3 represents an array of pseudoskin factors, such as

phase-dependent a nd r ate-dependent e ffects that c ould b e altered b y hy draulic f racturingtreatments. The other three terms are the common skin factors. The third term refers to the

damage skin e ffect as defined in equation 2.1. The fi rst term + is the skin effect caused by

partial completion and slant. Cinco-Ley et al. 11 documented a detailed approach of estimating the

skin f actor du e t o partial completion a nd slant. T he pa rameters needed for t he estimation a re:

completion t hickness, r eservoir thickness, elevation, a nd penetration r atio. An e xample t o


24/147


illustrate the c alculation o f this s kin e ffect is do cumented b y Economides and Nolte 10. The

second term represents the skin effect resulting from perforations. It is described by Harris12

and also expounding the concept, Karakas and Tariq 13

have shown that:

= + + ……………………………….…………….2.5In e quation 2.5, t he ho rizontal ps eudoskin factor, is a function of the pe rforation ph asing

angle and the wellbore radius. The vertical pseudoskin factor and the wellbore skin effect

are functions of some dimensionless v ariables. A us eful definition of t hese v ariables a nd t he

application of equation 2.5 are also documented by Economides and Nolte 14

.

Karakas and Tariq13

also shown that a combination of the damage and perforation skin effects( ) can be approximated, for a case where the perforations terminate inside the damaged zone,

by:

( ) = −1 + = ( ) + ………………………....2.6 is the damaged zone radius, and ( ) is the equivalent openhole skin effect (Eq. 2.1)

According to Economides and Nolte 10

, it is of extreme importance to quantify the components of

the s kin e ffect in o rder to e valuate t he e ffectiveness of s timulation tr eatments. I n fact, t he

pseudoskin effects can overwhelm the skin effect caused by damage. They explained that it i s not

inconceivable to obtain extremely large skin effects after matrix stimulation. This may be

attributed to the usually irreducible configuration skin factors.

2.1.3.2

Yan et al.

Depth of Damage15

correlated t he depth of invasion of drilling a nd completion f luids by regression

analysis of e xperimental data o btained by means of the s lice cutting of d amaged c ore plugs.

Their empirical correlation is given by:

= 1.612 0.521 ∅

0.271

(0.043 ) ………………………………….2.7


25/147


where is the invasion depth in cm, p is the pressure in MPa, is the cumulative filtrate lossin 3 ,∅ is porosity in percentage, and is permeability in 2 (~ Darcy).

McLeod a nd C oulter 16

used t he a pproximate s olution t o t he diffusivity e quation for

dimensionless time, greater than 100,

( , ) = + 162.6 ℎ( 2 −3.23) ……......…………….………2.8to obtain an expression that can be used to estimate the damaged radius, ,

=

1690

12

………………………………………………………2.9

In equation 2.9, is the time at which the two straight lines representing the damage zone and

undamaged formation intersect on a plot of log .

Appendix B of t he pa per pr esented b y Raymond and Hudson 17

also contained a detailed

approach of estimating the radius of the damaged zone.

2.1.3.3 Damage Ratio

Amaefule et al 18

= − = 1 − ….….……………..……………………2.10expressed the damage ratio (DR) as a change in production due to the effect of

the damage.

where and the undamaged and damaged standard flow rates, respectively.

Using Muskat 19

equation for the undamaged flowrate:

= 2 ℎ( − ) …………………………………………….……..2.11and, also, Amaefule et al 18 equation for the damaged flowrate:


26/147


= 2 ℎ( − ) + ………………………………....…………2.12

Civan 20

expressed equation 2.10 in terms of 2.11 and 2.12 as:

= −1 + ……………….……….……………….…………..2.13

where and in Equations 2.11 and 2.12 are the f luid viscosity and formation volume factor.

and are t he u ndamaged a nd damaged effective permeabilities, ℎ is t he thickness of t heeffective pay zone, and are the wellbore and r eservoir drainage boundary fluid pressures,

and are t he wellbore and reservoir drainage r adii, and is the r adius of t he d amaged

region.

Combining equation 2.1 and 2.13, t he damage ratio can be expressed i n t erms o f the effective

skin factor , as:

= + …………………………….………..……….…2.14

is as defined in equation 2.1. Equation 2.14 gives the production loss by alteration of formation

properties. Leontaritis 21

= = ………………………………………..……………2.15

stated t hat r apid flow o f o il a nd water i n t he near-wellbore r egion

promote mixing a nd e mulsification. T his causes a r eduction in t he hy drocarbon e ffectivemobility λ, because emulsion viscosity is several fold greater than oil and water viscosities. The

mobility λ is defined by:

and are respectively the absolute and relative permeabilities. High viscosity emulsion forms

a stationary block which resists flow. It is usually called “emulsion block”. If and represent

the v iscosities of oil a nd emulsion, r espectively, a nd a s teady-state and i ncompressible radialflow i s considered, t he t heoretical u ndamaged and damaged flow rates a re given, r espectively,

by:

= 2 ℎ( − ) ………………………………………………….…………...2.16and,


27/147


= 2 ℎ( − ) + ………………………..….…………………….2.17where represents the formation volume factor of the emulsion.

Civan 22

= −1 + …………………………….…….….2.18

substituted Equations 2.16 and 2.17 into Eq. 2.10 to obtain the following expression for

the damage ratio:

Equation 2.18 gives a means to calculate the production loss by alteration of fluid properties.

The viscous skin effect is also expressed similar to Zhu et al 23

as:

= −1 …………………………………………………….……2.192.1.3.4

Flow efficiency ( FE ) i s defined a s the r atio o f t he damaged t o u ndamaged formation flow

(production or injection) indices.

Flow Efficiency

= = − −∆− ......…………………..........….……2.20where and denote t he a verage reservoir fluid and flowing well bottom hole pressures,

respectively, and ∆ is the additional pressure loss by the skin effect.Mukherjee a nd Economides 24

presented the f low ef ficiency o f v ertical w ells f or radial and

incompressible fluid flow at a steady-state condition as:

= + …………………………………………………………..2.21

Where , the effective skin factor is as defined by Hawkins 7

in equation 2.1.

2.1.3.5

Civan

Permeability Variation Index25 presented a n i ndex which can be u sed t o express t he variation i n permeability due t o

near-wellbore damage. This index known as permeability variation (or reduction) index can be

expressed mathematically as:


28/147


= −= 1 − ………………………………………………………2.22where and denote the formation permeabilities before and after damage, respectively.

2.1.4 Economic Impact of Formation Damage on Reservoir Productivity

Amaefule et al. 18

$ = 365 $ ℎ …………………………….2.23

presented a model that can estimate the economic impact of formation damage

on r eservoir productivity, in t erms o f the annual r evenue l oss by formation da mage per well

( FD$L ) at a given price of oil, p, as:

Li et al 26 and a lso L ee a nd Kasap 27

stated t hat b ecause t he d egree o f damage variation in t he

near-wellbore region, i t is more appropriate to express t he total skin, used in any of the

equations above as a sum of t he individual skins over consecutive c ylindrical s egments of t he

formation as:

……………………………..2.24

where is the number of cylindrical segments considered.

2.2 Matrix Acidizing Models

The optimal volume of acid for a particular acidizing job may be selected based on a laboratory

acid response curve or an acidizing model 28. These models consider both the modification of the

pore structure as i t dissolves and the change in acid concentration as a function of both time and

position within the pore system.

29

Dullien 30 presented a c omprehensive literature r eview of t he models a nd the methods us ed t o

determine pore-size distributions i n a po rous medium. Scheidegger 31 reviewed capillary models

and concluded that to predict quantities that relate to the geometric structure of a porous medium,

such as permeability and capillary pressure, an empirical correlation factor called tortuosity must

be introduced. Scheschter and Gidley 32

= =1

= −1 −1=1

proposed a capillary model to describe matrix acidizing.


29/147


In their model pores are assumed to be interconnected so that a fluid can flow through the matrix

under the influence of a p ressure g radient, and as the acid reacts with the matrix the pores

increase in size.

2.2.1 Sandstone Acidizing Models

Very many models of the sandstone acidizing pr ocess have been presented over t he y ears. The

models o nly differ in t he d etail in w hich they d escribe the chemical interactions b etween t he

acids and the formation minerals and the extent to which they handle or model complexities such

as multiple reservoir zones, diversion methods, wellbore flow e ffects, and other factors. T he

acidizing models can be divided i nto equilibrium models and kinetic models. The equilibrium

models 33-35 assume a ll c hemical r eactions a re a t e quilibrium a nd have been u sed p rimarily t o

study t he t endencies f or precipitation r eactions t o occur in a cidizing. T he ki netic models 36-

40

consider the kinetics of the relatively slow reactions occurring in sandstones.

• The two-mineral model

The t wo-mineral m odel lumps all m inerals i nto on e of t wo c ategories: fast reacting and slow

reacting species; a nd i t i s t he most common model i n u se today. 36, 41-42 Schechter 43 categorizes

fieldspars, a uthogenic clays, a nd a morphous silica a s fast-reacting, w hile d etrital c lay p articles

and qu artz gr ains are the pr imary s low-reacting mi nerals. This model a s presented by

Economides a nd N olte 44

consists o f material b alances ap plied t o t he H F a cid a nd r eactive

minerals, which for linear flow, such as in core-flood, can be written as:

(∅) + = −∗ , + ∗ , (1 − ∅) …….…………………….2.25[(1

− ∅) ] = − ∗ , ……………………………………………….....2.26

[(1 − ∅) ] = − ∗ , ………………………………….………………2.27where is the concentration of hydrofluoric acid (HF) in solution and is its molecular

weight, is t he a cid flux, is th e d istance, ∗ and ∗ are the s pecific s urface a reas p er unit


30/147


volume of solids, and are the volume fractions, , and , are the reaction rate constants(based on the rate of consumption of HF), and are the molecular weights, and

are t he dissolving powers of 100% H F, and and are the densities of the fast- and slow-

reacting minerals, respectively, denoted by the subscripts F and S .

When t he equations above are made d imensionless f or a c ore-flood of length with constant

porosity, two dimensionless groups were observed for each mineral: the Damkohler number

and the acid capacity number . These two groups describe the kinetics and the stoichiometry of theHF-mineral reactions. The shape of t he acid reaction front depends on the Damköhler number . The

acid ca pacity n umber regulates h ow m uch l ive acid reaches t he f ront, in ot her w ords, itaffects the frontal propagation rate directly.

The Damköhler number is the ratio of the rate of acid consumption to the rate of acid convection,

which for the fast-reacting mineral is:

( ) =(1−∅0 ) 0 ( ) ∗ ……………………………………..….2.28

The acid capacity number is the ratio of the amount of mineral dissolved by the acid occupying a

unit vol ume o f rock por e s pace to the amount o f m ineral present in the u nit vol ume o f rock,

which for the fast-reacting mineral is:

( ) = ∅0 (1−∅0 ) 0 ….……………………………...…………2.29In equation 2.29, the acid concentration is in weight fraction (not moles/volume).

The dimensionless form of equations 2.25 through 2.27 can only be solved numerically in their

general f orm, th ough a nalytical s olutions a re p ossible for certain simplified situations.

Schechter 43 presented an approximate solution to these equations that is valid for relatively high

Damköhler number ( ( ) > 10 ). Numerical m odels providing solutions t o t hese equations,such as that presented by Taha et al. 36

are frequently used for sandstone acidizing design.


31/147


• The two-acid, three-mineral model

Bryant 45, and also, da Motta et al. 46

shown that at elevated temperatures the sandstone acidizing

process i s not well described by the two-mineral m odel. These studies suggest that the reaction

of fluosilicic acid with aluminosilicate (fast-reacting) minerals may be quite significant. Thus, an

additional acid and mineral must be considered to accommodate the following reaction, which is

added to the two-mineral model:

H 2SiF 6 + fa st-reacting mineral Si(OH) 4

+ Al fluorides …………...2.30

The practical implications of the s ignificance o f this reaction a re th at le ss H F is required to

consume the fast-reacting minerals with a given volume of acid because the fluosilicic acid also

reacts with t hese m inerals a nd t he r eaction product of silica gel ( Si(OH) 4) p recipitates. T his

reaction allows live HF to penetrate farther into the formation; however, there is an added risk of

a possibly damaging precipitate forming. An example presented by Sumotarto 47

shows improved

performance with t he t wo-acid, t hree-mineral model when compared with t he one -acid, two-

mineral model. This is an example of a kinetic model.

• Precipitation Models

Though t he t wo-acid, t hree-mineral model c onsiders th e p recipitation o f silica g el i n it s

description of the a cidizing process, yet other numerous r eaction pr oducts t hat may precipitate

were not considered.

Walsh et al. 33

described a l ocal equilibrium model, a common type of geochemical model (that

considers a l arge number of possible r eactions) used t o study sandstone a cidizing. This model

assumes that all reactions are in local equilibrium; i.e., all reaction rates are infinitely fast.

Sevougian et al. 34 presented a geochemical model that includes kinetics for both dissolution and

precipitation r eactions. T his model shows t hat precipitation damage will be l essen i f either the


32/147


dissolution or the precipitation reactions are not instantaneous (i.e. if the reaction rate decreases,

the amount of precipitate formed will also decrease).

• Permeability Models

Predicting permeability change as acid dissolves some of the formation minerals and precipitate

is f ormed i s a necessary s tep n eeded to predict the f ormation response to acidizing. The

permeability increases as the pores and pore throats a re enlarged by mineral d issolution. At the

same t ime, small particles ar e r eleased a s c ementing m aterial i s dissolved, and some of t hese

particles lodge (perhaps temporarily) in pore throats, reducing the permeability. Any precipitates

formed a lso t end t o d ecrease the permeability. T he formation of carbon d ioxide ( CO 2) a s

carbonate mi nerals a re dissolved m ay a lso cause a t emporary r eduction i n t he r elative permeability t o li quids. 48The complex n ature o f the p ermeability response h as m ade its

theoretical pr ediction f or r eal sandstones impractical. For t his r eason empirical correlations

relating the permeability increase to the porosity change during acidizing are used. Guin et al. 49

however a chieved s ome s uccess when a more i deal systems su ch a s si ntered disks was

considered. Labrid 50

presented the following useful relationship:

=

∅

∅

…………………………………………………………..................2.31

The correlation presented by Lambert 51

is:

= [45.7 (∅ − ∅)] ……………………………………………………..…2.32Lund and Fogler 52

correlation is:

=

∅−∅∆∅

……………………………………………………………2.33

In Eq. 2.31 through 2.33, and∅ are the initial permeability and porosity and and∅ are the permeability and porosity after acidizing. and are empirical constants. In Eq. 2.33, and

are reported to be 1 and 3 for Fontainbleau sandstone. In Eq. 2 .32, = 7 .5 and ∆∅ = 0.08 best fit data for pha coides sandstone. The best approach i n u sing these correlations i s to select


33/147


the e mpirical constants b ased o n core f lood responses, if s uch ar e available; and also, lacking

data for a particular formation, equation 2.31 will yield the most conservative design.

48

2.2.2 Carbonate Acidizing Models

Mcleod 53

shown t hat t he fundamental di stinguishing f eature of a r ock t reatment i s t he H Cl

soluble fraction; and that for formation rocks largely soluble i n HCl, carbonate acidizing u sing

HCl (without H F) is recommended. For rocks with H Cl solubility less than 20%, sandstone

acidizing using mud acid is recommended.

Shaughnessy a nd K unze 54, a nd a lso, Schechter 43 have shown t hat he c hemistry of c arbonate

acidizing processes is much simpler than that of sandstone acidizing because there is no tendency

of precipitate being formed (the reaction products CO 2 and CaCl 2 are both quite water soluble).

But the physics i s complex because t he surface r eaction r ates i n carbonates a re very hi gh, so

mass t ransfer o ften l imits the overall r eaction r ate, l eading t o hi ghly n on-uniform d issolution

pattern. Hofefner and Fogler 55

have shown that due to the non-uniform dissolution of limestone

by HCl, a few large channels called wormholes are created. This unstable wormholing process is

not completely understood, but the knowledge of the depth of penetration of wormholes and the

physics o f wormhole growth i s n eeded t o predict t he effectiveness o f c arbonate a cidizing processes.

•

Schechter and Gidley

Pore Level Model32

used a model of pore growth and collision to study the natural tendency

for wormholes to form when r eaction i s mass t ransfer l imited. I n t his model, t he change i n the

cross-sectional area of a pore is expressed as:

= 1− ………………………………………………………………2.34where is the pore cross-sectional area, is the time, and is a pore growth function that doesdepend on t ime. If > 0 , s maller pores gr ow faster than l arger p ores a nd wormhole cannot

form; when < 0 , larger pores grow faster than smaller pores and wormhole will develop. They


34/147


showed that if = 1 2⁄ , surface reaction rate controls the overall reaction rate, and if = −1,diffusion controls the overall reaction rate. This model does not give a complete picture of the

wormholing process because it does not include the effect of fluid loss from the pores.

• Mechanistic Models

Hung et al. 56

considered fluid loss in their cylindrical model of the wormhole growth, and also

took i nto a ccount a number o f factors, i ncluding t he contributions of both a cid diffusion a nd

convection resulting from fluid loss to the walls of the wormhole where the acid reacts. They

found t hat the w ormhole velocity increases linearly with the i njection rate i nto the w ormhole,

implying that t he v olume of a cid needed to pr opagate a wormhole a gi ven distance i s

independent of injection rate. The model also predicts that wormhole velocity will be constantly

decreasing because t he a cid flux t o t he end of t he wormhole i s de creasing a s t he wormhole

length increases ( grows). The w ormhole ve locity is e xpressed in t erms o f the acid ca pacity

number (which had been defined for a fast-reacting mineral in Eq. 2.29) as:= ∅ ……………………………………………….………..2.35

where and are the flux and a cid concentration ( mass fraction), t he subscript o refers to the

initial condition, the subscript e refers to conditions evaluated at the end or tip of the wormhole,

and L is the length of the wormhole.

• Network Models

Hofefner and Fogler 55

presented n etwork m odels in which the porous m edium i s approximated

as a collection of i nterconnected capillaries. T o model wormhole b ehavior, t he a cidconcentration i n each capillary is calculated a nd the radii of the capillaries are i ncreased as

dissolution occurs. These models appear t o give t he best r epresentation of wormhole behavior

over a wide range of conditions, but they are difficult to generalize for treatment design.


35/147


• Stochastic Models

Daccord et al. 57

= ∅ 2 3⁄ ………………………………………………..……………2.36

recognized t he importance of propagating the wormhole to the fullest extent

possible; hence, ba sed o n laboratory experiments they p roposed a m odel of w ormhole

propagation that c onsidered the s tructures o f w ormhole ob served w hen f luid loss-limited

behavior occurs. Daccord et al. ’s model for the rate o f wormhole propagation in l inear systems

is:

where a is a constant determined experimentally, D is the molecular diffusion coefficient, A is

the cr oss-sectional area o f t he wormhole and is the injection rate. This model considers the

influence of acid diffusion but does not take into account fluid loss; therefore, this equation does

not indicate a plateau value as the wormhole lengthens. Thus, the equation is only applicable to

short wormholes where fluid loss i s not a f actor, and it should not be u sed for the prediction of

wormhole penetration l ength. For a c onstant i njection r ate, t he skin e ffect pr edicted b y t he

Daccord et al. ’s model is:

If there is a damaged zone,

= − + ℎ −2 3⁄ ℎ−1 3⁄1

⁄ − ……………………..……….2.37If there is no damaged zone or if the wormholes penetrated beyond the damaged region,

= − 1 + ℎ−2 3⁄ ℎ−1 3⁄ 1 ⁄ ………………………..………………….2.38

where b is a constant, ex perimentally reported t o be 1.5 × 10 −5 in S I units, is th e fractaldimension equal to about 1.6 and is the cumulative volume of acid injected. Eq. 2.37 and 2.38

do not apply if the injection rate is changing during the treatment because of the dependence of

the wormhole velocity on injection rate in the Daccord et al. ’s model.


36/147


Pichler et al .58

presented a stochastic m odel of wormhole growth b ased on diffusion-limited

kinetics and included pe rmeability anisotropy, permeability heterogeneity and na tural fractures.

This model predicts the branched wormhole structures found in carbonate acidizing.

• Volumetric Model

Economides et al. 59

proposed a n empirical volumetric model t o predict t he volume of a cid

required t o pr opagate wormholes a gi ven distance, a ssuming t hat a cid will di ssolve a c ertain

fraction of the r ock penetrated. F or r adial flow, the r adius of wormhole pe netration ℎ isexpressed as:

ℎ= 2 + ℎ …….……………………….…………….…..……2.39where , the w ormholing e fficiency, is de fined as the f raction of r ock d issolved in the r egion

penetrated by the acid, mathematically expressed as:

= ……………………………….……………………………2.40where is the number of pore volumes of acid injected at the time of wormhole breakthrough

at the end of the core. The skin effect during injection is expressed as:

If there is a damaged zone,

= − 2 2 + 2 ℎ − ……………………………….…...2.41If there is no damaged zone or if the wormholes penetrated beyond the damaged region,

= −12 1 + 2 ℎ ……………………………………………..………2.42


37/147


• Generalized Carbonate Dissolution Model

In or der t o p resented a generalized d escription o f carbonate d issolution process which a ccount

for the various transport and reaction processes that may influence the rate of dissolution, Fredd

and Fogler 60

modeled the overall carbonate dissolution mechanism as three sequential processes

of the mass transfer of reactants to the surface, reversible surface reactions and mass transfer of

products a way from t he surface. In t he generalized m odel, t he rate of reactant c onsumption can then be expressed as:

= − 1− ……………………………………………………..…2.43Where is the s toichiometric ratio of reactants consumed to pr oducts pr oduced, is th e

effective equilibrium constant, is the initial reactant concentration a nd is t he o verall

dissolution rate constant which depends on the sum of resistances in series, i.e.

=1+ 1

1

1+ 1 + 1 3

…………………………………………………………....2.44

K r is the effective surface reaction constant. K 1 and K 3

are the mass transfer coefficients for the

reactants a nd products, r espectively. Eq. 2 .43 and 2.44 can be u sed t o determine t he r ate of

carbonate dissolution in any flow geometry, provided that an appropriate expression for the rate

of mass transfer is available.

2.3 Acid Fracturing Models

The f ollowing e quations d escribed linear flow of a cid down a fracture, with fluid l eakoff a nd

acid diffusion to the fracture walls.

+ ( ) + − = 0 …………………………2.45


38/147


( , , = 0 ) = 0 ………………………………2.46

( = 0, , ) =

( ) ………………………….2.47

− − = (1 − ∅) ………...…….2.48where is the acid concentration, is the flux along the fracture, is the transverse flux due

to fluid loss, is an effective diffusion coefficient, is the injected acid concentration, isthe r eaction rate co nstant, is t he or der of the r eaction, a nd ∅ is porosity. Ben-Naceur a ndEconomides 61, Lo and Dean 62, and S ettari 63 provided complex numerical solutions t o t he a bove

equations considering c omplications s uch as t he temperature d istribution along the f racture,viscous fingering of low-viscosity acid through a vi scous pad, the e ffect of the acid on leak-off

behavior, a nd various fracture geometries. Neerode a nd Williams 64

also pr esented a solution t o

the a bove e quations by a ssuming a steady state, laminar flow of a N ewtonian fluid between

parallel plates with constant fluid loss flux along the fracture. They presented the solution for the

concentration p rofile as a f unction of t he leakoff P eclet n umber. At l ow Peclet n umbers,

diffusion controls a cid propagation, while a t hi gh P eclet numbers, fluid l oss i s t he c ontrolling

factor.

The conductivity ( ) of an acid fracture depends on a stochastic process. Nierode and Kruk 65

presented the following correlation for the acid fracture conductivity based on the ideal fracture

width ,

= 1 −2 ……………………………………………………….2.49where

1 = 1.47 × 10 7 2.47 ……………………………………………………2.50

and for

< 20,000 psi: 2 = (13.9 −1.3 ) × 10 −3 ………………………….2.51


39/147


> 20,000 psi: 2 = (13.9 −1.3 ) × 10 −3 ………………………....2.52In Eq. 2. 49 t hrough 2. 52, is the f racture closure s tress and is the r ock e mbedment

strength. The average ideal fracture width is defined as:

= 2(1 −∅)ℎ …………………………………………………………2.53

where is the volumetric dissolving power of the acid, is the total volume of acid injected, ℎ is t he fracture height, a nd is the f racture h alf-length. The conductivity varies a long t hefracture; hence Bennet 66

defined an average conductivity ( ��) that can be used to estimate the productivity of the acid fracture well.

�= 1 ∫ 0 …………………………………………….….2.54For lower values of Peclet number (< 3), this average overestimate the well productivity, hence

Ben-Naceur and Economides 67

presented a harmonic a verage which better a pproximates the

behavior of the fractured well as:

�= ∫ / 0 ……………………………………………………..2.55

Ben-Naceur and Economides 67

also presented a series of performance type curves for a cid-

fractured wells producing at a constant bottomhole flowing pressure of 500 psi.

2.4 Hydraulic Fracturing Models

Hydraulics fractures c an b e c lassified a ccording to one of three m odels: infinite conductivitymodel (assuming no pressure loss in the fracture), uniform flux model (assumes a slight pressure

gradient i n t he fracture), a nd finite c onductivity m odel (assumes co nstant a nd l imited

permeability i n the fracture f rom proppant crushing o r p oor pr oppant distribution). Every

hydraulic fracture i s characterized by i ts length, conductivity a nd r elated equivalent skin effect.


40/147


The fracture length, which is the conductive length and not the hydraulic length, is assumed to be

consisting of t wo e qual half-lengths, in e ach s ide of the w ell. Prats 68

provided p ressure

profiles in a fractured r eservoir as a function of t he f racture h alf-length and t he relativecapacity, a , which he defined as:

= 2 ………………………………………………..………………2.56

where is the r eservoir p ermeability, is t he fracture permeability, a nd is t he proppedfracture w idth. A rgawal et al. 69 and Cinco-Ley and Samaniego 70

introduced the dimensionless

fracture conductivity, which is defined as:

= .. ……………………………………………………..…….2.57The dimensionless fracture conductivity is related to the relative capacity by:

= 2

………………………………………………………….…...2.58

Prats68

́ = ́ ………………………………………………...…………2.59

showed t hat for a s teady-state f low, a fracture affects productivity t hrough t he

dimensionless equivalent (effective) wellbore r adius

́

which i s related t o the fracture h alf-

length or penetration by the dimensionless fracture conductivity .

where ́ is expressed in terms of the equivalent skin effect and the wellbore radius as:

́ = − …...................................................................................2.60For infinite conductivity fractures, Prats 68

showed that:

́ = 0.5 ……………………………………………….…………2.61


41/147


Cinco-Ley et al .71

integrated t his i nto a full description of r eservoir r esponse by i ncluding

transient f low and pseudoradial flow ( where t he pressure-depletion r egion >> but i s notaffected by e xternal boundaries). Cinco-Ley et al.’s descriptions presented in form of charts can

be used a s powerful reservoir engineering tools to assess p ossible post-fracture p roductivity

benefits from propped fracturing. The productivity index in the pseudosteady state flow regimeis expressed as: = 2 ℎ× 1ln 0.472 +0.5 ℎ + 0.5 + + …....................................2.62

= 1.6 , is t he optimum value of the dimensionless fracture conductivity for which the

productivity index is maximum.2.5 Literatures on Stimulation Candidate Selection

Several techniques for stimulation candidate selection exist in l iteratures a nd a lso in practice i n

the i ndustries. Stimulation jobs ha ve witnessed bot h successes and failures, and in some c ases

yield less than the expected result. Stimulation failure is usually due to poor candidate selection,

inaccurate treatment de sign or improper f ield pr ocedures 72. Nnanna et al. 73

cautioned t hatapplying t he b est t reatment d esign and field pr ocedures t o the wrong candidate w ill r esult i n a

failure, while a poor treatment design and good field procedures on the right candidate will also

result i n a failure. They added that t hough treatment design and field procedures are fairly well

understood, candidate selection has been approached in different ways by various operators and

service companies.

Nitters et al. 74

presented a structured a pproach t o stimulation candidate selection and treatment

design. They i solated t he r eal skin caused b y da mage ( the p ortion o f t he t otal skin t hat can be

removed by matrix treatment) from the total skin as follows:

= − + + + + ………..….2.63


42/147


where is the skin due to formation damage, is the total skin factor (Eq. 2.1), is

the skin resulting from limited perforation height, is the skin due to turbulent (non-Darcy)

flow, is t he skin due t o wellbore deviation, is the skin due to gravel packing, and

is the skin resulting from a small perforation. Nitters et al then suggested the ranking of

stimulation candidates based on the magnitude of the damage skin factor.

Jones 75 presented a nalytical r elationship which i s convenient t o estimate productivity

improvement achievable by skin removal. At equal pressure and also approximating ( ⁄ ) to7, Jones defined the ratio of rates before and after stimulation (the stimulation ratio, ) as:

= 21

= 7+ 17+ 2

…………………………………………………….2.64

where is flow rate, is the skin factor, and t he subscripts 1 an d 2 refer t o before and a fter

stimulation.

To properly interpret t he skin and therefore determine the appropriate r emedial action r equires

analysis of t he contributing factors. Nnanna and Ajienka 76 used the simplified approach for

determining the c ompletion s kin f actor as developed b y A l Qahtani a nd A l Shehri 77 in

combination w ith t he non-linear summation r elationship between the pseudoskins and the totalskin as demonstrated by Yildiz 78 to present a method for stimulation candidate selection. Nnanna

and Ajienka expressed the removable skin factor in the form presented by Lee 79

as:

= ℎℎ

( + + ) − …………………………………………2.65where + is the skin factor due to partial penetration and deviation, is the total skin

factor as d eternmined f rom a w ell t est. is t he perforation skin factor. h p is th e perforation

interval t hickness and h is the thickness of the oil sand. They used the stabilized inflow equation,

approximating the natural logarithm of t he ratio of drainage radius t o wellbore radius a s 8 , a nd

the cu t-off of O nyekonwu 80

to define a simplified R -factor which c an b e used for c andidate

selection. The factor is defined as:


43/147


= ℎℎ ∗ 8+ …………………….………............................................ 2.66

They concluded that if R

≥ 0.6, then the well is a good stimulation candidate in the Niger Delta.

Afolabi et al. 81

also presented candidate selection criterion that is based on minimum economic

reserve, productivity Index (PI) of less than 10bpd/psi, flow efficiency of less than 0.5 and the PI

decline rate that is greater than 30%.

Jennings 82

presented a methodology for candidate selection ba sed o n w ell c apacity a nd

concluded that well stimulation tr eatments in high-productivity wells a llow better r eservoir

management through sustained productivity and more uniform reservoir depletion throughout thelife of the well, and that good wells make better candidates for matrix stimulation.

Kartoatmodjo et al. 83 presented a risk-based c andidate selection a pproach by c onsidering the

range of probability of all the possible outcomes in a stimulation campaign using Monte Carlo

simulation technique. They concluded that decision risk analysis i s a valuable tool for candidate

selection. Stimulation c andidate selection c ampaign ba sed on highest expected ga in a nd/or

lowest expected risk has also been reported.

84

The published literatures reviewed did not consider a detailed and efficient optimization process

for s timulation candidate selection, especially i n t he N iger D elta, a nd hence t he n eed f or this

study.


44/147


Chapter Three

Methodology

This methodology is a modification of t he modular approach to stimulation decisions presented

by S inson et al .85

The m odels pr esented are de rived f rom i ndustry-wide a ccepted well

stimulation procedures and techniques.

3.1 Well Screening Technique

It i s a ssumed that from well t est da ta, t he well pr oblem could b e diagnosed a nd then matched

with either of acidizing, gravel-packing or re-completion. It is also assumed that all wells can be

acidized, recompleted or gravel-packed successfully if necessary.

Diagnose each well pr oblem. For w ells w ith s kin va lues s howing formation da mage problems,

acidizing i s t he r ecommended t reatment. Wells with m echanical pr oblems such a s pa rtially or

totally plugged perforations, insufficient perforation density, low depth of perforation or water

production, r e-completion i s r ecommended. I f t he pr oblem i s sand production, t hen gravel

packing i s r ecommended. A s imple screening module flow chart f or t his s ection i s s hown i n

Appendix A.

3.2 Design of Stimulation Treatment Models

The treatment m odels p resented in t his s ection are to b e used f or the s timulation t reatment

design. The choice of which model to use is dependent on the nature of well problem diagnosed

and the result of the screening module.

3.2.1 Matrix Acidizing Design Model

The extent to which acid will penetrate a rock is dependent on both the rock properties and the

local acid reaction rate. The reaction rate in turn depends on matrix properties and other variableslike temperature, pressure, and composition of the reacting fluids.


45/147


The m odel p resented here i s a c ombination o f t he a pproaches presented b y S chechter a nd

Gidley 32 and E conomides a nd N olte 86

. I n t his model, pores ar e assumed to be i nterconnected

such that the acid can flow through the matrix under the influence of a pressure gradient.

The Niger Delta formation is c hiefly made up of sandstone. S andstone formations are of ten

treated with a mixture of hydrochloric a cid (HCl) and hydrofluoric a cid ( HF) commonly called

mud acids. T he t reatment is done at l ow injection rate to prevent fracturing. The mud acid,

chosen because of its ability to dissolve the clay found in drilling mud, also will react with most

constituent of naturally occurring sandstones, including silica, feldspar, and calcareous materials.

The following steps are presented for sandstone acidizing design:

• Determine the present fracture gradient for the well. If the instantaneous shut-in

pressure value is not available, use the following equation to calculate the fracture

gradient:

= + ( −) …………………………………………….….3.1where:

= fracture gradient, psi/ft

= 0.33 to 0.50 psi/ft

= overburden gradient (1.0 psi/ft for formation depth less than 10,000 ft or 1.2 psi/ft

for depth greater than 10,000 ft )

= reservoir pressure, psi

= depth of formation, ft

• Predict the maximum possible injection rate that does not fracture the formation

using:

, = 4.917×10 −6 ℎ� × −∆ −

+ …………………………………….3.2

where:

, = injection rate, bbl/min


46/147


= effective permeability of the un

benson oghenovo ugbenyen

Documents