The effect of perforation technology on the productivity

of hydrocarbon wells

An MS thesis

by

Makok Ghafoor Darwesh

Submitted to the Petroleum and Natural Gas Institute of

University of Miskolc

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in Petroleum Engineering

May 2014

i

DEDICATION

This thesis is gratefully dedicated to my family, especially to my parents. Without their

continuous support and love, my work would never have been completed.

ii

ACKNOWLEDGEMENTS

I thank God for always being with me and for everything that he has been doing for me.

I would like to express my deepest and profound gratitude to my supervisor, Dr.Tibor Bodi,

for his continuous support and patience during my work. His guidance and encouragement

really helped to complete this project; it has been a great experience.

I am very thankful to Dr.Tibor Szabo for his guidance, advice and support during this thesis.

His contribution to this project was a key part of it.

I am particularly grateful to the Kalegran MOL Company in Kurdistan, for providing my

scholarship and for a lot help to finish my MSc successfully.

Special thanks to the Ministry of Natural Resources in Erbil for giving me the opportunity of

study in Hungary in order to finish my MSc.

I would like to thank all of my friends who helped me during this experimental work,

especially Muhammad A. Ali and Blend Nader.

iii

Abstract

This study evaluates the impacts of perforation parameters on the productivity of

hydrocarbon wells. The damage and perforation parameters; formation penetration, hole size,

number of shots and the angel between holes have significant impact on pressure drop near a

well and therefore on production .

The theoretical background and the steps of perforation skin effect depending on Karakas,

Tariq, Thompson and McLeod were explained. The inflow performance relation (IPR)

describes the effect of the reservoir on well performance. Empirical IPR equations were

suggested for undersaturated and saturated oil systems. They were used to illustrate how

reservoir inflow is integrated with the composite flow system making up the production unit.

Darcy’s law sets the foundation for all calculations of flow in porous media. It involves the

IPR equations of an ideal well and their derivatives. The ideal well model and the inflow

equations are then adjusted to account for real conditions in oil and gas wells by considering

the effect of pressure conditions at the outer boundary of the drainage area and flow

restrictions existing at the entry or near an actual wellbore.

The most common techniques of perforating gun were evaluated by using different

penetrating gun performances.

The economic value of an oil or gas well depends on the connection between the wellbore and

the formation. Perforation length is the most important parameter and performance improves

with increasing length. Initially, even a small increase in length gives a significant

improvement. Perforation density is an important parameter, but beyond an optimum number

of shots per foot is little gain in productivity ratio. This result will lead to a saving of cost,

since a higher shot density is generally used by industry.

The phasing of perforation influences the performance. A phasing of 60° with 6 shots per foot

in the same plane or along a spiral gives a significant advantage over a phasing of 90° with 4

shots per foot, and a phasing of 90° gives a significant advantage over a phasing of 0° with 4

shots per foot, this improvement increases with an increase in perforation length and radius.

iv

Table of Contents

DEDICATION ........................................................................................................................................ i

ACKNOWLEDGEMENTS .................................................................................................................. ii

Abstract ................................................................................................................................................. iii

List of Figures ....................................................................................................................................... vi

List of Tables ........................................................................................................................................ vii

1 Review of the Fundamentals of Perforation Technology ................................................................ 1

1.1 Review of Past and Newest Perforation Methods ......................................................................... 1

1.2 Methods of Perforation .................................................................................................................. 3

1.2.1 Wireline-Conveyed Casing Gun ............................................................................................. 3

1.2.2 Wireline-Conveyed Through Tubing Gun ............................................................................. 4

1.2.3 Tubing Conveyed Gun ........................................................................................................... 4

1.3 Basics of Perforation ..................................................................................................................... 5

1.4 How to start Perforation Reservoir Interactions ............................................................................ 8

1.5 Perforation Fragments and Role of Underbalanced or Overbalanced Perforation ...................... 10

1.6 Extreme Overbalanced Perforating and Formed (EOB) .............................................................. 11

1.7 Rationale behind (EOP) ............................................................................................................... 12

1.8 Perforation for Stimulation .......................................................................................................... 14

2 Well Performance from the point of view of reservoir .............................................................. 16

2.1 Flow in direction of the Borehole and Fundamental Concepts ................................................... 16

2.1.1 Drainage Radius, re ............................................................................................................... 16

2.1.2 Average Reservoir Pressure, Pr ............................................................................................ 17

2.1.3 Flowing Downhole pressure, pwf .......................................................................................... 17

2.1.4 Pressure Drawdown .............................................................................................................. 17

2.2 Steady-state radial flow for ideal liquids and the idea of Productivity Index ............................. 18

2.3 Skin Effect ................................................................................................................................... 23

2.4 Cased and perforated well performance ...................................................................................... 27

3 Limited Flow into the Borehole .................................................................................................... 31

3.1 Impact of Damage of Formation on the Productiveness of a Perforated Well ............................ 31

3.2 Skin Factor and Associated Approaches ..................................................................................... 31

3.3 Impacts of Perforation Parameters on Productiveness of Well ................................................... 33

3.4 Combined Skin Factor ................................................................................................................. 46

4 Calculation Results ......................................................................................................................... 49

4.1 General Data of the Wells ........................................................................................................... 49

v

4.2 Basic Data Collected in Well 1: ................................................................................................. 49

4.3 Basic Data Collected in Well 2: ................................................................................................. 50

4.4 Calculation and Final Results of the Effect of Perforation Technology on the Productivity of Hydrocarbon Wells ............................................................................................................................ 51

4.4.1 Calculation of the Penetration Depth (L P): ........................................................................ 53

4.4.2 Calculation of the Perforation Skin Effect by using Karakas and Tariq Method: .............. 54

4.4.3 Calculation of the Effect of a Crushed Zone Skin Factor (Sdp): ......................................... 55

4.4.4 Calculation of the Composite Skin Factor (S): ................................................................... 56

4.5 The Effect and the Evaluation of Perforating Parameters on Well Productivity According to Porous Oil Reservoir ......................................................................................................................... 57

4.5.1 Effects of perforation penetration, phasing, density and raduis: ......................................... 57

4.6 The Evaluation of Different Perforation Methods and High Shot Density Guns ........................ 61

4.6.1 Basic Data Collected in Well 3 ........................................................................................... 61

4.6.2 Basic Data Collected in Well 4 : .......................................................................................... 62

4.7 Comparison of the best high Shot Density Guns for each perforation method ........................... 66

5 CONCLUSIONS AND RECOMMENDATIONS ......................................................................... 68

5.1 CONCLUSIONS ....................................................................................................................... 68

5.2 Recommendations for further work ........................................................................................... 69

6 APPENDICES .................................................................................................................................. 70

APPENDIX A ................................................................................................................................... 70

APPENDIX B.................................................................................................................................... 71

APPENDIX C.................................................................................................................................... 72

REFERENCES .................................................................................................................................... 73

vi

List of Figures

Figure1: The development of perforation technology as applied in the oil field ................................ 2

Figure 1.1: The three kinds of perforation guns ...................................................................................... 4

Figure 1.2: Shaped charge outlined ......................................................................................................... 5

Figure 1.3: Perforation gun and sequence of detonation ........................................................................ 6

Figure 1.4: Usual geometry of a perforation. Sources of pressure drop in a perforated system ............. 7

Figure 1.5: Over and Underbalanced perforating ................................................................................. 11

Figure 1.6: Extreme overbalances perforating. ..................................................................................... 13

Figure 1.7: Extreme overbalance surging. ............................................................................................. 14

Figure 2: Pressure profile surrounding a well in the formation .......................................................... 17

Figure 2.1: A radial flow model ........................................................................................................... 19

Figure 2.2: Variation of undersaturated oil pressure ............................................................................ 22

Figure 2.3: Real pressure profile of a well with changed near-borehole area ...................................... 24

Figure 2.4: Perforated wellbore geometry ............................................................................................ 27

Figure 3: Real IPR vs. IPR derived from the perfect well model . ..................................................... 33

Figure 3.1: Skin factors for perforation at a phasing of 0° . .................................................................. 35

Figure 3.2: Skin factors for perforation at a phasing of 180° ............................................................... 36

Figure 3.3: Typical API test assembly for the assessment of depth of perforation ............................. 38

Figure 3.4: Adjustment to typical Berea depth of penetration proposed by Saucier and Lands .......... 39

Figure 3.5: Flow tests for the characterization of impact of perforation .............................................. 41

Figure 3.6: Assessment of smashed area permeability compared to permeability formation .............. 42

Figure 3.7: Perforation and backflush in the API test .......................................................................... 43

Figure 3.8: Effectiveness of core flow vs. backflush pressure. ............................................................. 44

Figure 3.9: Perforation model by McLeod. ........................................................................................... 45

Figure 3.10: Simplified combined skin factor model ............................................................................ 48

Figure 4.1: Perforation depth vs. skin factor (well no.1) .................................................................... 58

Figure 4.2: Perforation depth vs. skin factor (well no.2) ..................................................................... 58

Figure 4.3: Perforation depth vs. flow rate (well no.1) ....................................................................... 59

Figure 4.4: Perforation depth vs. flow rate (well no.2) ....................................................................... 59

Figure 4.5: Skin factor vs. flow rate (well no.1).................................................................................. 60

Figure 4.6: Skin factor vs. flow rate (well no.2).................................................................................. 60

Figure 4.7: Flow rate vs. perforation depth through phasing of 60° .................................................. 65

Figure 4.8: Flow rate vs. perforation depth through phasing of 90° ................................................... 65

Figure 4.9: Flow rate vs. perforation depth through phasing of 0° ..................................................... 66

Figure4.10: Compare the guns according to their performances ......................................................... 67

vii

List of Tables

Table 1: Four main geometry factors for the three types of completion ................................................ 9

Table 2: Properties of damaged, incited, and unchanged (perfect) wells ............................................. 27

Table 2.1: Phasing dependence of αθ ................................................................................................. 28

Table 2.2: Coefficients of vertical skin correlation ............................................................................... 29

Table 2.3: The values of c1 and c2 constants ......................................................................................... 30

Table 4.1: Basic data collected in well 1 ............................................................................................... 49

Table 4.2: Basic data collected in well 2. .............................................................................................. 50

Table 4.3: Four different kinds of high shot density guns .................................................................... 52

Table 4.4: Berea compressive strength and cement sheath with casing thickness ................................ 53

Table 4.5: Perforation depth .................................................................................................................. 54

Table 4.6: Perforation skin effect .......................................................................................................... 55

Table 4.7: Raduis of smashed area ........................................................................................................ 55

Table 4.8: Crushed zone skin factor ..................................................................................................... 56

Table 4.9: Composite skin factor and damaged zone skin factor .......................................................... 56

Table 4.10: Flow rate and composite skin factor.................................................................................. 57

Table 4.11: Basic data collected in well 3. ........................................................................................... 61

Table 4.12: Basic data collected in well 4 ............................................................................................ 62

Table 4.13: The different flow rate and perforation depth for different wells . ................................... 64

Table 4.14: Compare the best high shot density guns for each perforation methods .......................... 66

1

1 Review of the Fundamentals of Perforation Technology

1.1 Review of Past and Newest Perforation Methods

The method of perforation is crucial in achieving the subsurface layers and borehole,

which is finished by cemented casing. The most widespread well-completion method applied

in oil fields is perforation. The main goal of the perforation methods is to establish channels

of flow through the casing so that the fluid from the formation can enter. The perforation

occurs often in separated several intervals in the length of the borehole.

At an early stage, oil wells had low depth, simple boreholes for which no metal casing was

necessary. These wells usually had an open hole or shot-hole (barefoot) finishing. At times

shot charges were applied in order to incite the in-flow of hydrocarbons in the borehole. With

the advent of increasing depths of wells and as reservoir circumstances getting harsher, the

casing with perforation finishing evolved into standard and integral part of an oil field

development. At the time, just like today, the duty of engineers was to select the best method

of providing holes in the metal casing so that hydrocarbons can enter the well.

In the beginning of 1900s, mechanical methods were incorporated for punching, among others

the single-knife casing ripper, which was based on a rotating mechanical blade to create a

perforation in the casing. Projectile perforation technology was implemented in the middle of

1920s.

A patent was created for bullet perforation in 1926, which was adopted in many places by the

1930s. In a bullet perforation apparatus the bullet was fuelled by a propellant to form holes

through the casing, cement, and formation. The apparent disadvantage was the placement of

the bullet or projectile in the perforation space, and this reduced the entry of formation fluid in

the borehole. Further disadvantage was that the depth of penetration attained by bullet

perforation was rather small, generally just the depth of some inches. Bullet perforators are

rarely used today except in cases where uniform casing hole size is required for utilizing ball

sealers for acid diversion.

The first large-scale perforation apparatus was the bullet gun, which was first implemented in

1932. In this technology, a hardened steel-bullet was shot through a gun with an extremely

short barrel. The cement sheath or casing underwent low damage due to the developed

perforations; however, the depth of penetration depths reached was rather small.

Shaped charges or jet perforators were made of use in the field of oil industry in the last years

of 1940s. The shape and use of the charges relied on the same fundamentals just as the

bazooka technology which penetrated armored tanks in World War II. These days, shaped

2

charges make up the global share of over 95% of the cased and perforated completions.

The lined, shaped-charge perforator obsoleted this simple technology were in the last years of

1940s, called also jet perforator or jet charge in the oil industry. Unique through-tubing gun

systems (small OD hollow steel carriers and expendable strip guns) were created in the 50s,

which meant an edge over the casing gun technology as this latter was carried out in an

overbalanced state and enabled the user to perform the completion as well as create a

Christmas tree for well control and afterwards reach an underbalance before the perforation.

In 1970, the company Vann Tool Co., today Vann Systems, was the first to create and operate

as well as market successfully a tubing-conveyed perforating system (TCP) and it was this

company that remained at the edge of incorporating this technology.

In October 1985, Halliburton acquired Vann Systems and has still been the forerunner in

industrial R&D (research and development), and implementation of pioneer technologies in

the oil industry.

In order to achieve production increase, a new method was applied, called Extreme

Overbalance Perforation (EOP). Handren et al. 1993 stated that stress exerted as an effect of

jet entering the rock develops fractures around the perforation wall. This method is based on

this phenomenon of establishing pressure so that the fractures developed will increase in their

size.

Another kind of shaped charge was implemented by Langan, T. et al. in 2007 to the oil

industry. This type of shaped charge creates a subsequent reaction right after its use where an

exothermic reaction takes place incited by the liner metallurgic properties, leading to a rise in

temperature and pressure in the perforation tunnels. Due to the pressure rise, the liner debris

and fragmented rock is driven out to the borehole. This technology is said to be suitable for

ensuring clean tunnels, no matter the pressure difference circumstances.

Figure1: The development of perforation technology as applied in the oil field

(Roscoe, B and Lenn, C et al. 1996)

3

In the following years numerous perforation systems were elaborated for the use in a number

of specific fields. Furthermore, research aimed at understanding the basic phenomena taking

place from a physics aspect of perforation. These days advanced perforating gun systems with

a proper configuration shaped explosive charges and control and adjust the right perforating

depth can be used on wireline, tubing, or coiled tubing. Perforation guns are conceived for the

desired arrangement of perforations in the selected segment of the borehole, with various

sizes and methods.

1.2 Methods of Perforation

The method must be selected based on a balance of various factors:

� Restraints in well:

� Reservoir pressure (standard or elevated pressure).

� Effluents: whether oil, gas, water, with or with no H2S.

� Indication if plugging was used beforehand.

� Thickness, porosity, permeability and homogeneity properties of reservoir.

� Position of casing and the cementing operation.

� Whether there is a risk of sand entry.

� If it is a production or injection well.

� Safety aspects.

� As well as the most favorable perforation circumstances (that are not necessarily

interchangeable):

� Underbalanced shot (1 to 2.5 MPa in case of an oil well, higher in case of a gas well).

� Not contaminated fluid in the well.

� Perforator with high diameter with high power charges.

� Minimum two directions of shot.

� Removal after perforation clearing following shooting in the shortest time frame.

In the following the three most applied fundamental techniques:

1.2.1 Wireline-Conveyed Casing Gun

In this case a high-diameter gun is let through the casing suspended on an electrical

wireline, perforating with pressure overbalance in which the fluid in the well forms a pressure

differential in direction of the formation, thereby providing that the well does not effuse right

after the perforation. This activity is carried out using a drilling rig on the site and controlled

by full blowout preventer (BOP) protection.

4

1.2.2 Wireline-Conveyed Through Tubing Gun

In this case a gun with a low diameter is let through the Christmas tree and tubing string

after that the tubing is lowered and the packer is settled above the segment for the perforation.

The gun is normally operated under underbalanced conditions, in which the borehole fluid has

an underpressure compared to the formation pressure, so that right after perforation the

formation starts the production.

1.2.3 Tubing Conveyed Gun

This is where a gun with high diameter is fitted on a tail pipe at the tubing bottom and is

let along with the tubings. Following the setting up the Christmas tree and packer settlement,

the gun is fired by dropping a detonation bar, where the conditions are can be either under- or

overbalanced. The gun itself is left suspended or let in the rat hole after the perforation.

Figure 1.1: The three kinds of perforation guns (Prentice et al. 1991)

Figure 1.1 illustrates the three kinds of perforation guns. Every gun has an edge over the

others, yet it appears that the industry is skewed towards the concept that underbalanced

perforation is clearly more favorable from the aspect of production of well and perforation

flow abundance (Bell 1984, 1985), therefore the through tubing and tubing conveyed guns are

used in an increasing rate. Casing guns with high diameter with deeper penetration charges

yield more effectiveness than through-tubing guns with smaller size, the penetration produced

thereof can be the double compared to the latter. The shot phasing (meaning how the shots are

5

arranged in an angled pattern) is optimum in a 90° helix and the other extreme is 0°, which is

the least favorable option for the majority of through tubing guns.

Wireline conveyed casing guns have two drawbacks namely:

� The overbalanced condition leads typically to skin damage as borehole fluid intrudes

the formation.

� It is necessary to kill the perforated well for letting through the tubings, thereby taking

out the Blow-Out Preventer and installing the Christmas tree.

1.3 Basics of Perforation

The primary goal of up-to-date perforation methods is to create a connection of fluids

between the cased borehole and reservoir, where the perforation guns are the means of

establishing the connection path. Formerly, bullet perforation was mostly preferred to form

holes on the casing and cemented parts; this method clogs the extremity of perforation tunnels

leading thereby to limited flow conditions. Consequently an alternative, shaped charges

shown in Figure 1.2 were conceived for enhancing perforation methods and widespread these

days.

Figure 1.2: Shaped charge outlined

In order to connect perforation guns in modern applications, a wireline or coiled tubings are

made of use. A gun system with shaped charges can be seen in Figure 1.3, presenting the key

system parts and the sequence of detonation. The power released from the detonation is

guided by the conical case, also the charge liner performing a relevant role that is at these

locations where intense velocities occur so a jet of metal particles is generated.

6

The velocity of the pulse released is approx. 10000 m/s exerting thereby a pressure of 34 to

103 GPa (Bellarby, 2009). The elevated pressure misshapes the casing, breaks the cement

and formation, however, the borehole material is not damaged nor undergo vaporization in

this step but fragments are formed (liner material and destroyed rock pieces), which are to be

removed prior to proper operation of perforation tunnels.

Figure 1.3: Perforation gun and sequence of detonation (Economides et al. 1994)

The type of gun, characteristics of reservoir and stresses in formation determine the diameter

and length of the perforation tunnels, which have typically 0.6 and 1 cm in diameter and 15

and 30 cm in length (Economides et al. 1994).

There are a number of aspects that influence the well productiveness, for instance the flow

constraint (pressure drop) in the proximity of the borehole, which pressure drop is considered

in the so-called ‘skin factor’. It is well known that perforations do cause damage to formations

derived from destroyed rock surrounding the perforation tunnels and liner fragments that are

still in the tunnels. The scheme of a perforation of such nature can be seen in Figure 1.4. The

skin of perforation is mainly affected by three key factors such as; the geometry of

perforation, characteristics of formation and environment of perforation. Let us have a look at

this one-by-one:

7

� Shot density (number of shot tunnels per length unit), the depth of penetration and

phasing (that is the angle of perforations) and diameter of perforation tunnel determine

together the geometry of perforation.

� The geometrical factors should be accompanied by the properties of formation as the

length of perforation and extent of damage is influenced largely by the formation

characteristics and the existing stress state.

Figure 1.4: Usual geometry of a perforation. Sources of pressure drop in a perforated system (Bell et al .1995)

It is common knowledge that drilling and cementing activities lead to an area with decreased

permeability surrounding the borehole, whose origin is the mud and cement filtrate or soils

intrusion. This area with decreased permeability has a negative impact on the environment of

perforation, and this must be taken into account when planning the activities of perforation. It

is important that perforation tunnels are sufficiently long to detour this area so that production

and injection can be boosted.

The perforation is often performed in an underbalance state (static or dynamic) for clearing

the tunnels by means of the removal of liner fragments to the borehole and reducing the

destroyed rock around the perforations to a minimum. The majority of the liner fragments are

removed by a transient flow at a suitably underbalanced pressure so that the flow in stabilized

state at that point decreases step-by-step the damage of perforation. Note that the state of

underbalance is a prerequisite for this practical operation. A pressure that is not

underbalanced enough would cause improper clearing; furthermore a pressure of too much

8

underbalance could lead to mechanical damage of the formation and movement of fine

particles. The permeability of formation and properties of the reservoir fluids mostly

determine the effectiveness of this method, therefore the performance is restricted in narrow

and low quality rock formations.

1.4 How to start Perforation Reservoir Interactions

The perforation program that utilizes the properties of reservoir defines the flow

performance of perforated completion and stimulation success.

The program is composed of defining two key components:

� An adequate differential between pressures of the reservoir and borehole (in general,

underbalance is favored where the pressure of borehole is lower than that of reservoir

while the perforation is in progress).

� Selection of guns, which is important for the length of penetration tunnel, shot

phasing, shot density and entry hole of perforation.

In the case of the majority of formations, permeability is lower in vertical than in horizontal

direction. In these instances the production can be simply boosted by the application of guns

that have huge shot densities.

Fractures occurring naturally are typical in a number of reservoirs ensuring large efficient

permeability even in case the permeability of the matrix is reduced. Nevertheless, productivity

of perforations and fractures couples. To make efforts of crossing fractures, the length of

penetration is of utmost relevance with a phase angle second. The density of shots is tertiary

as fissures of planes and elevated density do not necessarily enlarge the contact area with the

fracture system in fractured formations, a standard gun necessitates 60° phasing and 5 SPF

(Shots per foot).

Another relevant aspect in term of geometry for perforation is the question of depth of

penetration of the perforation that if it surpasses the area damaged during drilling or

communicates with the existing fractures. The penetration of various shaped charges is

archived in surface tests and in stress tests with API target values. Length of perforation and

diameter calculations for estimations are performed in the penetration module under

downhole circumstances for configurations of gun, charge and casing sizes and the

penetration in multiple casing strings can also be calculated.

The productivity module includes the mentioned parameters for the purpose of assessment of

the simulated production level of the perforation completion. A further effect that can come

into play in the effectiveness of flow is the damage of formation typically taken into account

9

concerning skin, in the index of flow effectiveness in relation to characteristics from various

sources: flow confluence, borehole, and perforation damage.

One can talk about partial penetration where the length of the perforation is inferior to the

height of reservoir and the angle between the perforation and the stratum plane. The intention

is to make perforations that lower the skin to a minimum and consequently optimize flow

effectiveness. The damage to formation is brought about by intrusion of mud filtrate and

cement fluid loss to the formation, where an area in the proximity surrounding the borehole

arises having poorer effective permeability.

In case the perforation is stretched over the damaged area, it can decrease skin considerably

and boost productiveness but the same damaged area makes the effective tunnel length lower.

Perforation Geometry

Completion Type Consolidated Unconsolidated

Natural Stimulated Sand Control Shot

Density 1 or 2 2 2

Perforation Diameter

3 or 4 3 1

Perforation Phasing

3 or 4 1 3

Perforation Length

1 or 2 4 4

Perforation Geometry

Isotropic Permeability

Anisotropy Natural Fractures

Wellbore Damage Of Any

Cause Laminar

Shale Shot

Density 2 1 1 3 2

Perforation Diameter

4 3 4 4 4

Perforation Phasing

3 4 3 2 3

Perforation Length

1 2 2 1 1

Table1: Four main geometry factors for the three types of completion, showing 1 (highest) to 4 (lowest)

The optimized design includes an adequate adjustment between these factors presenting e.g.

natural completion perforation-related aspects. In case natural fractures can be observed,

phasing gets the upper hand over density to enhance connection between the fractures and

perforations.

10

1.5 Perforation Fragments and Role of Underbalanced or Overbalanced

Perforation

The detonative energy of a perforation forms a hole through an externally oriented

pressure, which breaks cement and rock. These undergo no devastation in this operation but

move into the perforation together with pieces of perforation component as is illustrated in

Figure 1.5. To enable production, these fragments composed of smashed as well as fracture

rock along with smaller share of charge segments must be taken out for perforation

(Behrmann et al. 1992).

The term overbalanced expresses that prior to perforation, the well is killed by means of a

high-density perforation fluid, and therefore the pressure at the bottomhole surpasses the

reservoir pressure. Under these circumstances the fluids in the borehole enter the perforation

in the shortest time, on which grounds it is favorable that clean fluids with no solids content

are applied in order to clog the perforation process. The cleaning step may take place once

production starts.

To prevent this damage, various techniques can be used. If the well is made to flow following

the perforation, drawdown emerges at all perforations, however once a few perforations are

released, drawdown drops at the rest of the perforations causing them not to cleaned. Just 10

to 25% of the perforations get typically freed to take part in the flow. In places where the

formation is not strong and sensitive to sand production, this phenomenon is not relevant as

the clogged perforations get unclogged with time and the formation undergoes a plastic

deformation as stresses rise.

To overcome clogged perforations is normally achieved by perforating in underbalanced

conditions in other words in the presence of a casing pressure lower than the reservoir

pressure. To reach the best underbalance several recommendations exist, for instance one of

the first ones was provided by King et al. (King et al. 1986) originated from data of a field

with 90 wells, mostly onshore in the United States or Canada .Whether the underbalance was

of proper nature or not was evaluated according to the subsequent acidizing contributed to

boosting productiveness by over 10%. The variation vs. permeability relies on the fact that a

sufficient perforation flow is required to elevate fragments where poor permeability

necessitates larger underbalance to attain the same lift velocity.

11

Figure 1.5: Over and Underbalanced perforating (Roscoe, B. and Lenn, C. et al. 1996)

Three conditions in a perforation tunnel that are perfected, namely pre-flow overbalance

perforation, post-flow overbalance and underbalanced perforation. The figure at the top shows

that a perforation tunnel is clogged without cleaning due to smashed rock and charge

fragments, underneath the case is presented where the flow has taken away the majority of

charge fragments yet, a part of the smashed area generated by the flow stays in position and

the third case is where an adequate underbalance has taken out all the charge fragments and

smashed rock pieces during perforation.

1.6 Extreme Overbalanced Perforating and Formed (EOB)

The perforation method allows for other simulation techniques as well and accordingly

omits the perforation breakdown methods applied earlier. In the EOB method the borehole is

applied an overpressure by compressible gases and small quantity of a liquid where the gases

have high intrinsic energy and as they expand, they fracture the formation and when this

occurs in a split second, they redirect the liquids to all segments. It is reckoned that the

elevated flow rate across rather tight fractures improves the conductivity in the vicinity of the

12

well by expanding the fractures beyond all formation damage due to drilling. It was Marathon

Oil Company that implemented lately proppants that are carried into the perforation assembly

into the flow path when the gun is fired. Most operation using EOB is conceived with a

minimum level of pressure of 0.12 psi per inch of real vertical depth and to obtain the best

results it is recommended that the highest pressure level with no risk of borehole integrity or

the safety of operations.

1.7 Rationale behind (EOP)

The forerunners of extreme overbalance perforation, Dees and Handren can be seen in

Figure 1.6 and 1.7, at Sun Company (today Oryx Energy Company) initialized research on

overbalance techniques as issues emerged in West-Texas fields when overbalance was

applied. In case the pressure in the reservoir is small or it is depleted, pressure differential can

be insufficient to perform cleaning in the perforation, but should permeability be small below

10 millidarcy (mD) presumably, the extent reliant on the pressure of reservoir or viscosity of

oil, the formation fluid may fail to flow violently enough to reach cleaning effects. Also, in

case the strength of rocks is little, the underbalance pressure differential can be sufficiently

high for efficient cleaning to be able to collapse the formation.

Inadequate killing of a well, this can happen as perforation can clog again in case the filter

cake cannot be removed during production. This EOB technique can resolve these issues

namely in EOP completions, the pressure in the tubings is raised before the gun is triggered

and afterwards let into the borehole by the gun detonation. At this moment due to the pressure

of borehole surmounting that of rock yield strength, perforation incites tiny fractures that do

not lead to obtaining fractures measurable to the length of height of traditional hydraulic

fractures but they are sufficient to carry the fractures over the area damaged by the intrusion

and beyond the tip of perforation, where EOP fractures are smaller in terms of length and

height. It is possible that they gain larger width and thereby larger conductivity per unit length

than hydraulic fracture. In the borehole the space over the liquid is occupied by compressible

gas, generally nitrogen or sometimes carbon-dioxide or air, respectively.

Then a pressure builds up in the gas column similarly to a pressed coil spring, the liquid is

seen as well to be compressed more. It happens on rare occasions that the liquid goes through

the gas as the latter with a pressure of 27500 kPa has a rather high density of 0.12 to 0.36 g

per cm3 and an elevated surface tension leading to a contact surface that blocks liquid through

the gas in the lesser diameter of tubings. As the gas surface pressure may attain or surpass 69

13

MPa, tubing conveyed perforation (TCP) guns are favored against wireline-conveyed ones as

they are easier to operate in high-pressure environments.

Through gun detonation, the liquid is pushed at extremely high flow rates by the expanding

gas and expelled into perforations. As the liquid close to a state in which it is impossible to

compress, it functions as a wedge resulting in the generation of fractures and unfolds the

effective borehole radius. Abrasion exerted by the liquid and – if any- contained proppant

with a flow velocity higher than 16 m3/min can scrub the formation and leading to tunnels of

steady flow.

Figure 1.6: Extreme overbalances perforating

The majority of processes are based on the version of the fundamental approach.

14

Figure 1.7: Extreme overbalance surging

This is carried out in wells that contain perforations usually right after the perforation process

or in a matter of few hours or days following the perforation. By and large, if the time frame

of applying the surge is short following the perforation, the surge will be more efficient. The

relation of time 1 and time 2 displays the liquid penetration in the rock and the spread of

facture vs. time.

1.8 Perforation for Stimulation

It is evidenced that low perforation design can result in insufficient stimulation

especially with processes and decreased polymer loads typical today. Above all, low-level

perforations lead to elevated risk of having screening due to higher crookedness, backward

pressure as well as the emergence of several fractures and obviously the optimum method for

perforation aimed at stimulation differs from non-stimulated wells. Considering that normally

a fracture implies propagation in a largely preferential direction, the best would be to arrange

the guns towards this direction of propagation. Behrmann and Nolte recommend a tolerance

±30° for this, however, these directions are in specific cases unknown or the well is possibly

15

has a deviation. In case the perforation occurs in an angle of 60° to 45° of phasing, the

majority of situations can be handled but this means that no proppant can be let in most of the

perforations or they may be insufficiently connected to the fracture. This means higher

relevance on proper (open) perforations but not necessarily entirely open and fully clean

perforations that is dynamic underbalance condition of perforation can be proper. Perforation

with extreme overbalance or propellant driven can also be a solution for the removal of

fragments from the entry hole. Provided that the fracture starts normally at the contact surface

of cement and rock, it is necessary that a suitable entry hole is available not to cause bridging,

however, the aim is not to possess a big hole charge. Big hole charges establish higher stress

cage surrounding the perforations and accordingly a crooked connection is developed from

the perforation to the fracture (Pongratz et al., 2007).

Big hole charges also include the risk that under downhole circumstances the length of

perforation tunnel does not reach the critical length and this is typical for the case where the

guns are not in a central position. Example for this is a reservoir at large depth, with low

permeability and high strength. If fracturing is performed for sand control (in other words frac

pack) that is a fully other situation where large hole charges are relevant and probably they

have suitable lengths in less hard rocks. For the stimulation of hard rocks (just on the contrary

to soft ones) the communication of borehole with the reservoir requires the presence of

perforations. The role of perforation is that it links the borehole to the fracture and the fracture

is communicated with the reservoir, which is crucial if the preferential plane of fracture

propagation is different from parallel to the borehole. The perforation of an elongated

segment under such conditions support several fractures and lead to low performance and too

early screening (Lestz et al., 2002), and as far as the high-angle fracturing is concerned

having an angle of the fracture (beyond 20°) to the borehole, a small perforation segment is

necessary where the chances for decreasing several fractures are higher as the segment is

getting smaller. Nevertheless, in this case a high-shot density or hydrojet perforation is meant

for creating a slot in the casing.

For several other methods, unique perforating approaches are necessary, for instance acidizing

by means of a constrained entry-perforation or ball sealer diversion needs some controlled

diameter holes where the ball sealer diversion can be promoted by application of high or side

perforation.

16

2 Well Performance from the point of view of reservoir

2.1 Flow in direction of the Borehole and Fundamental Concepts

The flow of reservoir fluid in direction of the borehole is generated by a pressure

gradient along the path of flow and/or gravity damage. It is the sandface that is crossed

through by the well and the formation that produces it is namely a cylindrical envelope in

which the reservoir is opened. If the well is maintained in a shut state, the sandface pressure is

the same as the reservoir pressure and as a result no intrusion takes place in the well. One can

notice that similarly to the flow in surface pipes that is solely generated once there are

different pressures at two places (pressure difference) and accordingly, a well starts

production in case the pressure at the sandface is lower than the reservoir pressure. In the

proximity of the well the particles of fluid starts maneuvering towards the lower pressure and

an early time frame passes a steady rate is reached, which is mostly regulated by the dominant

pressure at the sandface and also influenced by a great number of parameters, for instance

reservoir characteristics (permeability of rock, thickness of pay etc.), the properties of fluid

(its viscosity, density etc.) as well as effects of well completion (perforations, well damage).

The effects of well completion are constant in case of a specific well, if one takes a significant

time period into account where the production rate can be controlled by one mechanism,

namely downhole pressures. The adequate characterization of the well behavior needs the

clarification of downhole pressure and the relevant production rates leading to the function by

the name of Inflow Performance Relationship (IPR) gained normally by performing well tests.

2.1.1 Drainage Radius, re

If one takes a well with a steady production fluid rate producing from a homogeneous

formation that where the fluid particles surrounding the well stream in direction of the

sandface. Under ideal circumstances the drain zone e.g. the zone in which the fluid is flowing

to the well can be regarded as a circle, at the limit of which there is a lack of flow and

reservoir conditions are in a state of rest. The drainage radius re, represents the radius of the

circle and shows the effect of the farthest distance of the well in question on the reservoir

conditions at rest. This parameter is normally based on the well spacing, production rate,

geological structures and regional change in rock characteristics. The drain zone depends on

the location of well, production rate and flow-free external boundary that describe the

reservoir.

17

2.1.2 Average Reservoir Pressure, Pr

If we take a look at the formation pressure out of the drain zone of a well, its value is

identical to the undisturbed reservoir pressure that can normally be regarded as having a

stabilized value if considerable time frames are taken as a base. This is actually the pressure

that can be measured in a shut-in well as illustrated in Figure 2.

2.1.3 Flowing Downhole pressure, pwf

The pressure distribution in the well and in the proximity of a production well is plotted

in Figure 2 where the average reservoir pressure Pr, is common under shut-in circumstances

and it can be measured in the well as SBHP. Following the start of flow, the drop of downhole

pressure occurs and the dashed lines show the pressure profile at average times. In case of a

steady-state, the production of the well runs with a steady state of liquid and the downhole

pressure achieves a steady value that is pwf, whose pressure profile in continuous line can be

seen in the figure below.

Figure 2: Pressure profile surrounding a well in the formation (Takacs et al. 2012)

2.1.4 Pressure Drawdown

The pressure drawdown describes the deviation of static downhole pressure from the

flowing one and which pressure drawdown bring about the flow of formation fluids to the

well, in addition, influences most the production rate of a specific well.

18

2.2 Steady-state radial flow for ideal liquids and the idea of Productivity Index

To describe best the in-flow efficiency of oil wells in a simplistic way, the productivity

index, PI can be used, assuming the below simplifications:

• There is a radial flow surrounding the well.

• The flowing liquid is only one phase.

• The permeability is distributed uniformly in the formation and,

• The saturation of liquid in the formation is reached.

It is Darcy's equation (Eq. 2.1) that can be applied to resolve concerning the production rate:

� =�.������������

���(� − ���) (2.1)

q = liquid rate, STB/d

k = effective permeability, mD

h = thickness of pay, ft

µ= viscosity of liquid, cP

B = volume factor of liquid, bbl/STB

re = drainage radius of well, ft

rw = radius of borehole, ft.

The majority of parameters of the right side are constants allowing the establishment of a sole

coefficient gathering them, which is called Productivity Index, PI:

(2.2)

Predicted by Darcy’s law, Equation 2.2 was created on the basis of observations from field

measurements.

J, index of productiveness, is touched upon in this chapter along with the properties that

define it.

A cylindrical/radial model of the ideal well entering a reservoir formation with a constant

thickness is presented in Figure 2.1. By an ideal well a well is meant that discharges the rock

with homogeneous permeability and that in any direction, with full penetration and is

connected with the production segment through a circular borehole where the flow occurs

solely radially while the external limit is a circle.

The flow-related Darcy’s law expressed in differential form via a circular envelope of

infinitesimally small thickness dr, at a random distance from the center line can be written as:

(2.3)

( )wfRo PPjq −=

dr

dp

µ

k

πrh

qBv

==2

19

Figure 2.1: A radial flow model (Michael Golan et al. 1991)

qB is the volumetric flow rate through the surface area of 2�rh under reservoir circumstances

where q is the surface volumetric rate and B represents the formation volume factor (FVF).

A pressure increase through an extremely thin radial wall part is expressed by the term dp/dr,

considering a constant rate the pressure decrease can be calculated via Equation 2.3, where it

is a prerequisite to isolate variables (meaning p and r, which are pressure and radius) and

integrate the borehole with a random radius:

(2.4)

Where

(2.5)

Equation 2.4 can be expressed as follows, resolved for pressure:

(2.6)

Equation 2.6 should be expressed in the following form in case field units are favored:

(2.7)

in terms of units: qo is expressed in STB/D, �o (cP), Bo (bbl/STB), k (mD), h (ft), p (Psia), and

r (ft). Equation 2.7 showing the pressure profile in terms of IPR, the external boundary

∫ ∫=p

p

r

rwf wr

drdp

Bq

kh

µπ2

( )∫ =r

r

w

w

rrrdr /ln/

( )wwf rrkh

Bqpp /ln

2πµ+=

( )wooo

wf r/rkh

Bµq.pp ln

2141+=

20

conditions are needed to be determined and solved for the pressure decrease rate where two

types of external circumstances are taken into account:

• External limit where pressure is constant showing the boundary on which the reservoir

pressure remains at the early value and which condition is generally brought about by

water intrusion from an immense aquifer or by water or gas entry in offsetting wells or

these phenomena coupled of these.

• Flow-free external limit appearing as a boundary through which no fluid penetrates the

drain zone and these boundaries usually derive from the pressure of offsetting

production well and/or geological barriers like a fault or pinch-out traps.

At a transitory pressure and rate of the well, following an early production time frame, the

external limit begins the influence of the production at the borehole and the flow reaches a

steady rate. Once it is stabilized, the external condition with a constant pressure boundary

achieved a so-called steady-state flow is taking place meaning that wells under these

circumstances have no depletion as the average reservoir pressure stay as was before that is

constant. Steady-state flow with flow-free limits is normally called pseudosteady-state flow.

Production in pseudosteady-state is a result of depletion and is mostly occurs when the

average pressure of a reservoir drops.

Considering again Equation 2.7, the IPR must be looked at as first for steady-state flow where

the external drainage limit is pe, which stays constant by the invasion of foreign fluids

originated from the surrounding the drain zone. By replacing pe and re by p and r in Equation

2.7 the following equation is yielded:

(2.8)

However, in reality the pressure (pe) at the external limit is hard to measure but its value does

not differ much from the early reservoir pressure if a robust aquifer is concerned and active

(meaning that permeability is large and field withdrawal rate is constrained).

The volumetric average pressure pR is a property frequently indicated in wells tests,

determined by the equation as follows:

(2.9)

( )( )weoo

wfeo /rrBµ.

ppkhq

ln2141

−=

∫

∫=

e

w

e

w

r

r

r

rR

dV

pdV

p

21

To perform calculus of material balances in reservoirs, average reservoir pressures can come

handy as was shown by (Craft and Hawkins et al. 1959), in concrete terms that the

volumetric average pressure is approx. 60 % of the drainage radius re in case of steady-state

flow and replacing 0.61re in the radial pressure profile (Equation 2.7) shall result in a nearby

approach of the volumetric average pressure PR:

(2.10)

Alternatively, expressed for rate,

(2.11)

However, as ln (0.61re/rw) =ln (re/rw)-0.5, one can define:

(2.12)

In the case of pseudosteady-state flow the volumetric average reservoir pressure can be found

at around at fifty percent of the distance from the outer radius:

(2.13)

Expressed for rate,

(2.14)

Alternatively, as ln (0.472) = - 0.75,

(2.15)

In practice it is indifferent if values of 0.5 or 0.75 is used in productiveness calculations but

the assumptions behind the steady as well as pseudosteady-state flows are very much

different. These differences matter in the reservoir performance in concrete terms steady-state

flow means that pR is independent of time and pseudosteady-state relies on the phenomenon

that pR drop takes place due to depletion. The majority of reservoirs experience mostly partial

( ) ( )weooo

wfRe rrkh

Bqpprrp /61.0ln

2.14161.0

µ+===

( )( )weoo

wfRo rrB

ppkhq

/61.0ln2.141 µ−

=

( )( )[ ]5.0/ln2.141 −−

=weoo

wfRo rrB

ppkhq

µ

( ) ( )weooo

wfRe rrkh

Bqpprrp /472.0ln

2.141472.0

µ+===

( )( )weoo

wfRo rrB

ppkhq

/472.0ln2.141 µ−

=

( )( )[ ]75.0/ln2.141 −−

=weoo

wfRo rrB

ppkhq

µ

22

drop and the industry uses standards for productiveness calculations assuming the

pseudosteady-state (Equation 2.15). Equation 2.15 is the same as 2.2 that is IPR continuous

line facilitating the determination of productiveness index J regarding reservoir parameters:

(2.2)

Where

(2.16)

Properties that vary with pressure are viscosity (�o) and formation volume factor (Bo) and in

specific cases the change in �oBo in case of unsaturated oil is low as is illustrated in Figure

2.2. However, viscosity varies (rises) with pressure, in contrast to oil formation volume factor,

which drops as pressure decreases. The coupled impact is that 1/�oBo drops nearly in a linear

fashion as pressure varies.

Figure 2.2

Figure 2.2: Variation of undersaturated oil pressure (Curtis H. Whiston et al. 1991)

In order to include the pressure variation of viscosity and FVF, they must be contained in the

pressure integral of the radial flow equation (Equation 2.4):

(2.17)

In case the equation is solved for oil rate qo:

( )wfRo ppJq −=

( )[ ]75.0/ln2.141 −=

weoo rrB

khJ

µ

w

e

r

r

p

p ooo r

rrdr

B

dp

q

kh e

w

e

wf

ln/2.141

== ∫∫ µ

23

(2.18)

The area of pressure integral is identical to the area under the curve if l/�Bo is depicted vs.

pressure (shaded zone in Figure 2.2) and as 1/�oBo is approached by a continuous line, this

area has the shape of a trapeze. If one considers the determination of (1/�oBo) as the value

having average pressure pav= (pe+pwf)/2, it can be readily revealed that:

(2.19)

In case of the pseudosteady-state, the derived intrusion equation is as follows:

(2.20)

Where (�oBo) av is assessed at pav= (pR+pwf)/2.

2.3 Skin Effect

Part 2.2 includes an infinitely large reservoir drained by an oil well and its radial

pressure profile written:

(2.21)

Various assumptions were used to simplify the equation namely the uniformity of the

reservoir thickness, the full penetration via the formation and that the flow has only a radial

direction. As far as permeability is concerned, it also includes that borehole is free from

clogging and has no casing.

In the last instance Darcy’s law is assumed and it is characteristic for the flow in the whole

drain zone. By means of these assumptions part 2.2 suggest that the pseudosteady-state flow

expressed in equation (Equation 2.15) has an ideal pressure decrease, pR-p’wf:

(2.22)

( ) ∫=e

wf

p

p ooweo B

dp

rr

khq

µ/ln2.141

( )avoo

wfep

p oo B

pp

B

dpe

wfµµ

−=∫

( )( ) ( )[ ]75.0/ln2.141 −

−=

weavoo

wfRo rrB

ppkhq

µ

( ) ( )wooo

wf rrkh

Bqprp /ln

2.141 µ+=

( )[ ]75.0/ln2.141, −=− we

ooowfR rr

kh

Bqpp

µ

24

Where, p’wf represents the flowing pressure of borehole in the case of a perfect well with a

production assuming the use of ideal radial model.

In the real world, the production of a well follows the ideal well model in small numbers. It is

usual that formation permeability in the proximity of the borehole is modified over the

drilling and completion operations, carried out using well pressure that overbalances the

formation pressure. The intrusion of solids and fluids from the borehole are expected to

impair the permeability in the vicinity of the borehole, also changed by cleanup and

incitement processes that were designed to take out the damaged part of the formation and

boost the well production. Flow constraints in the perforations and confluence to the

perforated segments lead to other differences from the perfect well, resulting in many cases to

a share of the net zone of pay.

Figure 2.3: Real pressure profile of a well with changed near-borehole area

(Michael- Golan et al. 1991)

The pressure deviation of the ideal flowing pressure in the borehole and real flowing pressure

p’wf -pwf, is an extra loss of pressure caused by the damage of formation, incitement of the

near-borehole area and further flow constraints at the entry of the well, which extra loss of

pressure is indicated as ∆ps or loss of pressure caused by ‘skin’. Skin factor S, which is

dimensionless, is proportional to ∆ps, and can be determined as:

(2.23)

In turn,

(2.24)

sooo

pBq

khs ∆=

µ2.141

skh

Bqp ooo

s

µ2.141=∆

25

After all p’wf - pwf = ∆ps, thus, putting equations 2.22 and 2.24 together results in the real loss

of pressure, pR-pwf concerning skin factor:

( )[ ]75.0/ln

2.141, −=− weooo

wfR rrkh

Bqpp

µ

Additionally,

kh

Bqpp ooo

wfwf

µ2.141, =−

Yielding,

(2.25)

Repositioning equation (2.24) and finding the solution for rate expresses:

(2.26)

The skin defines the nature of the flow in the vicinity of the borehole namely compared to a

perfect well where a positive value connotes impairment or constraint of flow and a negative

value implies incitement less constraint of flow. The extent of kin factor just like +4 or -1 is a

subjective value of a nonperfect impact on the intrusion performance of the well in question

where a +1 skin in a well can cause extra loss of pressure leading to not economical

production circumstances, while +10 skin can pose no problem to production with this extra

loss of pressure. The characterizations of the real impact in quantified terms the calculation of

the constant (141.2qo�oBo/kh) s, (alternatively an equal term for gas wells) is required

yielding loss of pressure caused by skin. This loss of pressure is related to pressure found in

other segments of the well (reservoir, tubings for example).

The result of impairment and incitement can be written for flow effectiveness Ef, which can

be more beneficial as it describes the quotient of the real to perfect rate in case of a specific

pressure drawdown.

(2.27)

For flowing pressure in a real and perfect borehole necessary for a production of a certain

level, flow effectiveness can be written as follows:

( )[ ]srrkh

Bqpp we

ooowfR +−=− 75.0/ln

2.141 µ

( )( )[ ]srrB

ppkhq

weoo

wfRo +−

−=

75.0/ln2.141 µ

ideal

actualF q

qE =

26

(2.28)

Regarding skin it can be readily presented that flow effectiveness has the following form:

(2.29)

In case of the majority of wells, the ln (re/rw) spans from 6.5 to 8.5 where an average of

ln (re/rw)-0.75 = 7.0 can be of help to express an approach in the definition of flow

effectiveness for skin:

(2.30)

What to use as a guideline to follow? Service provider companies frequently state that

nonperfect circumstances expressed for Rd, which term is basically the reciprocal of flow

effectiveness:

(2.31)

The apparent borehole radius rwa is an additional term to characterize nonperfect

circumstances of flow,

(2.32)

Resulting in the following expression, in case replacing rwa in Equation 2.26 for the radius of

borehole:

(2.33)

If the radius of apparent borehole is lesser than the real one, it means the damage of the well.

Furthermore, in contrast to the previous case, a larger apparent borehole to the real one

implies an incited (simulated) well, in which case the value approximates the drain radius re.

wfR

wfRF pp

ppE

−−

=,

( )( ) srr

rrE

we

weF +−

−=75.0/ln

75.0/ln

sEF +

=7

7

Fd ER /1=

swwa e r r −=

( )( )[ ]75.0/ln2.141 −−

=waeoo

wfRo rrB

ppkhq

µ

27

The characteristics of different wells are listed in Table 2, with references to skin, flow

effectiveness, ratio of damage as well as apparent radius of borehole.

In order to determine nonperfect flow circumstances, skin factor (also known as skin) is

definitely the utmost expression to be utilized by professionals and it can be derived from

steady well test measurements. Alternatively, if data from tests lack, a correlation can be used

for the estimation.

Status of

well

Quantifiable Effect of Nonideal Flow

∆ps s EF RD rwa

Damaged

Unaltered

Stimulated

∆ps>0

∆ps=0

∆ps<0

s>0

s=0

s<0

EF<1

EF=1

EF>1

RD>1

RD=1

RD<1

rwa<rw

rwa=rw

rwa>rw

Table 2: Properties of damaged, incited, and unchanged (perfect) wells

2.4 Cased and perforated well performance

The definition of general productiveness or skin of perforation requires the knowledge

of performance of one sole perforation (See Figure 1.4 in Section 1), which must be coupled

subsequently with the phasing and shots per length (ft) of manifold perforations, whose

graphic can be seen in Figure 2.4 containing the damage from drilling and smashed areas.

Figure 2.4: Perforated wellbore geometry (Halliburton et al. 2001)

28

Main geometry parameters defining the effectiveness of flow in a completion with perforated

flow, which includes four relevant parameters such as shot density, angle of phasing,

penetration of perforation in the formation and the diameter of perforation. The well

productiveness is also based on the smashed area, if the perforation reaches past the smashed

area and to what extent the smashed area and charge fragments are cleared from the tunnel.

It was Karakas and Tariq in 1988 who established a process for the calculation of skin

effect caused by perforations, which is a coupled effect including the plane-flow effect Sh, the

vertical confluence effect Sv, and the borehole effect Swb, therefore:

(2.34)

The pseudoskin factor Sh, is expressed as follows:

(2.35)

Where ���(�) is the effective radius of borehole and depends on the angle of phasing �:

When θ ≠ 0 (2.36)

Where, �� represents the length of the perforation and �� is a variable dependent on phasing

and can be gained from Table 2.1.

Perforation phasing αθ

0˚(360˚) 0.250

180˚ 0.500

120˚ 0.648

90˚ 0.726

60˚ 0.813

45˚ 0.860

Table 2.1

Table 2.1: Phasing dependence of αθ

wbvhp ssss ++=

)(ln ' θw

wh

r

rs =

04/)('

=

+=

θ

θ

when

)p

lw

αθ(r

lr

p

w

29

The vertical pseudoskin factor, SV, can be derived following the determination of specific

dimensionless variables:

(2.37)

Where h is the spacing between perforations and varies conversely with the shot density, in

addition �� and �� represent the horizontal and vertical permeabilities.

(2.38)

Where ���� represents the diameter of the perforation,

(2.39)

The vertical pseudoskin effect is afterwards can be expressed as follows:

(2.40)

Where a and b can be derived from:

(2.41)

(2.42)

Table 2.2 lists the values of a1, a2, b1, and b2 as they vary with the angle of phasing, θ.

Phasing a1 a2 b1 b2

0˚(360˚) -2.091 0.0453 5.1313 1.8672

180˚ -2.025 0.0943 3.0373 1.8115

120˚ -2.018 0.0634 1.6136 1.7770

90˚ -1.905 0.1038 1.5674 1.6935

60˚ -1.898 0.1023 1.3654 1.6490

45˚ -1.788 0.2398 1.1915 1.6392

Table 2.2

Table2.2: Coefficients of vertical skin correlation

v

h

pD k

k

l

hh =

)1(2 h

vperfpD k

k

h

rr +=

wp

wwD rl

rr

+=

bPD

bD

av rhs 110 −=

21 log araa pD +=

21 brbb pD ++=

30

After all, the borehole skin effect, swb, can be approached by;

(2.43)

The values of c1 and c2 can be gained from Table 2.3.

Perforation Phasing c1 c2

0˚(360˚) 1.6E-1 2.675

180˚ 2.6E-2 4.532

120˚ 6.6E-3 5.420

90˚ 1.9E-3 6.155

60˚ 3.0E-4 7.509

45˚ 4.6E-5 8.791

Table2.3: c1 and c2, constants

wDrcwb ecs 2

1=

31

3 Limited Flow into the Borehole

3.1 Impact of Damage of Formation on the Productiveness of a Perforated Well

The perforation process and drilling damage compose the compaction damage leading to

perforated completion generating damage of the formation, which is seemingly impacts the

productiveness of the well. In the jet penetration method the rock matrix around the

perforation tunnel is somewhat impaired, presented in (Figure 1.4, Section 1). The modified

zone also known as the damaged zone (smashed and compacted) is originated from highly

influencing pressure values taking place in the perforation process. Smashed and compacted

grains create the damaged zone having an about 6.3 mm to 0.012 mm layer surrounding the

perforation tunnel (Asadi and Preston, 1994; Pucknell and Behrmann, 1991). Following

this, Halleck et al. 1992, affirmed that this damaged area was not uniformly thick and their

thickness declines as deeper the perforation tunnel. It is evidenced by some sources that big

hole charges can bring about damaged area layers nearing 2.5 mm surrounding the perforation

tunnel, furthermore, it turned out by laboratory investigations that the extent of permeability

in the damaged area can be 10 to 20% of that of the formation in the vicinity (Bell et al.,

1972). As a result it has become a prerequisite in the planning of the perforation process to

reduce this impact as much as possible on the performance of the well.

3.2 Skin Factor and Associated Approaches

It was Hurst (1953) who initiated the concept of skin factor; the suggested concept was

the basis for a characterization of nonperfect flow. Later on, Van Everdinen incorporated the

concept of skin using the specific field cases to use the skin for the characterization of damage

of formation and restrained flow caused by perforation. These represent the background of

near-borehole flow constraints.

To characterize the deviation of perfect pressure drawdown to the real one, the skin factor can

be used in connection with the relationship of intrusion performance, shown in Figure 3, the

relevance of skin impact by a rate vs. pressure diagram of a well. This figure reveals that the

real IPR of a well differs from the IPR with continuous line of the perfect model by the skin

effect with constant value, the skin that varies with rate and the coupled impacts of pressure-

based characteristics of the fluid as well as concurrent oil and gas flow, the latter two of

which can be written as the pressure function mentioned in section 2, whereas the first two are

touched upon in this section. By and large, the focus is only placed on the pseudosteady-state

skin but the transient skin effect is negligible, the same goes for the skin with high velocity. If

we want to write the skin in the form of an equation, skin can be found intrinsically in the

32

derived pressure drop pR-pwf in total in case of pseudosteady-state circumstances in an oil well

as:

P − P�� = P − P`�� + (P`�� − P��)

│ideal│ │nonideal│

(2.25)

The drop of pressure caused by skin can be written as follows:

wfwfS ppp −′=∆

(2.24)

The perfect radial flow (e.g. lacking skin) leading to the flowing pressure pwf is:

(2.22)

If Equations 2.22 and 2.24 are reckoned with the total pressure pR–pwf is obtained, described

by Equation 2.25.

Skin s combines every nonperfect circumstance that influence the flow, of which the main

ones are:

sd = skin of formation-damage,

sc = skin of completion caused by partial penetration,

sp = skin of perforation,

sb = skin of blockage,

sG = skin of gravel-pack,

sA = skin of external limit geometry.

The impact of high-velocity flow is alternatively written as the equivalent skin, Dq, in which,

D = DR+Dd+Ddp+DG, contains the components as follows:

DR = high-velocity flow part of reservoir in the area past near-borehole damage r >ra,

Da = damaged area with the part of high-velocity flow at rw < r < ra,

Ddp = high-velocity flow part in the damaged area directly around the perforations,

DG = high-velocity flow part in a gravel-packed perforation.

( )[ ]srrkh

Bqpp we

ooowfR +−=− 75.0/ln

2.141 µ

skh

Bqp ooo

s

µ2.141=∆

( )[ ]75.0/ln2.141, −=− we

ooowfR rr

kh

Bqpp

µ

33

In general, the combined skin factor s + Dq are derived from data obtained drawdown and

build-up tests.

Figure 3: Real IPR vs. IPR derived from the perfect well model (Michael G. et al. 1991)

3.3 Impacts of Perforation Parameters on Productiveness of Well

The geometry and quality of perforation determine the perforation skin factor Sp in

which certain geometrical parameters influencing productiveness of the perforated segment

were investigated using analytical tools by Muskat (1943). McDowell and Muskat (1950) as

well as and Howard and Watson (1950) employed analogy models, whereas Harris (1966),

Hong (1975), and Locke (1981) applied numerical simulation methods for the studies,

whereby the following parameters acknowledged were:

� Depth of penetration: The productiveness quotient of an oil well grows as the depth of

penetration of perforation increases.

� Diameter of perforation: If the diameter of the perforation tunnel increases, an

improved flow performance will be obtained (this is not a main aspect, the impact is

just a fraction in relation to the depth of penetration).

� Shot density: The higher the number of shots per length unit, the more improved the

performance, even though more than 4 shots per length (ft) increase deteriorates and

the risk of damage to casing is more elevated.

34

� Impact of angle of phasing: The factors that impact productiveness are phasing and

angular arrangement of shots surrounding the borehole, taking capacity of flow as a

basis, the least. Unfavorable angle of phasing is 0°, also known as strip shooting, in

which case every shot is on a single side of the borehole, 0° is still typical for through

tubing guns as proper penetration can be reached by means of this.

The impact of perforation exerted on the productiveness is most thoroughly described by

Harris (1966), whose results were repositioned by Standing (1980) into two practical graphs

shown in Figures 3.1 and 3.2 that provide skin according to depth of perforation past the

casing (0 to 0.76 m), density (3, 6 or 12 shots per m) and phasing of 0° to 180°. Standing

stated that the graph with 180° can also be used for the case with 120°. Locke’s study advises

that the graph with 180° should be also valid for 90° with no considerable erroneous

implications. The same author reviews that every perforation can be found in a single

horizontal plane and skin factors presented in Figures 3.1 and 3.2 will differ to some degree

from that having subsequent perforations placed in a setting in angles along a segment of a

certain length (1 ft). Locke stated that the skin factors by Harris are much too high regarding

penetration and too low for deep penetration, however, deviations are tiny.

The edge of Figures 3.1 and 3.2 over Harris’s initial curves without dimensions is provided

by their fast overview of the subjective relevance of different parameters of the perforation

and Harris did not include the option of appearance of damage of formation in the vicinity of

a borehole. In all likelihood, penetration surpassing the depth of damage promotes

considerably the intrusion but it is not at all viable to assess the value and spread of damage to

the formation in case acidizing was applied to the well for cleanup previously, thus, when

deriving skin factor of perforation the damage to formation can be dismissed.

35

Figure 3.1: Skin factors for perforation at a phasing of 0° (Michael G. et al. 1991)

36

Figure 3.2: Skin factors for perforation at a phasing of 180° (Michael G. et al. 1991)

37

Characteristically for one-half-inch perforations via cemented casing are meant the Standing-

Harris curves for a 9 ½-in. borehole (where the bit diameter is indicated). The depth of

penetration is determined from the sand face and if a borehole with another diameter d is

intended to be justified, the real penetration Lp is adjusted into an apparent penetration,

Lpa = Lp (9.5/d) but the impact of the deviation in the diameter of perforation (of 1/2-inch) is

negligible.

In order to reach an estimation that makes sense it is necessary that the penetration be

assessed but actually it is strived to reach an approaching value of the depth of penetration.

Companies specialized in perforation generally create standard depths of penetration for the

charges they apply on the basis of experiments observing processes and the standard of Berea

sandstone target as shown in Figure 3.3.

The difference of API test depth of penetration in real wells can be derived from a variety of

issues such as:

1. Deviation of clearance between the gun and the casing.

2. Deviation of density of well fluid.

3. Casing mechanical properties.

4. Formation mechanical properties.

5. Effective stress and/or compressive strength of formation rock under reservoir

circumstances.

6. Smashed (consolidated) area surrounding the perforation.

An empirical relation was established by Thompson (1962) linking penetration of perforation

with the compressive strength of rock, simply providing an equation with the purpose of the

correction coming from the Berea penetration LpB to real penetration Lp (in):

(3.1)

Where,

Lp = depth of penetration from the face of formation (in),

(total core penetration= TCP).

LpB = depth of penetration from the internal side of the casing, via a 3/8-in, casing

and 3/4-in. cement sheath (in.) (total target penetration = TTP),

CB = compressive strength of Berea ≈ 6500 Psi,

C = compressive strength of rock (Psi),

Ts = thickness of cement sheath (in.) (generally 19.05 mm),

( )[ ] ),()(10*5107.3

CSBpBp TTCCLL +−−=−

38

Tc = thickness of casing (in.) (usually 9.525 mm.).

Jet guns with shaped charges constitute the case that Equation 3.1 is valid for and the depth of

perforation Lp computed (from the face of formation until the top of effective perforation) can

serve as the basis straightly along with Figures 3.4 and 3.5 for the estimation of the skin

factor of perforation.

Saucier and Lands (1978) propose that the stress of formation is a parameter has higher

reliability to make a correlation of the adjustment for the depth of API penetration but on the

basis of a defined set of data.

Figure 3.4 presents a correlation for the quotient Mp = Lp/0.7 [LpB – (Tc + Ts)] where three

classes are distinguished namely:

• Austin limestone (that is chalk),

• Wasson dolomite, and,

• Berea sandstone.

It is worth to notice that the Berea curve shifts from 1.0 at 800 Psi to 0.73 at about 5000 Psi so

it stays constant. The Berea curve can serve in case of other sandstones provided no further

correlation is available.

Figure 3.3: Typical API test assembly for the assessment of depth of perforation (Michael G. et al. 1991, by courtesy of Schlumberger)

The Saucier and Lands correlation application process is as follows:

1. Contact the perforation charge maker to provide data about the Berea TTP (total target

penetration) LPB for the gun in use as it was gathered in the API test.

39

2. Adjust LPB for the cement and casing at the level of API target for the availability of

TCP (total core penetration) measured from the face of formation until the top of

perforation.

3. Perform the multiplication of the TCP by 0.7 so that the extent of penetration decrease

can be determined monitored with real casing as well as cement sheath applied in the

API target.

4. Define the effective stress of formation, which is to be computed from the pressure in

pore space deduced from the overload. The overload is to be approximated by the

multiplication of depth by the overload gradient of 1.1 Psi/ft and where the pressure in

the pore space is the pressure in the reservoir at the moment when perforation takes

place.

5. Define the rock type of the formation. Give figure 3.4 for effective stress and select

one of the three rock types and read off the adjustment for penetration caused by

effective stress.

6. In step five the adjustment factor is to be multiplied by the depth originating from step

three, equaling the real penetration of rock from the face of formation until the top of

penetration Lp.

It follows from the process of adjusting the depth of perforation that (expressed in the form of

equation):

(3.2)

Figure 3.4: Adjustment to typical Berea depth of penetration proposed by

Saucier and Lands (Saucier and Lands et al. 1978).

[ ] pCSpBp MTTLL )(7.0 +−=

40

Where equation presents adjustment factors for Berea sandstone, Austin limestone and

Wasson dolomite are indicated in Figure 3.4.

However, a disadvantage of Saucier and Lands’ adjustment that cannot be applied generally

and a variety of rock types of formation are not contained, other authors remarked that the

justification of their results require a large amount of further experiments others than them,

such as Klotz et al. 1974; Locke 1981; McLeod 1983 proposed that the smashed area around

the perforation should be the cause of the skin effect, for instance, the API RP 43 test data

provide the impact of smashed area concerning the CFE (core flow efficiency), which equals

to the permeability KP of a core perforated with a jet charge down to a depth of LP.

A typical API test determines KP straight away after a flow of cleanup and the permeability to

the Berea sandstone with no perforation KO. Also, computer software provided by API

computes the quotient of KI/KO according to depth LP and diameter dp, after which CFE is

computed as follows:

),//()/(/ OIOPIP KKKKKKCFE ==

The API RP 43 flow test is plotted regarding to KO, KP, and KI in a schematic way in Figure

3.5.

The value of CFE around 1 means an almost clean perforation with no damage, the value of

CFE< 1.0 shows a contaminated or perforation with damage. CFEs in the literature including

the majority of the guns span the 0.65 to 0.85 values. As far as the thickness of the smashed

area surrounding the perforation is concerned, visual checks of API targets for perforation

propose that it is approx. 0.5 in.

If permeability is computed by means of CFE from 0.65 to 0.85, the initial permeability of the

formations amounts to 10% to 35%. Figure 3.6 indicates an approaching correlation to be

applied for the definition of the permeability of a 0.5 in. smashed zone from a CFE appeared

in a publication.

41

Figure 3.5: Flow tests for the characterization of impact of perforation according to API recommendation (Bell et al. 1972).

Investigations performed with the aim of API targets reveal that CFE rises progressively with

backflush via the perforation, in the end stabilizing and achieving a value as indicated in an

API form. Figure 3.7 reports a residing smashed area that might be present in the target core.

The backflush perforated in the API is composed of streaming kerosene of a pressure

differential of 20 Psi as long as the CFE reached a stabilized value.

42

Figure 3.6: Assessment of smashed area permeability compared to permeability formation in the proximity around a perforation (Kl otz et al. 1974).

The monitored tendency of rising CFE as backflush pressure expands is shown in Figure 3.8

up to a point of 200 Psi. In case of API backflow tests as well as in real wells a thorough

cleaning was contemplated but it remains unsure that the backflow leaving the smashed area

undamaged in the API test incites the real flow circumstances predominant in a well

especially in the case of a gas well, which has an extremely high flowing velocity in the

vicinity of the borehole. Consequently it is hard to evaluate if the smashed area stays in place

or is taken away by washing in the production process.

43

Figure 3.7: Perforation and backflush in the API test (Bell et al. 1984).

In the field of perforation specific tendencies emerge, which are geared to attain perforations

with flow-efficiency, recapped by Bell (1984) as follows:

1. Choice of charges and guns providing penetration with larger depth.

2. Preference of charges that has elevated CFE according to publications.

44

3. Higher shot density, above 4 shots per length (ft) and until 8 or even as high as 12

shots per length (ft) in gravel-packed completions.

4. Perforation at essentially larger underbalance pressure and augmentation of the early

flow rate through perforations.

5. In case of the perforated segment is elongated and not homogeneous, perforation as

well as and backflow should occur in the small permeability segments of a production

area, and thereafter perforation and flow segments with augmented permeability.

Figure 3.8: Effectiveness of core flow vs. backflush pressure (Bell et al., 1984)

Among others Locke (1981) and McLeod (1983) propose that the smashed area can be

characterized as a skin factor as well as involved in IPR computations, McLeod even

developed a model with a ‘horizontal micro well’ with a damage of formation in the vicinity

similarly to a perforation enclosed by a smashed zone, where his model provides a

relationship for a steadystate skin caused by decreased permeability of the smashed area as

follows:

(3.3)

This includes the following:

K = permeability of formation (mD),

kdp = permeability of smashed area in the vicinity of the borehole (mD),

ka = radius of damaged zone (in.),

rdp = radius of smashed area (in.),

rp = radius of perforation (in.),

( ),/ln12

pdpp

p

adpdp rr

nL

h

k

k

k

kS

−=

45

Lp = depth of penetration (in.),

hp = perforated segment (ft),

N = number of perforations in total.

The parameters included in Equation 3.3 are shown in Figure 3.9 as well. It is necessary to

know a number of parameters for the application of Equation 3.3, which parameters fail to be

assessed with any degree of confidence such as permeability of real damaged zone, effective

number of shots, real depth of penetration and permeability of the smashed area surrounding

the perforations.

Figure 3.9: Perforation model by McLeod (McLeod et al., 1983)

The impact of perforations is accounted for a share of the skin that depends on the rate. Some

authors mentioned alterations of rate-dependent skin derived from variations in perforation

regimes, for instance McLeod (1983) developed this kind of monitoring for the demonstration

of a model forecasting rate-dependent skin brought about by perforations. As a matter of fact

he proposed that the majority of the rate-dependent skin in gas wells is derived from the flow

with high velocity across the smashed area surrounding the perforations. Based on a

comparison to a damaged well, McLeod established an equation for computing the part of

high velocity Ddp:

46

(3.4)

In which βdp represents the factor of turbulence of the smashed area and can be approximated

by,

(3.5)

3.4 Combined Skin Factor

So far individual flow constraints have been taken in consideration in the vicinity of the

borehole and characterized every of them in the form of skin factor and the overall impact of

the totality of nonperfect conditions in the proximity of the borehole is a combination of

separate impacts. The total skin factor is not just a summation of the singular factors, it is

more of a presentation of the presence of a certain extent of a synergy between various flow

constraints that can or not amplify the combined impact.

It is quite hard to characterize the intercommunication between two or more flow constraints

in the proximity of a borehole. Besides, it is not feasible to solve this issue by means of

mathematical methods. Most likely the most manageable point to take into account is the

communication caused by restrained entry and partial penetration. A simplified state flow

limited bound by a restrained entry generates more elevated flow velocities according to the

proportion of h/hp. The augmented total skin factor is demonstrated in the increased velocity.

Rowland (1969), and Jones and Watts (1971) suggested uncomplicated models to correct

singular factors for the impact of restrained entry, taking the flow model into account that is

presented in Figure 3.10. In this model flow confluence into the open segment is already

terminated prior to attaining the zone in which damage, elevated velocity flow, impediment

and perforation impacts gain relevance.

,10*84.3 22

15

= −

pp

dp

g

gdp

rLn

KhD

βµ

γ

1045.11010*73.2 −= dpdp kβ

47

By means of the formally defined skin factor and h/hp growth in the local velocity (compared

to perfect flow), pressure drawdown equivalent to perfect flow and different skins are as

follows:

∆�1 =���.�������

���ln ��

��− 0.75� For ideal flow (Darcy)

For partial penetration (Darcy) For drainage area shape (Darcy) For gravel pack (Darcy)

For damage perforation (Darcy)

For perforation (Darcy)

For damage/stimulation (Darcy)

For reservoir (High-Velocity Flow)

For damage/stimulation (High-Velocity Flow)

For damage perforation (High-Velocity Flow)

For gravel pack (High-Velocity flow)

(3.6)

Where s is expressed by,

(3.7)

And D is expressed by,

( ) apooo

p Shhkh

Bq/

2.1417

µ=∆

oaooo

p qDkh

Bq µ2.1419 =∆

oRooo

p qDkh

Bq µ2.1418 =∆

odpooo

p qDkh

Bq µ2.14110 =∆

Cooo

P Skh

Bq µ2.1412 =∆

oGooo

p qDkh

Bq µ2.14111 =∆

Aoo

P Skh

Bq µ03

2.141=∆

Gooo

P Skh

Bq µ2.1414 =∆

dpOoo

P Skh

Bq µ2.1415 =∆

( ) PpOoo

p Shhkh

Bq/

2.1416

µ=∆

[ ]oweooo

pt DqSrrkh

Bq ++−=∆ 75.0)/ln(2.141 µ

apppdpGAC ShhShhSSSSS )/()/( +++++=

48

(3.8)

Equations 3.7 and 3.8 are similarly valid for gas wells based on pressure-squared, pressure or

pseudopressure method. It is to be noticed that SC, SA, SG, and Sdp are not adjusted for

restrained entry on the grounds that restrained entry is intrinsically taken into account in case

these skin factors are computed separately. An analogue circumstance goes for the singular

elements D.

Figure 3.10: Simplified combined skin factor model

GdpAR DDDDD +++=

49

4 Calculation Results

4.1 General Data of the Wells

I collected some data about the wells from the MOL Company and I chose four of them

to study in my work. For these wells I have got a well test evaluation report which includes

some of the parameters which are necessary for my work such as: reservoir description and

fluid properties as well the layer properties.

In this section I will show the data which I used in my calculation. I made assumption in some

of the data that were not included in the well test data and the perforation information.

As far as the perforation data are concerned I couldn’t get them from the MOL Company that

is why I made assumptions of many parameters depending on the Hungarian oil vertical well

situation. I used twelve different guns depending on the Schlumberger and Weatherford

design report; we can see the different kinds of guns for the various perforation parameters in

the appendix A, B and C.

The damage zone permeability I assumed equal to the formation oil permeability divided by

five. The vertical permeability usually equals to the damage zone permeability, and the

horizontal permeability usually equals to the oil permeability. My assumptions of some

parameters were for radius of formation damage, horizontal permeability, vertical

permeability, damaged zone permeability, crushed zone permeability, and crushed zone

thickness.

4.2 Basic Data Collected in Well 1:

Table 4.1: data and results of the well parameters matching well 1 including the reservoir

description and the perforation information.

Perforation section:- 5895.8 – 5900.72 ft

Formation thickness, ft 4.9213

Reservoir pressure, psia 2270.691064

Flow Bottom hole pressure, psia 2226.469443

Oil viscosity, cp 0.28194

Oil formation volume factor, bbl/STB 1.37042

Reservoir permeability, mD 243

Well radius, ft 0.292

50

Drainage radius, ft 4641.2

Average Formation Porosity 0.25

Perforation interval, ft 4.92

Rock compressive strength, psia (calculaled). 4217.39

Perforation tunnel diameter for the different guns

(1,2,3,4), in

Phase

Angle

(°)

Entrance hole

(in)

1 2 3 4

60 0.3 0.29 0.3 0.28

0 0.22 0.21 0.22 0.20

90 0.25 0.24 0.25 0.27

Perforation phasing, (°) 60 , 0 , 90

Shot density, shots/ft 6 , 4 , 4

Crushed zone thickness, ft (assumed) 0.0416667

Crushed zone permeability, mD (assumed) 5.0

Damaged zone permeability, mD (k/5, assumed) 48.6

Vertical permeability, mD (equal ka) 48.6

Horizontal permeability, mD (equal k) 243

Radius of formation damage, ft (assumed) 1.375

Formation Temperature, deg ℉ 201.4690

Table 4.1

4.3 Basic Data Collected in Well 2:

Table 4.2: data and results of the well parameters matching well 2 including the reservoir

description and the perforation information.

Perforation section:- 5625.2 – 5641.6 , 5658 – 5674.4 ft

Formation thickness, ft 193.57

Reservoir pressure, psia 2112.8947

Flow Bottom hole pressure, psia 2075.5463

Oil viscosity, cp 0.39349

Oil formation volume factor, bbl/STB 1.6428

51

Reservoir permeability, mD 301

Well radius, ft 0.187

Drainage radius, ft 1705.6

Average Formation Porosity 0.07

Perforation interval, ft 32.8

Rock compressive strength, psia (calculaled) 4101.8853

Perforation tunnel diameter for the different guns

(1,2,3,4), in

Phase

Angle

(°)

Entrance hole

(in)

1 2 3 4

60 0.3 0.29 0.3 0.28

0 0.22 0.21 0.22 0.20

90 0.25 0.24 0.25 0.27

Perforation phasing, (°) 60 , 0 , 90

Shot density, shots/ft 6 , 4 , 4

Crushed zone thickness, ft (assumed) 0.0416667

Crushed zone permeability, mD (assumed) 5.0

Damaged zone permeability, mD (k/5, assumed) 60.2

Vertical permeability, mD (equal ka) 60.2

Horizontal permeability, mD (equal k) 301

Radius of formation damage, ft (assumed) 1.375

Formation Temperature, deg ℉ 210.5590

Table 4.2

4.4 Calculation and Final Results of the Effect of Perforation Technology on the

Productivity of Hydrocarbon Wells

The Purpose of this study is to show how to calculate the effect of different perforation

parameters on the flow rate of the hydrocarbon wells by using different perforation methods.

During my calculation I considered those wells that produce only single oil phase, thus I

calculated what would be the flow rate of the examined well if the three different perforation

technologies were used in it.

52

I looked through the Schlumberger and Weatherford engineered perforation systems for the

power jet, and I tried to select the best guns for each perforation method.

Regarding my theoretical overview on perforation, I have chosen four different kinds of high

shot density guns (HSD) for different perforation technologies as shows in the table below:-

Perforating Techniqus

Perforating HSD Guns Performance

Gun number

Shot Density

(spf)

Phasing (°)

Temperature Rating, (℉)

1hr.100hr

Entrance Hole (in)

Penetration ���

(in)

Differencial Pressure

Wireline-conveyed

casing gun

1 6 60 400 300 0.3 19.2 Overbalance Pressure 2 6 60 400 300 0.29 20.6

3 6 60 400 300 0.3 22 4 6 60 400 300 0.28 26

Wireline-conveyed through tubing gun

1 4 0 400 300 0.22 9.2 Underbalanced Pressure

2 4 0 400 0.21 9.7

3 4 0 340 0.22 10.5

4 4 0 400 0.20 13 Tubing-

conveyed gun

1 4 90 400 204 0.25 13.3 Over &Under balance Pressure

2 4 90 400 204 0.24 14.4 3 4 90 340 0.25 15.4 4 4 90 400 0.27 17.5

Table 4.3

I used equation number (2.26) to determine the flow rate. To calculate the flow rate I needed

to find the perforation depth by using the Thompson method considering equation number

(3.1). To calculate the perforation depth it is necessary to know the compressive strength of

the formation and, I also needed to calculate the skin affect caused by perforation Sp, and

crushed zone skin factor Sdp, considering all of the equations in section 2.4 with equation

number 3.3.

I considered the effect of the parameters on the skin factor like perforation skin factor,

crushed zone skin factor, formation damage skin and composite skin factor.

The calculation of perforation skin factor and the calculation of the damage zone skin factor,

as well as the calculation of the crushed zone skin factor were explained in section 2 and 3.

In my calculation I ignored the value of the other parameters such the completion skin due to

the partial penetration (SC), and the outer boundary geometry skin (SA), as well the gravel-

pack skin (SG), because my thesis considers the effect of the perforation skin.

In this thesis I calculated and focused on the perforation skin effect by using Karakas and

Tariq method because the other methods do not include all the phasing angles.

53

To calculate the perforation skin effect by using Karakas and Tariq method I had to consider

the equation numbers from 2.34 to 2.43.

In my project work I made calculation steps according to the followings:

1. Calculation of the penetration depth using Thompson correlation.

2. Calculation of the Perforation Skin Effect using Karakas and Tariq method.

3. Calculation of the effect of a crushed zone skin factor using Locke and McLeod.

4. Calculation of the composite skin factor.

5. Calculation of the flow rate.

I calculated the effect of a crushed zone skin factor by using equation number (3.3),

considering the damage zone permeability and damage zone radius.

Firstly, I calculated all the parameters of the well number one to get the flow rate.

4.4.1 Calculation of the Penetration Depth (L P):

To calculate the penetration depth we must know the compressive strength of the

formation oil well.

I used Thompson correlation equation (3.1) to calculate the penetration depth, and the data

from table (4.1).

Berea compressive strength ( CB ) 6500, psia

Cement sheath thickness ( TS ) Usually 0.75, in

Casing thickness ( TC ) Usually 0.375, in

Table 4.4

Perforation Depth interval is: 5789.2 - 5795.76 ft.

The determination of the effective compressive strength equals to overburden minus the

formation pressure. The overburden can be estimated by multiplying depth by the overburden

gradient of 1.1 psi/ft.

The formation pressure is the reservoir pressure at the time of perforating.

The overburden pressure = [1.1 psi/ft*(average perforation depth, ft)].

Average perforation depth, ft = ((5789.2+5795.76) / 2)

Compressive strength, psia = [1.1 psi/ft* (average perforation depth, ft) – (the formation

pressure, psia)].

54

Number of

Guns

Phasing

(°)

Shots

(spf)

Compressive

Strength

( Psia)

Total target

penetration

(in)

Depth of

Penetration

��, ( in )

1 60 6 4125.548 19.2 22.23943

2 60 6 4125.548 20.6 23.94309

3 60 6 4125.548 22.0 25.64674

4 60 6 4125.548 26.0 30.51433

1 0 4 4125.548 9.2 10.07046

2 0 4 4125.548 9.7 10.6789

3 0 4 4125.548 10.5 11.65242

4 0 4 4125.548 13 14.69467

1 90 4 4125.548 13.3 15.05973

2 90 4 4125.548 14.4 16.39832

3 90 4 4125.548 15.4 17.61522

4 90 4 4125.548 17.5 20.1707

Table 4.5

4.4.2 Calculation of the Perforation Skin Effect by using Karakas and Tariq Method:

I chose this method instead of the other method because in this method I can calculate

the perforation skin factor of the phasing angles of 60°, 0°, 90° for 6, 4, 4 shots per feet, for

which I couldn’t use the other method.

To find the perforation skin effect (Sp), I used all of the equations in section 2.4.

Then I found the perforation skin effect (Sp) as we can see in table 4.6.

Flow through perforation effects the productivity of a well primarily by changing the local

flow geometry near the wellbore. Unlike the effect of limited entry, which always impedes

inflow, perforations may result in enhanced productivity if the operations are successful.

Field results suggest, that, compared with open-hole completions, perforations most often

have a negative effect on flow, particularly if only some of the perforations are open to flow.

The effect of perforations on well performance is usually expressed as a skin factor.

55

No. of guns

Phase angle (°)

Shot density (spf) Sp

1 60 6 -4.13851 2 60 6 -4.21141 3 60 6 -4.27935 4 60 6 -4.45134 1 0 4 -2.15383 2 0 4 -2.2125 3 0 4 -2.29976 4 0 4 -2.53177 1 90 4 -3.63654 2 90 4 -3.72319

3 90 4 -3.79357

4 90 4 -3.92707

Table 4.6

4.4.3 Calculation of the Effect of a Crushed Zone Skin Factor (Sdp):

I found (Sdp), by using equation (3.3) and the data in table (4.1 & 4.2), as we can see the

result in table (4.8).

Total number of perforation (n) = Shots/ft, (spf) * Perforation interval (hp), ft.

Perforation radiuses (rp) are given in table 4.3 and the radius of crushed zone (rdp) are given in

the table below:

No. Radius of smashed area

(in)

1 0.65

2 0.645

3 0.65

4 0.64

Table 4.7

ka= ko/5 was being assumed by me, as usual in Hungarian oil wells.

Phase angle

(°)

ko

(mD)

ka

(mD)

ra

(ft)

kdp

(mD)

hp

(in)

Lp

(in)

rw

(ft)

Sp Sdp

60 243 48.6 1.375 5.0 4.92 22.23943 0.292 -4.13851 5.749455

60 243 48.6 1.375 5.0 4.92 23.94309 0.292 -4.21141 5.340356

60 243 48.6 1.375 5.0 4.92 25.64674 0.292 -4.27935 4.985608

56

60 243 48.6 1.375 5.0 4.92 30.51433 0.292 -4.45134 4.190313

0 243 48.6 1.375 5.0 4.92 10.07046 0.292 -2.15383 19.0455

0 243 48.6 1.375 5.0 4.92 10.6789 0.292 -2.2125 17.96035

0 243 48.6 1.375 5.0 4.92 11.65242 0.292 -2.29976 16.45983

0 243 48.6 1.375 5.0 4.92 14.69467 0.292 -2.53177 13.05214

90 243 48.6 1.375 5.0 4.92 15.05973 0.292 -3.63654 8.299011

90 243 48.6 1.375 5.0 4.92 16.39832 0.292 -3.72319 7.621566

90 243 48.6 1.375 5.0 4.92 17.61522 0.292 -3.79357 7.095052

90 243 48.6 1.375 5.0 4.92 20.1707 0.292 -3.92707 6.19616

Table 4.8

4.4.4 Calculation of the Composite Skin Factor (S):

The composite skin factor is determined by the equation below:

S=��� + (�

��∗ ��) + (

�

��∗ ��)

In my thesis I considered the effect of the perforation skin factor, the crushed zone skin factor,

and the damage zone skin factor.

I suggested that the completion skin factor equals zero, but if we consider the value of the

completion skin factor like 10, we will have the lower flow rate.

The value of the damaged zone skin factor is determined by the equation below:

Sa = � ��

������� ∗ln ���

���

Phasing (°)

Sp h (ft)

hp (ft)

h/hp Sa Sdp S

60 -4.13851 4.9213 4.92 1.000264 7.91 5.749455 9.521973 60 -4.21141 4.9213 4.92 1.000264 7.91 5.340356 9.039958 60 -4.27935 4.9213 4.92 1.000264 7.91 4.985608 8.617251 60 -4.45134 4.9213 4.92 1.000264 7.91 4.190313 7.649917 0 -2.15383 4.9213 4.92 1.000264 7.91 19.0455 24.80323 0 -2.2125 4.9213 4.92 1.000264 7.91 17.96035 23.65939 0 -2.29976 4.9213 4.92 1.000264 7.91 16.45983 22.07158 0 -2.53177 4.9213 4.92 1.000264 7.91 13.05214 18.43183 90 -3.63654 4.9213 4.92 1.000264 7.91 8.299011 12.57363

90 -3.72319 4.9213 4.92 1.000264 7.91 7.621566 11.80952

90 -3.79357 4.9213 4.92 1.000264 7.91 7.095052 11.2126

90 -3.92707 4.9213 4.92 1.000264 7.91 6.19616 10.18018

Table 4.9

57

4.5 The Effect and the Evaluation of Perforating Parameters on Well

Productivity According to Porous Oil Reservoir

I used equation (2.26) in chapter 2, and the data from table (4.1 & 4.2), to calculate the

flow rate considering the total skin factor that I calculated in step 4.4.4, then I could find what

I needed to evaluate the perforating parameters on the productivity of the hydrocarbon wells,

as shows in the table below:

Well Number

Gun Numbers

Phases (°)

Shot Density (shots/ft)

Lp (in)

S Q�

(bbl/day)

1

1 60 6 22.23943 9.521973 52.55092

2 60 6 23.94309 9.039958 53.961

3 60 6 25.64674 8.617251 55.26137

4 60 6 30.51433 7.649917 58.48674

1

1 0 4 10.07046 24.80323 28.74076

2 0 4 10.6789 23.65939 29.74972

3 0 4 11.65242 22.07158 31.27371

4 0 4 14.69467 18.43183 35.4348

1

1 90 4 15.05973 12.57363 45.09104

2 90 4 16.39832 11.80952 46.75286

3 90 4 17.61522 11.2126 48.13878

4 90 4 20.1707 10.18018 50.74033

2

1 60 6 22.47264 40.61719 486.7441

2 60 6 24.19334 39.6279 496.7768

3 60 6 25.914 38.74208 506.1177

4 60 6 30.83018 36.63995 529.7562

2

1 0 4 10.18222 73.03529 292.9036

2 0 4 10.79674 71.21282 299.6113

3 0 4 11.77998 68.65631 309.5556

4 0 4 14.85259 62.64945 335.7386

2

1 90 4 15.22131 48.53633 419.0063

2 90 4 16.45035 47.3234 428.132

3 90 4 17.8023 46.14775 437.3648

4 90 4 20.3833 44.25495 453.0963

Table 4.10

4.5.1 Effects of perforation penetration, phasing, density and raduis:

The productivity ratio of an oil well increases with an increase of perforation

parameters. It is important to recognize that the penetration does not occur by pulverizing

material in the path of the jet, but by crushing and compaction of the casing, cement and

formation.

58

Figure 4.1 (well no.1)

The deeper the penetration , the lower the skin factor

Figure 4.2 (well no.2)

The deeper the penetration is the better the performance and the lower the skin factor

Figure 4.1 & 4.2; show the relationship between the perforation depth and the skin factor.

Considering the theoretical overview as shows in the figure; the bottom curves are favorable

for us because the deeper penetration has the lower skin factor. Skin factor is decreased by

increasing depth of the formation penetration.

59

The figures below show the relationship between the perforation depth and the flow rate. The

higher flow rate refers to the deeper penetration, and the top curves which belong to the phase

angle of 60° with density of 6 shots per foot are favorable for us.

Figure 4.3 ( well no .1 )

The deeper the penetration , the better the performance

Figure 4.4 ( well no .2 )

The deeper the penetration , the better the performance

60

Figure 4.3 & 4.4 show improved productivity index ratios with increasing the depth of

formation penetration, considering the theoretical overview as shown in the figure; the top

curves are favorable for us because the deeper perforations give the lower skin factors.

Figure 4.5 & 4.6 show the relationship between the skin factor and the flow rate. Flow rate is

decreased with increasing skin factor.

Figure 4.5 ( well no.1 )

Increasing skin factor, decreasing flow rate

Figure 4.6 ( well no.2 )

Increasing flow rate, decreasing skin factor

61

The final result that I got in table 4.10 contains the flow rate of well 1 and 2 by using different

kinds of guns. As you can see in my work we can get the best flow rate by using gun 4 in well

2. I retested that the flow rate is quite low because the interval perforation is so small and in

this case I recommend that we should use the perforating with high interval perforation length

to increase flow rate.

4.6 The Evaluation of Different Perforation Methods and High Shot Density Guns

The aim of the evaluation is to know the effect of the guns for the flow rate of each well

and to show the effect of the reservoir, fluid and layer properties on the productivity index.

I needed two more wells to evaluate it clearly as shown in the tables below:

4.6.1 Basic Data Collected in Well 3:

Table 4.11: data and results of the well parameters matching well 3 including the reservoir

description and the perforation information.

Perforation section: - 5854.8 - 5858.08 ft

Formation thickness, ft 19.685

Reservoir pressure, psia 2347.9099

Flow Bottom hole pressure, psia 2322.512597

Oil viscosity, cp 0.67184

Oil formation volume factor, bbl/STB 1.25527

Reservoir permeability, mD 214

Well radius, ft 0.292

Drainage radius, ft 4336.16

Average Formation Porosity 0.32

Perforation interval, ft 3.28

Rock compressive strength, psia (calculaled) 4094.1741

Perforation tunnel diameter for the different guns

(1,2,3,4), in

Phase

Angle

(°)

Entrance hole

(in)

1 2 3 4

60 0.3 0.29 0.3 0.28

0 0.22 0.21 0.22 0.20

90 0.25 0.24 0.25 0.27

62

Perforation phasing, (°) 60 , 0 , 90

Shot density, shots/ft 6 , 4 , 4

Crushed zone thickness, ft (assumed) 0.0416667

Crushed zone permeability, mD (assumed) 5.0

Damaged zone permeability, mD (k/5, assumed) 42.8

Vertical permeability, mD (equal ka) 42.8

Horizontal permeability, mD (equal k) 214

Radius of formation damage, ft (assumed) 1.375

Formation Temperature, deg ℉ 194.3190

Table 4.11

4.6.2 Basic Data Collected in Well 4 :

Table 4.12: data and results of the well parameters matching well 4 including the

reservoir description and the perforation information.

Perforation section: - 5789.2 – 5795.76 ft

Formation thickness, ft 26.2467

Reservoir pressure, psia 2246.1799

Flow Bottom hole pressure, psia 2185.9326

Oil viscosity, cp 0.27377

Oil formation volume factor, bbl/STB 1.37151

Reservoir permeability, mD 169

Well radius, ft 0.292

Drainage radius, ft 4969.2453

Average Formation Porosity 0.30

Perforation interval, ft 6.56

Rock compressive strength, psia (calculaled) 4125.5481

Perforation tunnel diameter for the different guns

(1,2,3,4), in

Phase

Angle

(°)

Entrance hole

(in)

1 2 3 4

60 0.3 0.29 0.3 0.28

0 0.22 0.21 0.22 0.20

90 0.25 0.24 0.25 0.27

63

Perforation phasing , (°) 60 , 0 , 90

Shot density, shots/ft 6 , 4 , 4

Crushed zone thickness, ft (assumed) 0.0416667

Crushed zone permeability, mD (assumed) 5.0

Damaged zone permeability, mD (k/5, assumed) 33.8

Vertical permeability, mD (equal ka) 33.8

Horizontal permeability, mD (equal k) 169

Radius of formation damage, ft (assumed) 1.375

Formation Temperature, deg ℉ 206.5990

Table 4.12

After applying the procedures step by step as explained in section 4.4, we will have the table

below which contains the result for well numbers 1, 2, 3 and 4.

Well numbers Guns

Phase angle

(°)

Lp

(in)

��

(bbl/day)

1 Fisrt 60 22.23943 52.55092

4 First 60 22.4247 190.3363

2 First 60 22.47267 486.7441

3 First 60 22.48833 24.56318

1 Second 60 23.94309 53.961

4 Second 60 24.14187 193.58

2 Second 60 24.19334 496.7768

3 Second 60 24.21013 25.10832

1 Third 60 24.64674 55.25137

4 Third 60 25.85903 196.6287

2 Third 60 25.914 506.1177

3 Third 60 30.85138 26.94796

1 Fourth 60 30.51433 58.48674

4 Fourth 60 30.76522 204.4764

2 Fourth 60 30.83018 529.7562

3 Fourth 60 30.85138 26.94794

1 First 90 15.05973 45.09104

4 First 90 15.18807 166.9666

2 First 90 15.22131 419.0063

3 First 90 15.23215 22.76877

1 Second 90 16.39832 46.75286

4 Second 90 16.53728 170.6331

2 Second 90 16.45035 428.132

3 Second 90 15.585 23.30141

64

1 Third 90 17.61522 48.13878

4 Third 90 17.76382 173.725

2 Third 90 17.8023 437.3648

3 Third 90 17.81486 23.75312

1 Fourth 90 20.1707 50.74033

4 Fourth 90 20.33957 179.6104

2 Fourth 90 20.3833 453.0963

3 Fourth 90 20.39756 24.62014

1 First 0 10.07046 28.74076

4 First 0 10.15923 127.8735

2 First 0 10.18222 292.9036

3 First 0 10.18972 14.9553

1 Second 0 10.6789 27.74972

4 Second 0 10.77251 129.9889

2 Second 0 10.79674 299.6113

3 Second 0 10.80465 15.28531

1 Third 0 11.65242 31.27371

4 Third 0 11.75374 132.0026

2 Third 0 11.77998 309.5556

3 Third 0 11.78854 15.77664

1 Fourth 0 14.69467 35.4348

4 Fourth 0 14.82011 141.3533

2 Fourth 0 14.85259 335.7386

3 Fourth 0 14.86319 17.085

Table 4.13

Table 4.13 shows the different Flow rate and perforation depth for different phase angles, shot densities, and wells.

Here is relationship between the flow rate and the depth of formation penetration with

different designs of guns, and the influence of the effected guns with the perforation depth of

all the wells.

65

Figure 4.7: Well 2 has the higher flow rate and the lower flow rate refers to well 3.

Figure 4.8: Well 2 and 4 have the higher flow rates and the lower flow rates belong to well 3 and well 1.

66

Figure 4.9: The higher flow rate belongs to the best design of the guns.

The deeper perforation that I got by using gun 4 with highest API RP 43 penetrations, which

belongs to the Schlumberger engineered perforation systems.

There are different flow rates from the wells; the designs of the guns have big effect on the

performance of the perforation techniques.

I considered the damage zone thickness of all the wells are the same, if it is not the same the

property of the shot through the damage zone might be different by using the different kinds

of high shot density guns.

4.7 Comparison of the best high shot density guns for each perforation method

It is comparing between the results of the flow rate to the depth of formation penetration

through the best different high shot density Guns for each well and perforation method, which

is gun 4 as shows in the table below:

Guns Well

no.

60° phasing with

6 shots/ft

90° phasing with

4 shots/ft

0° phasing with

4 shots/ft

Lp

(in)

��

bbl/day

Lp ��

bbl/day

Lp

(in)

��

bbl/day

fourth 1 30.51433 58.48674 20.1707 50.740334 14.69467 35.434795

fourth 4 30.76522 204.47635 20.33957 179.61036 14.82011 141.35326

fourth 2 30.83018 529.75621 20.3833 453.09627 14.85259 335.73864

fourth 3 30.85138 26.947942 20.39756 24.62014 14.86319 17.085

Table 4.14: the best high Shot Density Guns for each perforation methods are compared.

67

Fig.4.10: The compare of the flow rate to the best gun from different perforation methods.

The higher flow rate through the phasing of 60° with 6 shots per foot refers to the wireline-

conveyed casing gun.

The lower flow rate from 0° phasing with 4 shots per foot belongs to the wireline-conveyed

through tubing gun method.

Each gun gives the highest flow rate in well 2, because of the gun designs and perforation

interval, reservoir, layer with fluid properties.

I got the best performance by using gun 4 with highest API RP 43 penetration, that was

designed by the Schlumberger engineered perforation systems.

68

5 CONCLUSIONS AND RECOMMENDATIONS

5.1 CONCLUSIONS

After finalizing my thesis and observing the results obtained from the effect of

perforation parameters on the productivity index, the resulting conclusions are:

� The most important parameters influence the productivity of the perforated

hydrocarbon wells are: Perforation penetration, density, phasing, and perforation

diameter. The four parameters in order from the most effective to less effective are:

Perforation penetration, density, phasing and perforation diameter, because;

• Perforation penetration is the most significant parameter in determining the

effectiveness of productivity index. Productivity increases with increase in perforation

length, even a small penetration into the formation gives a significant improvement in

productivity. The penetration of the fourth gun in well 2 is 30.83 inch, raises the flow

rate by about 529.75 bbl per day, while the penetration of the first gun in well 2 is

22.47 inch, and raises the flow rate by roughly 486.74 bbl per day. The productivity

index of the fourth penetration is 9.10% higher than the first penetration.

• Perforation density is also an important parameter. Productivity increases with greater

shot density. Using 6 shots directions (located at 60°) from the fourth gun in well 4,

rises the flow rate by about 204.47 bbl/day, while using 4 shots directions (located at

90°) from the fourth gun in the same well, rises the flow rate by about 179.61 bbl/day.

The productivity index of 6 shots per foot is 6.8% higher than the 4 shots per foot.

These relative differences in performance are smaller than an increase in perforation

penetration.

• Perforation phasing also influences the productivity of the hydrocarbon wells. An

arrangement of a phasing of 60° in the same horizontal plane gave the best result from

the fourth gun in well 1 which was 58.486 bbl per day. While the arrangement of a

phasing of 90° in the same plane gave the lower performance from the fourth gun in

the same well, that was 50.740 bbl per day. And the arrangement of a phasing of 0° in

the same plane gave the lowest performance from the fourth gun in the same well,

which was 35.43 bbl per day. These relative differences in performance are smaller

than an increase in perforation density.

• The value of perforation radius is influenced by the length, density, and phasing of the

perforations. This parameter usually has little impact. However, it is essential because

69

of pressure losses. It is not realistic to assume a common value for all arrangements of

perforations.

� A phasing of 60° with 6 shots per foot which belongs to the wireline-conveyed casing

gun in the same horizontal plane or along a spiral gives a significant advantage over a

phasing of 90° with 4 shots per foot, which refers to the tubing-conveyed gun. And a

phasing of 90° with 4 shots per foot gives a significant advantage over a phasing of 0°

with 4 shots per foot which belongs to the wire line conveyed through-tubing gun.

This improvement increases with an increase in perforation length and perforation

radius.

� There is a calculation method by which the flow rate of the well can be estimated

before the performance of the perforation technology. And the study expected what

the flow rate of the examined well would be if the three different perforation

technologies were used in it.

� Flow rate evaluation needs a good knowledge of reservoir data around the wells such

as; layer and fluid properties, reservoir pressure and temperature.

� Because the economic value of an oil and gas well depends on the connection between

the wellbore and the formation, we should choose the right design of the gun from the

right perforation method to have the best flow rate.

5.2 Recommendations for further work

� Consider the right design of the gun, because of the very nature of the shaped charge

method, the immediate vicinity around the perforation is damaged. This is expressed

to a certain extent by the core flow efficiency. This type of damage depends on the

charge itself (type of explosive and especially the shape and type of cone) and on the

target formation.

� Consider the distribution of perforations over the producing zone. This is particularly

significant if the vertical permeability is much lower than the horizontal permeability

or if the formation does not have a homogeneous vertical permeability. In all these

cases, productivity is improved by use of guns with high shot densities.

70

6 APPENDICES

APPENDIX A Perforating HSD Guns Performance (API Statistics)

Gun Designation Shot Density

(Spf)

Phase Angle (°)

Charge Temp. Rating (°F)

1 hr.100 hr.

Maximum

Explosive

Load

(g)

Entrance Hole (in)

Penetration ���

TTP, (in)

1.56-in.HSD 4 0 20J UJ, HMX 400 300 3.6 0.22 9.2 2-in.HSD 4 60 25J UJ, HMX 400 300 7 0.22 14.1 2¼-in.HSD 6 60 PJ 2306,HMX 400 300 - 0.273 17.43 2½-in.HSD 6 60 31J CS, HMX 400 300 10.7 0.3 19.2 2½-in.HSD^2/6 6 60 31J UJ, HMX 400 300 10.7 0.29 20.6 2½-in.HSD 6 60 35B UP,RDX 340 240 10.5 0.62 5.8 2⅞-in.HSD^2 6 60 34J UJ,RDX 340 240 15.2 0.29 20.6 2⅞-in.HSD 6 60 34J UJ,HMX 400 300 15 0.3 22 2⅞-in.HSD 6 60 PJ 2906,HMX 400 300 15 0.28 26 2⅞-in.HSD 6 60 34J UJ,HTX 500 460 19.4 0.32 21.3 2⅞-in.HSD 6 60 34J CS,RDX 340 240 19 0.273 17.73 2⅞-in.HSD 6 60 38C CP,RDX 340 240 15.5 0.62 8.3 3⅛-in.HSD 10 135/45 38C UP,RDX 340 240 15 0.63 5 3⅜-in.HSD^2 6 60 34B CS,RDX 340 240 21.7 0.31 18.5 3⅜-in.HSD 6 60 34B HJ II,RDX 340 240 21.7 0.4 21.9 3⅜-in.HSD 6 99 34B HJII,RDX 340 240 21.7 0.38 20.2 3⅜-in.HSD 6 60 34JLUJ,HMX 400 300 21.6 0.37 28.9 3⅜-in.HSD 6 60 PJ3406,HMX 400 300 22.7 0.45 38.6 3⅜-in.HSD 6 60 34JMUJ,HTX 500 460 21 0.33 25.3 3⅜-in.HSD 12 135/45 38CUP,RDX 340 240 15 0.64 5.9 3½-in.HSD 4 60 37JHUJ,HX 400 300 30.4 0.339 15.99 3.67in.HSD^2/6 5 60 37JCS,RDX 340 240 34.5 0.36 31.2 3.67-in.HSD 5 60 37JCS,HMX 400 300 34.5 0.383 32.73 3.67-in.HSD 5 60 37JUJ,HMX 400 300 34.4 0.453 32.33 3.67-in.HSD 5 60 37JHUJ,HX 400 300 30.4 0.339 15.99 4½-in.HSD^10 12 135/45 34B HJII,RDX 340 240 21.7 0.39 17.9 4½-in.HSD^10 4 90 34JLUJ,HMX 400 204 21.6 0.25 13.3 4½-in.HSD^10 4 90 51B HJII,RDX 400 204 38.8 0.24 14.4 4½-in. HSD (Frac Gun)^11,12

12 60 43CJUPII,RDX 340 240 19.4 0.833 6.83

4½-in.HSD^10,11 12 135/45 43CJ UPII,RDX”

340 240 19.4 0.753 6.73

4⅝-in.HSD Bigshot^ 2113

21 120/60 43NS UPIII,RDX

340 240 19.4 0.83 5.9

4⅝-in.HSD Bigshot ^2113

21 120/60 43NSUPIII,HMX

400 300 19.4 0.83 5.7

4.72-in.HSD^10 12 135/45 34BCS,RDX 340 240 21.7 0.31 15.4 4.72-in.HSD^10 12 135/45 34JLUJ,HTX 500 460 22 0.323 22.23 4.72-in.HSD^10 5 72 51JUJ,HNS 500 460 38.3 0.33 34.5 4.72-in.HSD 12 135/45 43BCP,RDX 340 240 24 0.65 8.4 5-in.HSD^10 12 135/45 34B HJ II,RDX 340 240 21.7 0.39 19.8 5-in.HSD Bigshot^ 2111,13

21 120/60 43CJUP II,RDX

340 240 19.4 0.74 7.9

7-in.HSD^2 27 120/60 34JL.UJHMX 400 300 22.7 0.27 26 7-in.HSD 12 135/45 51B HJ II,RDX 340 240 38.8 0.47 30.4 7-in.HSD 12 135/45 51JUJ,HMX 400 300 38.8 0.39 43.8 7-in.HSD 14 140/20 58CUP,RDX 340 240 63.5 0.95 12.2 7-in.HSD 12 135/45 64CUP,RDX 340 240 66.4 1.07 9.3 7-in.HSD 12 135/45 64CCP,RDX 340 240 63.3 1.13 10.1

71

APPENDIX B

CAPSULE GUN PERFORMANCE AND MECHANICAL DATA SUMMARY API RP 43 Fifth Edition Section 1 or API 19B Section 1

Perforating

System

Designation

Shot

Density

(spf)

Phasing

(°)

Charge Penetration

���

TTP, (in)

Entrance

Hole

(in)

Temp.

Rating For

1hr,

degF

Maximum

Gun Length

(ft)

111⁄16-in Pivot Gun

4 180 111⁄16-in Ultracap, RDX

27.8 0.38 330 15

111⁄16-in PowerPivot Gun

4 180 111⁄16-in PP,HMX

28.4 0.35 365 15

1.63-in Retrievable Enerjet

4 0 1.63-in EJ, RDX 18.0 0.28 330 50

1.63-in Retrievable Enerjet

4 0 1.63-in EJ, HMX 17.8 0.29 365 50

111⁄16-in Retrievable Power Enerjet

6 0 111⁄16-in PE,HMX

21.6 0.20 365 50

111⁄16-in Biphased Retrievable Power Enerjet6

6 -45 +45

111⁄16-in Ph PE, HMX

14.6 0.26 365 35

111⁄16-in PowerSpiral* Enerjet

7.5 45 111⁄16-in PowerSpiral EJ, HMX

19.5 0.22 365 30

3⅜-in. Retrievable Power Enerjet

4 0 41BUP,RDX 9.7 0.21 400 24

3½-in. Retrievable Enerjet

4 0 111⁄16-in PE,HMX

10.5 0.22 340 34.4

3½-in. Retrievable Enerjet

4 0 37JUJ,HTX 13 0.20 400 34

21⁄8-in Retrievable Big Hole

4 21⁄8-in EJ BH, RDX

0.57 0.51 330 50

21⁄8-in Retrievable Big Hole

4 0 21⁄8-in EJ BH, HMX

10.0 0.53 365 50

21⁄8-in Enerjet 0°–180°

5 0 21⁄4-in PE BH, HMX

10.5 0.49 365 30

21⁄8-in R.Big Hole

6 180 21⁄8-in PE BH, HMX

4.9 0.47 365 50

21⁄8-in Triphased Expendable Big Hole

6 -45 +45 0

21⁄8-in EJ BH, HMX

7.9 0.51 330 30

4½-in. PowerSpiral* Enerjet

4 90 51JUJ,HMX 15.4 0.25 340 38.8

4½-in. Retrievable Power Enerjet6

4 90 PJ4505,HMX 17.5 0.27 400 38.8

21⁄2-in Expendable Power Enerjet

4 0 21⁄2-in PE, HMX 34.8 0.28 365 30

21⁄2-in PowerSpiral Enerjet

5 45 21⁄2-in PowerSpiral EJ, HMX

36.6 0.39 365 30

72

APPENDIX C Vann Gunn, Phasing and Shot Patterns

73

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