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Copyright 2005, SPE/IADC Drilling Conference

This paper was prepared for presentation at the SPE/IADC Drilling Conference held in Amsterdam, The Netherlands, 23-25 February 2005.

This paper was selected for presentation by an SPE/IADC Program Committee followingreview of information contained in an abstract submitted by the author(s). Contents of thepaper, as presented, have not been reviewed by the Society of Petroleum Engineers or theInternational Association of Drilling Contractors and are subject to correction by the author(s).The material, as presented, does not necessarily reflect any position of the SPE, IADC, theirofficers, or members. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers orthe International Association of Drilling Contractors is prohibited. Permission to reproduce in

print is restricted to an abstract of not more than 300 words; illustrations may not be copied.The abstract must contain conspicuous acknowledgment of where and by whom the paper waspresented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A.,fax 01-972-952-9435.

Abst ractLong horizontal section wells are economical requirements forheavy oil fields in deepwater environments. This articlediscusses the operational limits for gravel pack placement insuch wells, considering the maximization of the horizontalsection extension in low fracture gradient scenarios. A

parametric study on the variables governing the gravel packoperations indicates that careful hydraulic design and detailedoperational procedures can guarantee a successful job.Alternative strategies are proposed to extended hydrauliclimits in critical conditions.

IntroductionThe new scenario for offshore development in Brazil includesheavy oil fields in deepwaters where 1000m to 2000mhorizontal section wells are required. Due to the non-consolidated formations found, sand control techniques arerequired in Campos Basin, offshore Brazil. Sand productionresults in several surface problems, such as: equipment erosionand sedimentation inside the oil/gas/water separator.

There are many techniques for sand control available in petroleum industry. Economic development of deepwater projects requires that a minimum number of wells be drilledand nevertheless getting effective reservoir drainage tomaintain a high productivity index of the wells.

An important option for accomplishing this task is to drillhorizontal wells. Open hole gravel packing of horizontal wellsin unconsolidated formations is a very effective way toachieve all of these goals.

The gravel packing technique consists in filling out theannular space between screen and producer formation withsand or ceramic particles with selected grain diameter. Theidea is to create a second porous medium with a pore throatdiameter smaller than the formation grain diameter and, in thiscase, fluid would easily flow through the gravel pack whileformation particles would not.

Due to the critical conditions, such as the deep and ultradeepwater and low frac gradients, a lot of precision is requiredto assure gravel packing success. Most models available in theindustry for horizontal gravel pack design are essentiallyempirical, resulting in imprecise predictions for extrapolatedconditions.

These aspects were the main motivators for a research project including theoretical and experimental development. Amechanistic model to calculate the pressure loss during thedisplacement, including sand injection and alpha/beta waves

propagation, taking into account fluid leakage, multi zonalisolation and beta wave pressure reduction optimization wasdeveloped. This paper discusses special issues to be addressedduring well design, which can extend the horizontal welllength during a gravel packing operation.

Brief Description of t he OperationFor displacement calculation purposes, the horizontal wellgravel pack operation can be divided in three different stages:the injection, the alpha wave propagation and the beta wave

propagation.The injection stage, as highlighted in Fig. (1), consists of

pumping a fluid-gravel mixture (red line) through the pipefrom the rig until a cross over tool located in the beginning ofthe open hole, where the flow will be diverted to the open holeannulus. At this moment, there is usually a decrease in themixture displacement velocity, due to the larger area, resultingthat the force which sustains the gravel particles is not highenough to maintain them in suspension. Consequently, thesolids begin to sediment in the lower portion of the annulus,forming a bed that, for a given flow rate, reaches anequilibrium height (h α ). The deposited sand length will

propagate till the extremity of the horizontal section, leaving a

free channel between the superior wall of the well and the topof the bed. This stage is known as alpha wave propagation andis illustrated in Fig. (2).

When the alpha wave arrives at the extremity of the well, anew step, called the beta wave propagation, begins: since thesand can not flow through the screens, it will start to depositabove the sand deposited in the alpha wave stage, beginning atthe extremity of the well and finishing at the crossover tool,traveling in the opposite way. Figure (3) highlights the

process.While during the alpha wave propagation, the fluid flow

totally happens through the annular space between the screenand the open hole, in the beta wave the fluid will flow radially

through the screen and then axially through the annular gapformed between the screen and the washpipe. Figure (4)

SPE/IADC 92428

Gravel Pack Placement Limits in Extended Horizontal Offshore Wells A. Calderon, J.V.M. de Magalhães, and A.L. Martins, SPE, Petrobras S.A.

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shows the cross section of the horizontal wells when equippedwith the gravel pack placement columns configuration.

Three points are relevant for the present study (Fig.3): pump pressure at the rig (P p), bottom hole pressure (P b) andcasing shoe pressure (P cs). The critical point as at the casingshoe where the pressure is maximum along the wholeoperation.

Theoretical Model and Software DevelopmentThe proposed model consists on the following steps:

pressure propagation during string injection, alpha waveheight calculation, pressure propagation during alpha wavedisplacement and pressure propagation during beta wavedisplacement. In order to predict alpha wave depositionheights, a two layer model was adopted. The present model isan extension, for horizontal gravel packing applications, of themodel proposed by Martins 1 for drilled cuttings transportanalysis. The whole theoretical model for alpha wave heightcalculation as well as the friction losses calculation can beseen in more details in Martins 2.

The proposed modeling was implemented in a computercode for use in projects and during the gravel packingoperations. This code was written in PASCAL language usingDELPHI™ 6.0 environment. More software details areexplained in Martins 3.

Computer Simulator Input Data: • Open hole diameter and length• Rathole diameter and length• Sea level and casing shoe measured depth• Casing internal diameter• Screen Diameters (OD and ID)•

Wash pipe and gravel diameters• Well path• Injection and return flow rates• Particle and fluid densities• Frac gradient

Defining the Operational WindowIn order to achieve a successful gravel pack operation,different hydraulic limits should be respected. Dynamic

pressures during the operation should be between a windowformed by the pore pressure and the fracture pressure. If thewellbore pressure, at any time, is below the pore pressure,there will be influx of formation fluid to the well. On the of

other hand if the wellbore pressure is greater than theformation fracture pressure, there will be influx of drillingfluid to the formation, possibly generating damage. Figures 5and 6 shows typical shallow water and deepwater pore andfrac pressure profiles. Operational windows are normallymuch narrower at deepwater environments were theformations are poorly consolidated and, consequently, presentlow frac pressures.

Another important issue is to guarantee that the operationwill be run at a minimum flow rate which avoids prematurescreen out of the rat hole. Since a larger diameter open holesection is exposed, if the flow rate is too low, alpha wavesformed may be high enough to block sand passage to the openhole, generating immediately a beta wave in the rat hole,

according to Marques 4. The consequence is that the pressure atthe casing shoe will immediately increase and the operationwill have to be aborted without packing the open hole. Figure7 shows a scheme of the process.

With the input data, the computer program previouslymentioned can predict alpha wave heights in the open hole andrat hole sections, besides pressure propagation duringinjection/alpha wave/beta wave stages with displacement time.These results generate outputs in two different ways:• Defining the operational flow rate window for a given

operation based on the minimum flow rate required toavoid premature screen out in the rat hole and maximumflow rate which does not lead to a formation fracture (Fig.8). Normally, the fluid density is designed to generatewellbore pressures in static conditions higher than pore

pressures.• Once the optimum flow rate is chosen inside operational

window (between maximum and minimum flow rate), predicting the pressure propagation with placement time(Fig. 9).

Field Parameters Sensitivit y AnalysisThis item details a sensitivity analysis on the impact of severalimportant parameters on the maximum horizontal wellextension which is possible to be gravel packed for a givenfrac gradient. The following geometric configurations wereconsidered:

Configuration #1: Open hole diameter = 8 ½ inExternal screen diameter = 6.54 inInternal screen diameter = 4.87 in

Configuration #2: Open hole diameter = 9 ½ inExternal screen diameter = 7.31 inInternal screen diameter = 5.47 in

Configuration #3: Open hole diameter = 12 ¼ inExternal screen diameter = 9.425 inInternal screen diameter = 7.05 in

The following parameters were considered as a base case:• Water depth: 1200 and 1800m• Kick Off Point: 1450 and 2000m (for 1200 and 1800 m

water depth, respectively).• Angle Build-up rate: 3.18 o/100 m and 7.2 o/100 m (when

changed water depth)• Reservoir depth: 3250 and 3850m• Fluid density: 10 lb/gal• Gravel concentration: 1 lb/gal• Gravel Type: sand 20/40 mesh• Open BOP configuration (friction losses between the sea

floor and the rig are negligible).

All plots in the next items represent the maximum dynamic pressures reached at the end of beta wave placement whichwill not to fracture the formation.

Effect of Wellbore Diameter. Figure 10 shows the effect of 3diferent wellbore diameters (configurations). Results indicate

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that, for gravel pack placement purposes, the larger thediameter the longer will be the achievable packing length. Ofcourse, wellbore diameter affects other important operationssuch as drilling and running the screen (Martins 5). Anyway,since gravel packing is the most critical operation among allthe drilling and completion hydraulically related ones, largerdiameter wells can be an interesting alternative.

Effect of Water Depth. Figure 11 shows the water deptheffect for the geometric configuration 1. For a similar fracgradient it would be easier to extend the horizontal section atshallow waters. Normally, the frac gradients decrease with theincrease of water depth due to the decreasing sedimentthickness. So, deepwater wells are normally much morecritical than shallow water wells and the analysis for a givenfrac gradient does not express operational reality.

Effect of Reservoir Depth. Figure 12 shows the effect ofreservoir depth for the geometric configuration 1. In this case,it seems easier to gravel pack the long section for, for the samefrac gradient, in the deeper reservoir. The frac gradient isdefined as the frac pressure divided by the sediment thicknessand, for the deeper reservoir, the same frac gradient means alarger frac pressure. Normally, this fact reflects the operationalreality since the deeper the sediment layer the more competentwill be the formation. For the case study at 4 bpm pump rate,an increase in 600m reservoir depth resulted in about 200mextension of the maximum horizontal well length.

Extending Hydraulic Limit sThe previous item details the effect of important parameters(hole diameter, reservoir and water depths) on the hydrauliclimits for successful gravel packing. Such properties, however,are normally defined (although some discussion can be madeon well diameter). In the present item some strategies whichmay be performed in order to extend hydraulic limits whilegravel packing are discussed. The objective now is todetermine the maximum horizontal section without exceedingfracture pressure during the gravel packing placement phase.

Fluid Density. Normally, the fluid density is designed in away that the hydrostatic pressure generated at down hole ishigher than the pore pressure and lower than frac pressure.Once the operational window gets narrower, dynamic

pressures will certainly overcome frac pressures. One possiblealternative is to reduce the fluid weight to levels whichguarantee the total gravel pack displacement in the extendedwell. Figure 13 shows the effect of weight reduction on theextension of the horizontal well section limits. Among thestrategies proposed in this article, the reduction of fluiddensity is a very effective but risky strategy, since at aneventual pump stop, wellbore static pressure may be too lowand formation fluid influx may occur.

Open BOP Configuration. The BOP (Blow out preventer) isan equipment installed at the sea floor which allows thecontrol of unexpected gas or oil influx. Normally, the gravel

pack operation would be conducted with the closed BOPconfiguration.

The return flow is diverted, at the sea floor, to two pipelines (called kill and choke lines) usually with 3 indiameter which conduct the fluid back to the rig floor. Theflow through these sections results in expressive frictionlosses, specially at deepwaters, where their length is large. Inthe limit situation, when low frac pressure is found, analternative is to open the BOP and allow the return flowthrough the riser (normally a 20 in pipe), where friction lossesare negligible. To control the return rate, during the operation,it was necessary to install a “U tube” and a flowmeter in theflowline (Fig 14). This strategy has been used, in the lastyears, to permit gravel packing in deep and ultradeep waterenvironments. Fig. 15 shows the impact of opening the BOPon the hydraulic limits extension. Note that, using open BOPconfiguration it is possible to extend well length in 400 m.

Low Friction Loss Crossover Tools. One point of expressivelocalized friction loses is the crossover tool, string elementwhich diverts the downward flow from the interior of thestring to the annulus and the upward flow in the oppositedirection. The service companies invest in different tooldesigns in order to optimize operational issues and minimizefriction losses through the restrictions which divert flow.Table 1 shows different friction loss behavior for twocommercial tools while Fig. 16 shows its impact on thehydraulic limits extension. Note that using tool #1, it is

possible to extend well length in about 50 m.

Zero Rat Hole Configuration. As previously stated, the rathole is a critical issue in the operational window definition.Several efforts are being spent by the casing designcommunity to make possible a zero rat hole well. In this case,the lower operational limit would be loosened and an extendedwell operation could be run with lower flow rates. Fig. 17illustrates the gain in well extension limits when pumping the

base case at 3.5 bpm (zero rat hole) when compared to 6 bpm(with the rat hole). An additional issue to be addressed when

pumping at low flow rates is the tendency of alpha wavedeposition inside the work string.

Use of Drag Reducers. Drag reducers are polymeric additivesadded to a fluid in order to reduce friction losses during

pumping. Turbulence suppression described by Lumley 6,7 anddecrease of kinetic energy transport described by Virk 8 are

possible mechanisms for the phenomenon. According to Virk,efficient drag reducers can minimize friction losses up to 80%in clear solutions and up to 20% in solid suspensions. Duringthe placement of the gravel pack friction losses are generated

both by the solids suspension (at the downward flow throughthe string and at the annular flow through the open hole/screensection) and by clear solution (at the annular flow through thescreen/wash pipe section and at all the return flow through thewash pipe, casing annulus and kill/choke lines or riser annulusin case of open BOP configuration. Figure 18 illustrates theimpact of drag reducers efficiency from 10 to 50% on thehydraulic limits extension.

Large Alpha Wave Design. During horizontal open holegravel packing placement, the beta wave phase is critical sinceit generates abrupt pressure increases due to the divergence of

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annular flow from the open hole/screen section to the narrowannular screen/wash pipe section. A last alternative to make

possible open hole gravel packing at extended horizontal wellswould be to design a large alpha wave which would cover thescreen without significant pressure increase. The beta wavestage would be initiated and performed until frac pressurelimits allow. By this point, the operation would be interruptedand when the pressure is alleviated, the non consolidatedformation would collapse on the top of the alpha wave at theregions which the beta wave could not be placed.Theoretically the formation material would not reach thescreen since the operation was designed for total screencoverage by the alpha wave.

Certainly, this is a risky strategy, but it can allow annular packing in extreme cases, where all the other alternatives werenot applicable or would not create an operational window.Figure 19 shows the hydraulic limits extension gain for thelarge alpha wave strategy, when compared to the normalalpha/beta wave approach.

Use of Flow Divergence Valves. Beta wave placement pressures can be reduced by the use of flow divergence valves.In this concept, when the pressure reaches a pre-defined value,flow is diverted directly from the open hole to the interior ofthe washpipe, reducing the water path dramattically and,consequently, minimizing friction losses. Figure 20(Coronado 9) shows schematically the flow divergence processand figure 21 shows the impact of this bypass in the dynamic

pressure reduction, for a real operation in a well equipped withuntil three valves. In front of low frac formations, where thedynamic pressures reach easily the fracture pressure, thesedevices can be an interesting alternative to enable beta wave

placement.The quantification of the effects of using flow divergence

valves were made by computational simulations usingconfiguration #1 as the base case. The well extension gain fordifferent sceneries (fracture gradients), for a well equippedwith zero, one, two or three valves is illustrated in Fig. 22. Thegraph shows when one valve is set, is possible to duplicatewell length for same fracture gradient.

Use of Low Density Proppant. The latest alternative forgravel packing accomplishment in extreme cases is the use oflight proppants. The idea is to change current proppant used(sand or ceramic) for other material with smaller density. Thischange enables several operations where the pump pressure atthe end of beta wave would exceed the fracture formation

pressure in normal operations. Using a light proppant is possible to work with lower flow rates for same alpha wavehights, decreasing dynamic flow pressures. Figure 23 showsthe hydraulic limits extension gain for use of low density

proppants. Note that, using low density proppant is possible toenlarge well length in 300m.

Final RemarksOpen hole gravel packs in long horizontal wells are criticaloperations, specially in deepwater environments. Thestrategies proposed in this work consist on effectivealternatives to extented hydraulic limits and achieve success in

critical operations. Some of the alternatives (such as reducingmud weights, zero rat hole configuration and considering largealpha wave displacement) are associated with reasonable riskand should be considered only in situations where no otheralternative was successful. Other alternatives (such as dragreducers, low friction loss tools and open BOP configurations)are less risky and should be considered whenever necessary.Each operation depends a lot of the specific data of each areaand well configuration and should require a singular solutioneven when compared with a quasi-similar well. Besides,different alternatives are also proposed by the industry, such asflow divergence valves (Coronado 9) and alternate pathtechnology (Hurst 10). Generalized well design strategies arenot recommended for such complex operations.

AcknowledgmentsThe authors would like to thank Petrobras S.A. for permissionto publish this paper.

SI Metric Conversion Factors bpm x 377.4 E 00 = m 3.s-1

in x 39.3701 E 00 = m

lb/gal x 8.3454 E-03 = kg.m -3

psi x 1.4504 E-04 = Pa

psi/ft x 4.4207 E-05 = Pa.m -1

Nomenclatureh α = Alpha wave height, in

ID = Inside diameter, inOD = Outside diameter, inP b = Bottom hole pressure, psiP cs = Casing shoe pressure, psiP p = Pump pressure, psi

References1. Martins, A.L., Santana, M., Costapinto, C.: Evaluation of

Cuttings Transport in Horizontal and Near Horizontal Wells - ADimensionless Approach, paper SPE 23643 presented at theSecond Latin American Petroleum Engineering Conference,Caracas, Mar 8 – 11.

2. Martins, A.L., Magalhães, J.V.M., Calderon, A., .: “AMechanistic Model for Horizontal Gravel Pack Displacement”,

paper SPE 82247 presented at the 2003 SPE Europe FormationDamage Conference, The Hague, May 13-14.

3. Martins, A.L., Magalhães, J.V.M., Calderon, A., Mathis, S.P.,Trujillo, C., Nguyen, H.T..: “Experimental and TheoreticalSimulation of Gravel Pack Displacement in Extended HorizontalOffshore Wells”, paper SPE 86509 presented at the 2004 SPEInternational Symposium and Exhibition on Formation DamageControl, Lafayette, Feb. 18–20.

4. Marques, L. et al .: “An Overveiw of More Than One HundredTwenty Horizontal Gravel Packing Operations in Campos Basin”,

paper presented at the 2004 SPE Offshore TechnologyConference, Houston, May 03-06.

5. Martins, A.L., Aragão, A.F.L., Calderon, A., Leal, R.A.F.,Magalhães, J.V.M, Silva, R.A., “Hydraulic Limits for Drillingand Completing Long Horizontal Deepwater Wells,” paper SPE86923 presented at the 2004 SPE International ThermalOperations and Heavy Oil Symposium and Western RegionalMeeting, Bakersfield, Mar. 16–18.

6. Lumley, J.L.: “The Toms Phenomenon: Anomalous Effects in

Turbulent Flow of Dilute Solutions of High Molecular Weight

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Linear Polymers”, Applied Mechanics Reviews, 20(12), pp.1139-1149, 1967.

7. Lumley, J.L.: “Drag Reductions in Two Phase and PolymerFlows”, The Physics of Fluids, 20(10), part II, pp. 564-571, 1977.

8. Virk, P.S.: “Drag Reduction Fundamentals”, A.I.Ch.E. Journal21(4) (July 1975), pags. 625-656.

9. Coronado, M.P. and Corbett, T.G.: “Beta-wave Pressure ControlEnables Extended-Reach Horizontal Gravel Packs”, paper

presented at the 2001 SPE Annual Technical Conference andExhibition, New Orleans, Sept. 30 – Oct. 3rd.

10. Hurst, G. et al .: “Alternate Path Completions: A Critical Reviewand Lessons Learned From Case Histories With RecommendedPractices for Deepwater Applications”, paper SPE 86532

presented at the SPE International Symposium and Exhibition onFormation Damage Control, Lafayette, Feb. 18-20.

Table1 – Friction loss t ool testing

Pump rate (bpm) Pressure (psi) Pump rate (bpm) Pressure (psi)4 41 2 155 94 3 306 141 4 667 145 5 868 155 6 136

**** **** 7 172

Tool #2Tool #1

Fig. 1 – Injectio n stage

Fig. 2 – Alpha w ave stage

Fig. 3 – Beta wave stage

h α

SCREEN

BED AREA

OPEN HOLE

RESERVOIR

Fig. 4 – Cross section well

Gravel-fluid mixture

Front of gravel displacement

Casing shoe

screen

Casing shoe andcrossover tool

Alpha wave propagati on

screen

Beta wave propagation

screen

P p

P cs

P b

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500

1000

1500

20002500

3000

3500

4000

4500

5000

5500

8,00 10,00 12,00 14,00 16,00 18,00

ECD (lb/gal)

W e

l l d e p

t h ( m )

Fracture pressurePore pressure

Fig. 5 – Wide pressure window for shallow waters

1000

1500

2000

2500

3000

3500

4000

4500

5000

6,00 8,00 10,00 12,00 14,00 16,00

ECD (lb/gal)

W e

l l d e p

t h ( m )

Fracture pressurePore pressure

Fig. 6– Narrow pressure win dow for d eepwaters

Fig. 7 – Rat hole sch eme

4000

5000

6000

7000

8000

0 5 10 15

Flow rate (bpm )

P r e s s u r e

( p s

i )

Pressure at casing shoe

Fracture pressure

Operational Window

Fig. 8 – Defining operational window

0

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140

Elapsed Time (min.)

P r e s s u r e

( p s

i ) Pump pressure

Pressure at casing shoe

Fracture pressure

Fig. 9– Pressure propagation during the operation

0

500

1000

1500

2000

0,5 0,55 0,6 0,65 0,7

Gradiente de Fratura (psi/ft)

W e

l l L e n g

t h ( m )

4 bpm; conf.#1 8 bpm; conf.#1 4 bpm; conf.#28 bpm; conf.#2 8 bpm; conf.#3 10 bpm; conf.#3

Fig. 10– Effect of Wellbo re diameter

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0

500

1000

1500

2000

0,5 0,55 0,6 0,65 0,7

Fracture Gradient (psi/ft)

W e l l

l e n g

t h ( m )

4 bpm; Water Depth=1200m 4 bpm; Water Depth=1800m8 bpm; Water Depth=1200m 8 bpm; Water Depth=1800m

Fig. 11– Effect of w ater depth

0

500

1000

1500

2000

0,5 0,55 0,6 0,65 0,7


W e

l l L e n g

t h ( m )

4 bpm ; Reservoir Depth=3250m 4 bpm ; Reservoir Depth=3850m

8 bpm; Reservoir Depth=3250m 8 bpm; Reservoir Depth=3850m

Fig. 12– Effect of reservoi r depth

0

500

1000

1500

2000

0,45 0,5 0,55 0,6 0,65 0,7


W e

l l L e n g

t h ( m )

4 bpm; Fluid Densi ty=10 lb/gal 4 bpm; Fluid Densi ty=9.5 lb/gal8 bpm; Fluid Densi ty=10 lb/gal 8 bpm; Fluid Densi ty=9.5 lb/gal

Fig. 13– Fluid weight reduction

Fig. 14– “ U Tube” equipped with fl owmeter

0

200

400

600

800

1000

1200

0,52 0,54 0,56 0,58 0,6 0,62 0,64

Frature Gradient (psi/ft)

W e

l l L e g

t h ( m )

BOP openedBOP closed

Fig. 15– BOP configurations

0

200

400

600

800

0,54 0,56 0,58 0,6 0,62 0,64 0,66


W e

l l L e n g

t h ( m )

Tool #1 - 8 bpmTool #2 - 8 bpm

Fig. 16– Comparison between two different tools

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0

500

1000

1500

2000

0,56 0,58 0,6 0,62 0,64


W e

l l L e n g

t h ( m ) Rat hole - 6 bpm

No rat hol e - 3.5 bpm

Fig. 17– Rat hole comparis on

0

500

1000

1500

0,56 0,58 0,6 0,62 0,64


W e

l l L e n g

t h ( m )

No drag reducer 10% fric tion loss r eduction20% fric tion loss r eduction50% fric tion loss r eduction

Fig. 18– Drag reducers action

0

400

800

1200

1600

2000

0,56 0,58 0,6 0,62 0,64


W e l l L e n g

t h ( m )

Normal operation - 7 bpmTotal screen cov ering - 6.38 bpm

Fig. 19– Operational chart

Fig. 20– Flow divergence valves wo rking scheme

Fig. 21– Valves actuation impact in th e pressure reduction d uringbeta wave stage

0

500

1000

1500

2000

0,5 0,55 0,6


W e

l l L e g

t h ( m )

No valve1 Valve2 Valves3 Valves

Fig. 22– Well length gain w hen flow divergence valves are used

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0

500

1000

1500

0,56 0,58 0,6 0,62 0,64


W e

l l L e n g

t h ( m )

Sand 20/40Light Proppant

Fig. 23– Well length gain when low density proppant are used

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