Society of Petroleum Engineers

SPE 25891

Perforation Friction Pressure of Fracturing Fluid SlurriesJ.D. Willingham, H.C. Tan, and L.R. Norman, Halliburton Services

SPE Members

Copyright 1993, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium held in Denver, CO, U.S.A., April 12-14, 1993.

This paper was selected for presentation by an SPE Program Committee following review of information contained In an abstract submitted by the author(s). Contents of the paper,as presented, have not been reviewed by the Society of Petroleum Engineers and are SUbject to correction by the author(s). The material, as presented, does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Societyof Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgmentof where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A. Telex, 183245 SPEUT.

ABSTRACT

Even though pressure drop across perforations forclean fracturing fluids can generally be accuratelypredicted, it is not well understood for fracturing slurries.In this paper, two wellbore models-one transparent andone high pressure-were used to study the perforationfriction pressure behavior of sand laden fluids. Thetransparent model constructed with cast acrylic allowedvisual observation of fluid exchange in the "rat-hole" andflow patterns of the slurries in the wellbore and throughthe perforations. Critical velocity at which sand beginsto screenout at the perforations was also determined.Tests were performed in the high pressure model varyinggel concentration, sand concentration, proppant size, andperforation diameter to gather pressure drop data. Theeffect of the ratio of perforation diameter to the averageproppant size on the sand screenout tendency at theperforation was also investigated.

A correlation to predict the change of perforationcoefficient due to proppant erosion was developed fromthe laboratory data. This paper presents a fieldprocedure to better estimate the change of perforationcoefficient during proppant stages for calculating thechange of perforation friction.

References and illustrations at end of paper

479

Incorporating this change of perforation pressure dropduring proppant stages in the real-time bottomholetreating pressure calculation will enhance interpretationof the treatment analysis.

INTRODUCTION

During a fracturing treatment, fluid containingproppant is pumped down a tubular string, throughperforations, and into a fracture. Without a bottomholetool or reference string, the bottomhole treating pressureis calculated from the following equation.

BHTP = Pw + Ph -P, - Ppi (1)

where:

Bottomhole Treating Pressure (psi)Wellhead pressure (psi)Hydrostatic pressure (psi)Fluid friction pressure in tubular goods(psi)Friction loss across the perforations (psi)

Using an on-site computer system to performreal-time fracturing pressure analysis to predict fracture

2 Willingham. J.D.• Tan. H.C.• and Norman. L. R. SPE 25891

propagation requires reliable estimates of the BHTP .1-3

With recent advances in computer data acquisition andmeasurement systems fairly accurate wellhead pressureand hydrostatic pressure in Eq. 1 can be obtained. Withbetter quality control of fracturing fluids and moreaccurate fluid rheological properties available on-site,friction pressure for various fracturing fluids can normallybe predicted accurately as we11.4

-10 The principal

unknown in BHTP prediction from Eq. 1 is Ppl ' It isusually assumed to be zero, or negligible in the analysisof BHTP. In some cases, especially for the treatmentswith high rates and in wellbores with small numbers ofperforations, this assumption may not be valid.

The Ppf may change during the proppant stagesdue to perforation erosion. 11 If it is not quantified beforetreatment, this change in PpI may mask the truebottomhole treating pressure behavior. It may beinterpreted as breaking out of the treated zone in theanalysis and the "screenout mode" may be indeterminate.A treatment may be terminated prematurely due to thismisinterpretation.

Limited entry fracturing techniques are normallyused for treating multiple zones. In the limited entrystimulation treatment design, the BHTP and PpI of eachzone are used to determine the number of perforations tobe shot in each zone to help control fluid entry. Successof the limited entry treatment depends on the accuratecalculation of the perforation friction. If the Ppl changesduring a limited entry treatment, the desired injectionprofile may not be achieved.

The pressure drop across the perforations isnormally calculated from the following equation. 12

•13

shown in Fig. 1. Determination of Cp can dramaticallyaffect the predicted pressure drop across theperforations. Based on the experimental data. Cp valuesare in the range of 0.5 to 0.6 for perforations that havenot had abrasive fluid pumped through them. 14 Whenpumping abrasive fluids such as sand slurries, the Cpvalue may change to a value of 0.6 to 0.95 due toperforation erosion. ll

•14 The exact value of change

cannot be well defined.

This paper addresses a method to better definethe Cp value for use in Eq. 2 during a fracturingtreatment. This is made possible by studying theperforation friction pressure behavior of various fracturingslurries in transparent and high pressure wellbore models.The phenomenon of flow approaching the "perforationscreenout" and the critical velocity required to suspendthe proppant particles as the slurry exits the wellborethrough the perforations were investigated in thetransparent model. The effects of slurry viscosity anddensity on the perforation friction pressures were studiedin the high pressure wellbore model. The effect of theratio of perforation diameter to proppant size, Dperl/Dprop,is also discussed in this paper.

This paper provides a recommendation on thedesign of perforation size for fracturing treatments toprevent bridging of proppant particles in the perforationstunnels. A field application method is proposed todetermine the change of Cp due to sand erosion beforethe treatment. This will allow a better interpretation ofthe real time bottomhole treating pressure analysis andhence improve the treatment optimization.

EXPERIMENTAL

0.2369Q2 eN,2 D4 2·

P Cp

(2) Transparent Model

Apparatus

Total flow rate (bbl/min)Density of fluid (lb/gal)Number of perforationsDiameter of perforations (in.)Coefficient of discharge

In Eq. 2, Cp is the ratio of diameter of the fluidstream at the vena contracta (point of lowest pressuredrop) to the diameter of the orifice or perforation as

480

Figure 2 shows the transparent modelconstructed with cast acrylic. The model was 12ft highand had an outside diameter of 5 in. (10 = 4 in.). Fourholes were drilled 90 0 offset from one another in a 1-ftsection to represent four shots per foot of perforations.The "rat-hole" below the perforations was about 4 ftdeep. The sizes of the perforations could be changedfrom 1/4 in. through 1/2 in. by replacing the bull plugs.Three sets of bull plugs with 1/2 in., 3/8 in., and 1/4 in.diameter holes were used as perforations in the tests.

A backpressure regulator with a sand screen

SPE 25891 Perforation Friction Pressure of Fracturing Fluid Slurry 3

installed upstream of the model was set at 200 psi toprotect the model from overpressure. The flow rate wasmonitored with a 1-in. 10 Foxboro magnetic flow meter.A 200 psi Viatran pressure transducer was installed atthe inlet to the model. A 5M Deming centrifugal pumpwas used to circulate the slurry in a 50-gal stainless steeltank to maintain the sand suspension in the slurry. Thiscentrifugal pump was also used to feed the slurry to a3L6 progressive cavity Moyno pump. A 1-in.Micromotion mass flow meter with density readout wasused to measure flow rate and slurry density of the flowexiting each perforation. The fluid was mixed in a 200­gal ribbon blender and crosslinker, if used, was injectedinto the eye of the centrifugal pump with an ISCO Model5000 syringe pump.

Procedure

Gelling agent used in the transparent model wasCMHPG at concentrations of 20,30,40, and 50 Ib/Mgal.For all tests in the transparent model, 20/40 Brady fracsand was used. Sand slurry was pumped through fourperforations starting at 40 gal/min and the rate wasreduced until screenout at the perforation occurred. Theflow behavior and the screenout phenomenon at theperforations were recorded with a video camera. Thesand concentrations tested were 1, 3, 5, 8, and 10Ib/gal. The velocity through the perforations(rate/perforation cross-sectional area) at which screenoutoccurred was determined to be the critical velocity for aparticular slurry tested. A few tests were also performedwith 40 Ib/Mgal CMHPG crosslinked with titanate and30 Ib/Mgal HPG crosslinked with borate.

High Pressure Model

Apparatus

Figure 3 is a schematic of the experimental highpressure wellbore model. The wellbore was constructedwith a 8-ft section of 5.S-in. 00, 5.0-in. 10, 14 Ib/ft J-55casing. Four holes were drilled 90° offset from oneanother in a 1-ft section. The bottom perforation was 1ft from the bottom of the model. The holes were 3/4 in.NPT drilled and tapped to accept a 3/4 in. nozzle with atungsten carbide insert through which the nozzle openingof 3/16 in. was drilled (Fig.4). The perforation tunnellength on these nozzle was 1 in. The carbide nozzleswere chosen over stainless steel because of theircapability to resist erosion by sand slurries.

481

This model allowed the tests to be performed atpressures up to 1,000 psi. A backpressure regulator setat 700 psi was installed on the pressure dampener of thepump to protect the pump and system fromoverpressure. The pump and plumbing system for testingwith the high pressure model was very similar to the onefor testing with the transparent model. A 1,000 psiValidyne pressure transducer was used to gather thepressure drop data across the perforation. As in thetransparent model, the slurry density and mass flow ratewere monitored with a 1-in. 10 Micromotion mass flowmeter and a magnetic flow meter.

Procedure

In the high pressure wellbore model, the pressuredrop data across a single 3/16 in. or 1/4 in. perforationfor 20, 40, and 60 Ib/Mgal HPG gel fluids containing 2,4, 6, 8, and 10 Ib/gal 20/40 or 8/16 Brady frac sandwere gathered. The tungsten carbide perforation wasreplaced after each test with one gel concentration.Before gathering data for each sand concentration, acalibration test was done with clean fluid to determinethe Cp value. At each sand concentration, the data weregathered at various rates. Data were also gathered forthe 3/8 in. perforations made with stainless steel.

DISCUSSION OF RESULTS

Flow Pattern Observed in Transparent Wellbore Model

"Rat-hole" Fluid Exchange

The fluid exchange in the "rat-hole" below theperforations was visually observed in the transparentwellbore model. Before the test, the entire wellbore andthe "rat-hole" were filled with 2% KCI. The fluid in the"rat-hole" was completely exchanged with the wellborefluid when the gelled fluid, either crosslinked oruncrosslinked, was pumped into the wellbore andthrough the perforations. When the sand stage wasstarted, the gelled fluid in the "rat-hole" was displacedwith the slurry in a few seconds. This fluid exchange inthe "rat-hole" may be due to the fluid density differencebetween the wellbore and the "rat-hole" fluids.

Slurry Flow Pattern for Linear Gel

After fluid exchange in the "rat-hole", the sandsettled in the "rat-hole" for the tests with linear gels.The level of sand bed in the "rat-hole" rose continuouslythroughout the test until within a few inches from thebottom of the perforations. Due to sand settling as the

4 Willingham. J.D.• Tan. H.C.• and Norman. L. R. SPE 25891

slurry travelled down the wellbore. the effluent from thebottom perforation exhibited the highest sandconcentration while the effluent from the top perforationhad the lowest sand concentration. Sand concentrationdistribution in the effluents from the four perforationswas more uniform for higher viscosity linear gels withlower sand concentrations.

While the rate was decreased. the sandsegregation in the wellbore grew substantially. At lowerrates. the sand began to form a dune in the wellbore onthe opposite side from the bottom perforation. When therate was dropped to below 1 gal/min per perforation withslurry flowing through the 1/4-in. perforations at avelocity of 6.5 ft/sec, sand began to bridge in the tunnelof the bottom perforation. This sand bridging at velocitiesbelow 6.5 ft/sec resulted in rapid screenout at thebottom perforation. Since sand settling placed a highsand concentration across lower perforations, screenoutalways started from the bottom perforation.

The critical velocity through the perforation atwhich screenout at perforation occurs is independent ofthe viscosity of the sand carrier fluids. Instead, itdepends on the perforation diameter and the sand particlesize. For all the gel concentrations tested, sand bridgingwas not observed until the velocity through theperforation was dropped to below 6.5 ft/sec.

Slurry Flow Pattern for Crosslinked Gel

For the tests with crosslinked slurries, sandsettling in the "rat-hole" and wellbore was not observed.Apparent flow stream and boundary were seen in thewellbore with the crosslinked slurries. The fluid near thewall appears to be stagnant.

Restriction of Flow outside Perforations

One interesting observation made in this studywas that the restriction of flow outside the perforationwould result in rapid perforation screenout. When thishappened, a particle node formed near the perforationand the slurry was diverted to other perforations through'a flow channel in the wellbore. Test pressure increasedas the cross-sectional area of the flow channel becamesmaller due to the growth of the particle node. Thisphenomenon of perforation screenout due to restrictionof flow outside the perforation (in the fracture) mayexplain the unexpected treating pressure increaseduring proppant stages.

Pressure Drop Across Perforations

A series of tests was conducted in the highpressure wellbore model using a 3/16 in. perforation tostudy the effects of slurry density and viscosity onperforation friction pressure. The pressure drop across

.the perforation was plotted versus square of flow rate(Q2) for each fluid. Figures 5 and 6 show the data for 60Ib HPG/Mgal gel and 60 Ib HPG/Mgal gel with 4 Ib/gal20/40 sand across the 3/16 in. perforation. Cp valueswere obtained from the slope and are summarized inTables 1 and 2.

Table 1 shows the Cp values before theperforations were exposed to abrasive fluids. The valuesare between 0.6 and 0.7. As shown in Table 2, the Cp

value changes slightly with the amount of sand flowingthrough the perforation even though high Rockwellhardness material such as tungsten carbide was used asthe perforation insert. To eliminate the effect of changeof Cp value on the analysis. the perforation pressure datawere multiplied with the square of Cp (P*C/) and plottedvs. square of flow rate.

Effect of Slurry Viscosity

Figure 7 shows the effect of viscosity on theperforation friction pressure across a 3/16 in. perforationfor gelled fluids without sand. The data for 4. 8. and 10Ib/gal 20/40 Brady sand in various gelled fluids arepresented in Figs. 8 to 10. In these figures. the term(P*C/) is plotted as a function of slurry fluid viscositywith flow rate as a parameter. The slurry fluid viscositywas obtained from the clean fluid viscosity multiplied bya factor to account for the effect of sand concentrationon fluid viscosity. IS The solid lines in these figures arecalculated (P*Cp

2) values at each flow rate from EQ. 2.Other than for the slurry fluids with 8-10 Ib/gal sand in20 Ib/Mgal gel, the data have indicated that the slurryviscosity has little effect on the perforation friction. Eventhough EQ. 2 was derived from the experimental datawith water,12'14 it is valid for use with slurries as long asthe gelled fluid maintains good proppant transport.

Pressure drop data across the perforationreported in this paper are the combination of the (1)pressure drop due to the orifice entry effect and (2)pressure drop across the 1-in. perforation tunnel. Asindicated by EQ. 2, the viscosity should not have any

482

SPE 25891 Perforation Friction Pressure of Fracturing Fluid Slurry 5

effect on the pressure drop due to orifice entry. For 40and 60 Ib/Mgal gels, the pressure drop across the 1-in.tunnel may be negligible or too insignificant to bedetected in the laboratory. The experimental data matchvery well with the calculated (P*C/) values from Eq. 2.The Reynold's number for the 20 Ib/Mgal gel through theperforation was much higher than the numbers for 40and 60 Ib/Mgal gels. Flow with higher Reynold's numbernormally exhibits higher friction pressure in the conduit.This higher Reynold's number, in conjunction with theeffect of high sand concentration, may result in higherfriction pressure in the 1-in. perforation tunnel for 8 to 10Ib/gal slurries in 20 Ib/Mgal gel. Therefore, theexperimental data for the slurries in 20 Ib/Mgal gel arehigher than the calculated IP*C/) values from Eq. 2which only considers the pressure drop due to orificentry.

Effect of Slurry Density

In Figures 11 to 13, the P*C/ terms for 20, 40,and 60 Ib HPG/Mgal gels containing 0, 2,4,6, 8, and 10Ib/gal sand were plotted as a function of slurry density todemonstrate the effect of slurry density on theperforation friction. As shown in these figures, theexperimental P*C/ values and the slurry density show alinear relationship for gel fluids containing less than 8Ib/gal. Again the solid lines are the calculated P*Cp

2

values from Eq. 2. When the sand concentrations areabove 8 Ib/gal, some deviations from this linearrelationship are observed especially in the tests with 20Ib/Mgal gel. As discussed earlier, this may be due to thehigher friction loss in the 1 in. perforation tunnel for theslurries in 20 Ib/Mgal gel.

Effect of Perforation Diameter to Proppant Size Ratio

In the tests for the fluids containing 20/40 meshBrady sand through 3/16 in. perforations, the ratio of theperforation diameter to the proppant size was about 7.A series of tests was conducted in the laboratory using1/4 in. perforations and 8/16 mesh sand to study theeffect of this ratio on the perforation friction pressure.The ratio for the 1/4 in. perforation and the averagediameter of 8/1 6 mesh sand was about 3.1 . For 1 and2 Ib/gal sand, the effect of slurry density on the frictionpressure follows a similar trend as observed in the testswith the ratio of 7. However, when the sandconcentration was over 2 Ib/gal, the perforation screenedout at all rates. Some tests were also performed with3/8 in. perforations using slurries containing 8/16 meshsand in which case the ratio was about 4.7. The dataindicated that screenout at perforation occurred at a sand

483

concentration of about 8 Ib/gal.

Figure 14 shows the maximum sandconcentration that can be transported throughperforations. 16 Gruesbeck and Collins 16 have observedfrom their study that bridging occurred inside aperforation if the ratio of the perforation diameter toaverage proppant size was less than 6. The observationmade in this paper is in good agreement with their work.The experimental data using the ratio of 3.1 indicatedthat the perforation began to screenout due to bridgingat a sand concentration of about 2 Ib/gal. For the testswith the ratio over 7, our data have indicated that sandbridging will not occur for slurries up to 10 Ib/gal sand,even using water as the sand carrier fluid. However, therate has to be maintained above the critical flow ratewhich is about 1 gal/min per perforation. The ratio atwhich sand bridging occurs is insensitive to the viscosityof the sand carrier fluid. For the ratio of less than 5,sand bridging occurred for 60 Ib/Mgal linear gel. The 60Ib/Mgal gel has shown to have good proppant transportefficiency for the test with the ratio greater than 7.

For the slurry to flow through the perforationsduring a fracturing treatment, one needs to have the ratioof perforation diameter to proppant size greater than 5.0.

Effect of Rockwell Hardness of Perforation Materials

In this paper, Tungsten Carbide (RockwellHardness, Rc of 95) was used as an insert for most ofthe tests to minimize erosion. Some tests were alsoperformed with perforations made of stainless steel (Rcof 20). Figure 15 shows the change of Cp as a functionof a dimensionless term, S, which is defined in thefollowing Eq. 3.

S, = Scum / p*Dper, .......•..•............. (3)

Where:

Slurry density lib/gal)Cumulative amount of sand flowthrough the perf. lib)Diameter of the perforation (in.)

In Fig. 15, the perforation erosion behavior forTungsten Carbide material was compared with the datagathered with perforations shot in J-55 casing IRe of20).17 In the study by Crump,17 the perforation erosionbehavior due to sand-laden slurries was investigated in a4 1/2 in. J-55 casing with single drilled perforations of

6 Willingham, J.D., Tan, H.C., and Norman, L. R. SPE 25891

1/2 in., 7/16 in., 3/8 in. and 9/32 in. diameters. Variousamounts of 20/40 sand in 50 Ib/Mgal HPG gelled fluidswere pumped through the perforations. The sandconcentrations used were 12, 16, and 20 Iblgal.

As shown in Fig. 15, the change of Cp valuescaused by sand flowed through the stainless steelperforation gathered in our experiment matches very wellwith the erosion behavior for the perforations in J-55casing. The Rockwell hardness of stainless steel is verysimilar to J-55. Since the Rockwell hardness of thetungsten carbide material is much higher than the Rcvalue of J-55, the perforations with tungsten carbideshowed better resistance to the proppant erosion.

Correlation to Predict Perforation Erosion

7.

8.

proppant laden fluids, estimate the amount ofsand that had been pumped through theperforations (Scum) from the previous job report.From Scum' slurry density, and perforationdiameter, estimate the initial Cp value using Fig.15.

Use Fig. 16 to estimate the final Cp value fromthe initial Cp value and the amount of sand thatwill be pumped for the treatment.

With the known values of the change of Cp andthe number of perforations open, calculate thechange of the pressure drop across theperforations during the treatment.

. From the data gathered in our study and Crump'sReport,17 an empirical correlation was derived to predictthe change of perforation coefficient caused by erosionfrom sand slurry flowed through a perforation. Figure 19shows the plot of the final Cp values as a function of theamount of sand pumped through perforations for variousinitial Cp values.

PROPOSED FIELD PROCEDURE TO ESTIMATE CHANGEOF Cp

1. Break down or "bailout" perforations to ensurethat all perforations are open.

The empirical correlation shown in Figs. 15 and16 can be incorporated into a real-time BHTP computerprogram to facilitate the calculation on-site.

CONCLUSIONS

1 . Fluid viscosity has been experimentally found tohave little effect in transporting proppant from avertical wellbore through perforations as long ascritical velocity is maintained. However, forslurry with linear gel, proppant may be depositedin the "rat-hole" after the "rat-hole" fluid isdisplaced with the slurry. This "rat-hole" fluidexchange may be due to density differencesbetween the "rat-hole" fluid and the slurry.

2.

3.

4.

5.

Pump at least two tubing volumes of pre-pad orgel fluids at the designed treatment rate. It ispreferable to use 40 Ib linear gel to obtain moreaccurate pipe friction pressure. The effect ofpipe roughness on friction pressure can beminimized with 40 Ib linear gel.

Shut-in and take ISIP (Pi)'

From ISIP, wellhead pressure (Pw) and pipefriction (PI)' calculate the perforation friction (Ppl )

using the following equation.

Determine the effective perforation diameter fromthe perforation service company literature.

2.

3.

4.

To prevent sand bridging in perforation tunnels,it is important to have the ratio of perforationdiameter to average particle size over 5 andmaintain the velocity through perforation over 6to 7 ft/sec.

As long as the gelled fluid exhibits good proppanttransport characteristics in the wellbore and nosand bridging occurs in the perforation tunnel,pressure drop across the perforation for the slurryfluid can be calculated using Eq. 2.

Using the correlation provided in this paper, thechange of perforation coefficient during proppantstages due to erosion can be estimated.Knowing the change of Cp value, the perforationfriction during proppant stages could beaccurately predicted.

6. If the perforations have never been exposed toabrasive fluid, assume an initial Cp value of 0.6.If the well was previously fractured with

484

SPE 25891 Perforation Friction Pressure of Fracturing Fluid Slurry 7

REFERENCES

NOMENCLATURE

ACKNO~EDGEMENTS

p = Density of fluid or slurry, lib/gal)

Shah, S.N., Lee, Y.N., and Jensen, D.G.: "FracTreatment Quality Improved with Field RheologyUnit," Oil & Gas J., (Feb. 4, 1985), 47-51.

Shah, S.N., Lord, D.L., and Tan, H.C.: "RecentAdvances in the Fluid Mechanics and Rheology ofFracturing Fluids," paper SPE 22391, presentedat the SPE International Meeting on PetroleumEngineering held in Beijing, China, March 24-271992.

Shah, S.N.: "Correlations Predict FrictionPressure of Fracturing Gels," Oil & Gas J. (Jan.16, 1984) 92-98.

Melton, L.L. and Malone, W.T.: "Fluid MechanicsResearch and Engineering Application in Non­Newtonian Fluid System, SPEJ, (March 1964)56.

Shah, S.N.: "Effects of Pipe Roughness onFriction Pressure Fracturing Fluids," paper SPE18821 presented at the SPE ProductionOperations Symposium held in Oklahoma City,Oklahoma, March 13-14, 1989.

Hannah, R.R., Harrington, L.J., and Lance, L.C.:"The Real-Time Calculation of AccurateBottomhole Fracturing Pressure from SurfaceMeasurements Using Measured Pressure as aBase," paper SPE 12062, presented at the 58thAnnual SPE Technical Conference and Exhibition,San Francisco, (Oct. 5-8, 1983).

Crump, J.B. and Conway, M.W.: "Effects ofPerforation Entry Friction on Bottomhole TreatingAnalysis," paper SPE 15474 presented at the61 st Annual Technical Conference and Exhibitionof the Society of Petroleum Engineers held inNew Orleans, LA, October 5-8, 1986.

Lord, D.L. and McGowen, J.M.: "Real-TimeTreating Pressure Analysis Aided by NewCorrelation," paper SPE 15367 presented at the1986 SPE Annual Technical Conference andExhibition, New Orleans, Oct. 5-8.

10.

11 .

6.

4.

7.

9.

5.

8.

Bottomhole treating pressure, (psi)Coefficient of dischargeDiameter of perforations, (in.)Average proppant diameter, (in.)Number of perforationsInstantaneous shut-in pressure, (psi)Fluid friction pressure in tubular goods,(psi)Hydrostatic pressure, (psi)Friction loss across the perforations, (psi)Wellhead pressure, (psi)Total flow rate, (bbl/min)Dimensionless termCumulative amount of sand flowedthrough the perf, lib)

2. Nolte, K.G. and Smith, M.B.: "Interpretation ofFracturing Pressures," J. Pet. Tech. (September,1981) 1767-1775.

Ph =PpI =PwQ =St =

Scum =

1. Swanson, G.S. and Meeken, R.B.: "An Analysisof Fracturing Pressures in South Belridge and LostHills Field," paper SPE 9935 presented at the1981 SPE California Regional Meeting,Bakersfield, CA, March 25-26.

Greek Symbols

BHTPCp

Dperf

Dprop =Np =PiP,

The authors would like to thank themanagements of Shell Exploration and Production andHalliburton Services for their support and aid throughoutthis project. Special thanks is extended to Dr. JimLawson and Ms. Cindy Taff of Shell for their technicalsupport. The authors would also like to thank BennyHulsey, Bill Shipman, and Mike Clark of HalliburtonServices Research Center for their assistance in gatheringthe laboratory data.

3. Conway, M.W., McGowen, J.M., Gunderson,D.W., and King, D.G.: "Prediction of FormationResponse From Fracture Pressure Behavior,"paper SPE 14263 presented at the 1985 60thAnnual Technical Conference and Exhibition ofSPE, Las Vagas, September 22-25, 1985.

12. Crane Engineering Department, Eds. Flow ofFluids Through Valves, Fittings, and Pipe,Technical Paper No. 410, 1988, Crane Co. PP. 2­14, 2-15, 3-14, A-20.

485

8 Willingham, J.D., Tan, H.C., and Norman, l. R. SPE 25891

13. Perry R.H. and Chilton, C.H.: Chemical Engineers'Handbook, 5th Edition PP 5-14,5-15 & 5-16.

14. "Limited Entry for Hydraulic Fracturing,"Halliburton Internal Fracturing Technical PaperNo. F3077.

15. Shah, S.N.: "Rheological Characterization ofHydraulic Fracturing Slurries," paper SPE 22839presented at the 66th Annual TechnicalConference and Exhibition of the SPE held inDallas, TX, October 6-9, 1991.

16. Gruesbeck, C. and Collins, R.E.: "ParticleTransport Through Perforations," SPE 7006presented at the Third Symposium on FormationDamage Control of the Society of PetroleumEngineers held in Lafayette, Louisiana, February15-16, 1978.

17. "High-Sand ConcentrationTest for 1/2", 7116",Perforations, " HalliburtonReport, February, 1983.

Perforation Friction3/8", and 9/32"Internal Laboratory

486

Table 1

Perforation Coefficient Before Exposed to Abrasive Fluids

Fluid Perf Size Perf. Cp

Fluids Visco (cPs) (in.) Material Value

Water 1.0 3/16 Tungsten Carbide 0.59

20 Ib gel 9.0 3/16 0.6225 Ib gel 15.1 3/16 0.6340 Ib gel 31.8 3/16 0.6350 Ib gel 49.4 3/16 0.6560 Ib gel 62.0 3/16 0.65

Water 1.0 1/4 Tungsten Carbide 0.64

60 Ib gel 58.0 1/4 0.64

Water 1.0 3/8 Stainless Steel 0.7

60 Ib gel 58.0 3/8 Stainless Steel 0.63

Table 2

Perforation Coefficient After Exposed to Abrasive Fluids

Clean Fluid Sand Conc. Perf. Size Perf. Cp

Fluids Visc., (cPs) (Ib/gal) (in.) Material Value

Water 1.0 0 3/16 Tungsten Carbide 0.59

60 Ib gel 62 2 3/16 Tungsten Carbide 0.6560 Ib gel 62 4 3/16 Tungsten Carbide 0.6760 Ib gel 62 6 3/16 Tungsten Carbide 0.6760 Ib gel 62 8 3/16 Tungsten Carbide 0.7460 Ib gel 62 10 3/16 Tungsten Carbide 0.8

Water 1.0 0 3/8 Stainless Steel 0.7

60 Ib gel 62 4 3/8 Stainless Steel 0.760 Ib gel 62 8 3/8 Stainless Steel 0.9

487

5"0.0.

D

4"'.D.Cal Acrylic

P;pe

R•• Hole

~4'

~l'

o ,-

o4 Perf.-M-

1

DMoyna

Pump

M.. FIowmeter/DeDlOlllcler

Centrifupl

Pump

Fig. 2 Transparent Wellbore Model

D

1 Heat EtthaDler I (><:l MalDClic Flowmeter, , ,If')<j I

o v

Dperf

fDv

Cd

1

iD

perf

Flow

i

Fig.1 Orifice-Square Edge Perforation

Fig. 4 PerforaUon with InsertD

Steel Bull Plug 3/4' NPTL \

H'O.D. tS"I.D. I

~ IJ-55 .'Ribbon

"

I oiBlender rp CasiDa I ID Tungsten Carbide Insert

4 Perro I ~I'

Drain Flowmeten

Fig. 3 High Pressure Wellbore Model

60 Ib HPG/Mgal, 3/16" Perf.800 r-I----------------------,

60 Ib HPG/Mgal with 4 Ib/gal 20/40 sand, 3/16" Perf,1000, 1

- 600'iiiQ.-Q.0.. 400C(1)..::::Jfnfn(1)..D..

-'iiiQ.-Q.o..C(1)..::::Jfnfn(1)..

D..

Square of Flow Rate (gal/mln)2

Fig.6-Pressure Drop Across Perforation

325275225175125750' I ,

250' I

25 75 125 175 225 275 325

Square of Flow Rate (gal/min)2

Fig.5-Pressure Drop Across Perforation

10 20 30 40 50 60 70 80

Slurry Viscosity @ 170/sec (cps)

Fig.a-Effect of Fluid Viscosity

• 10 gpm. . ~• 8.7 gpm

0" " I

o

4 Ib/gal 20/40 Sand, 3/16" Perf.800..--,-----------

:=- 600 ...(I)c.- ... • 22.4 gpm

Na. •0>< 400 • .20 gpm

CD X..:::l X

X 17.3 gpm

(I)(I) ACDIi: 200 A

A 14.1 gpm

12010080604020

Clean Fluid Viscosity @ 170/sec (cps)

Fig.7-Effect of Fluid Viscosity

Ir ... 22.4 gpm... • ...... ...• • • • 20 gpm• • •~ X K R K 17.3 gpmX X

-,-...1,4.1 gpm- -

10 gpm• - ';'8.7 gpm•

o Ib/gal 20/40 Sand, 3/16" Perf.600

oo

-Ui.8:400

Na.o><~:::l

~ 200~D.

~

...

8 Ib/gal 20/40 Sand, 3/16" Perf.800,

_______....,, y 22.4 gpm

•

x

• • 10 gpm• •8.7 gpm

...

...

•

--------------......... 14.1 gpm

--------------.,.22.4 gpm

-------------~x17.3 gpm

x .20 gpm

••

•

...

...

-';;c.-N a., 600o><

f 400::s(I)(I)

fa. 200

10 Ib/gal 20/40 sand,3/1611 Perf.1000, ,

800

• .14.1 gpm

- z 17.3 gpm2{

:....... .20 gpm

•x

• .10 gpm• • •• 8.7 gpm

...

•:::- 600(I)C.-Na.,

o>< 400f::s(I)

~D:. 200

100806040200" I

o100806040200' I I ,

oSlurry Viscosity @ 170/sec (cps)

Fig.9-Effect of Fluid ViscositySlurry Viscosity @ 170/sec (cps)

Fig.10-Effect of Fluid Viscosity

22.4 gpm

20 gpm

17.3 gpm

...

, , I

2 4 6 8 10

ro

800-';;a.-N a., 600o><

~ 400 x ~ 14.1 gpm

= l~ ...Q) ... • 10 gpmIi: 200.-. ::~ .., gpm

til

,1000 , Sand Concentration In Ib/gal

40 Ib HPG/Mgal, 3/16" Perf.

22.4 gpm

20 gpm

17.3 gpm

14.1 gpm

10 gpm

8.7 gpm

...

•

- ...x

I , ,

2 4 6 8 10

Sand Concentration In Ib/gal,o

...- A• • • • • •. .,.

1200, ,

1000

-enS: 800

Na.,

o>< 600

f::s= 400fa.

200

20 Ib HPG/Mgal, 3/1611 Perf.8

0' , I , I I

8 9 10 11 12 13 14141312111090' I ! I I I

8

Slurry Density (Ib/gal)

Fig.11-Effect of Slurry Density

Slurry Density (Ib/gal)

Fig.12-Effect of Slurry Density

60 Ib HPG/Mgal, 3/1611 Perf.11000 1 Sand Concentration In Ib/gal

I I I I

o 2 4 6 8 10

•

From Ref.16

/

Bridging Region

81 t

6~

CD CDQ; .~EUJ.!"CC e 4

CISern.2 CD- C)e CIS.2 Q; 2lD~Q,

22.4 gpm

17.3 gpm

• ......... 14.1 gpm

A 20gpm

:&

a : L---+ 10 gpmI ;..8.7 gpm

Jr A

800-'iiic.-No. 600o><

2! 400:::JfI)fI)CD~

Q, 200

Initial Cp=O.9- -c.

o.:e 0.9CD'0

~00.8oeo:; 0.7~

.gCD

Q, 0.61iie

u:::0.5 r t I I

o 1 2 3 4 5 6

Amount of Sand Pumped during treatment (M Ibs)

Fig.16-Perforation Erosion due to proppant

1 1 t

01 I t 1

o 2 4 6 8 10 12

Max. Sand Concentration at Screen-out (Ib/gal)

Fig.14-Sand Bridging in Perforation

0 1 t 1

8 9 10 11 12 13 14

0'-"'"'= Itt ttl

o 1 234 5 6

Dimensionless Number S t (SIPOpe3rf)

Fig.15-Effect of Perforation Material on Erosion

Slurry Density (Ib/gal)

Fig.13-Effect of Slurry Density;

Perf. Dia.:9/32 11,3/1611, 1/411,3/811

, 1/211

- 0.5e.!

e l 'CD 0.4o ~

~ y J-55 Casing;: 0.3 ~ <7 &gCIS~

0

~ 0.2il Slalnless SI:el-

- ---- •CDC)

~ 0.1 ~-

•~ • Tungsten Carbide0

SPE 25891

Perforation Friction Pressure of Fracturing Fluid Slurry

J. D. Willingham, H. C. Tan, and L. R. Norman

Errata

Below please find the corrected Figure 1.

Flow----..

iD perf

--D v

D perf

Fig. 1 Orifice-Square Edge Perforation