Special Edition 1999, Volume 38, No. 13 Journal of Canadian Petroleum TechnologyPAPER: 97-136

Introduction

The drilling fluid consists of a mixture of solids, liquids (wateror oil), and chemicals, with the liquid being the continuous phase.The solids may be active solids such as bentonite and polymers orinactive such as barite. To stabilize the wellbore, the drilling fluidattempts to seal the borehole by the solid and polymer bridging onthe formation face. The deposition of the solids occurs only if apressure differential is established away from the wellbore. Sincethe solids do not readily enter the formation pore spaces, a layerof high-density cake deposits on the borehole wall. The thicknessof the cake increases until the cake’s permeability approacheszero. This can occur under dynamic or static fluid conditions. Thesolids and fluid loss polymers control the final thickness of thecake development.

There are situations where the filter cake is not completelyremoved during the cementing process(1-5). For example, whencementing some casing strings, especially the surface strings thatprotect the potable water sands, shear rates are low, filter cakebuild-up is the greatest, and drilling conditions limit mechanical

removal of filter cake. Therefore, the annulus is partially filledwith cement and filter cake. Initially, zonal isolation is achieveddue to the cement and filter cake possessing near zero permeabili-ty(1). However with time, the polymers and chemicals in the filtercake degrade allowing the permeability of the filter cake toincrease, which compromises the annular seal. This leads to fur-ther degradation of the filter cake, primarily from gas influx intothe permeability of the filter cake.

To provide long-term zonal isolation, the composite system ofcement and filter cake must seal the space between the casing andthe borehole from migrating formation fluids. The annular sealmust last over the economics life of the well. Ideally, the sealshould last forever to prevent pollution of the potable water bydeeper formation fluids.

By combining the two phenomena of a filter cake controllingthe cement slurry’s filtrate and long-term sealing of the annulus,there must be an optimum thickness of filter cake. On one hand,there exist a minimum thickness that limits slurry filtrate lossescontrolling short-term fluid migration balanced against a maxi-mum thickness to provide long-term sealing of the annulus.

TheoryUseful equations to determine the permeability of the drilling

fluid’s filter cake is Darcy’s equation for steady state flow:

..................................................................................(1)

where,Q = flow rate, cc/seck = permeability, darcyh = height of the core, cmPe = pressure at re, atm.Pw = pressure at rw, atm.µ = filtrate viscosity, assumed to be 1 cp.rw = radius of the core, cmre = radius of the core plus the thickness of the filter

cake, cmThis equation allows the calculation of the filter cake’s perme-

ability to filtrate or water if the filter cake’s thickness is known.Values of permeability of the high and low fluid loss drilling flu-ids will indicate the control of the filtrate loss. In the experiments,Q, h, the pressure drop, and rw will be measured. However, re,which involves the filter cake thickness, can be measured after thetest is completed, but that does not allow the development of arelation of permeability versus real time.

Qkh P P

r re w

e w

=−( )

( )µ ln

Effect of Drilling Fluid Filter Cake Thickness and Permeability on

Cement Slurry Fluid Loss

J. GRIFFITHHalliburton Energy Services, Inc.

S.O. OSISANYAUniversity of Oklahoma

AbstractExcessive cement filtrate loss is known to cause formation

fluid influx and migration through the setting cement. The filtercake deposited by the drilling fluid controls or limits the cementslurry’s filtrate loss. The effectiveness of a particular filter caketo limit cement slurry’s filtrate loss depends on its permeability.A series of dynamic fluid loss (DFL) tests were performed on a50.8 mm (2 in.) diameter by 63.5 mm (2.5 in.) long permeableman-made cores during which filtrate volume was measured as afunction of time for a constant shear stress. Two drilling fluidtypes, one with high fluid loss and the other with low fluid losswere used for the DFL tests. An equation was developed todetermine filter cake permeability based on filtrate volume,shear stress, plastic viscosity and yield point of the fluid.

In the DFL tests, the low and high fluid loss drilling fluidsstabilized in flow rate and thickness in less than 15 minutes. Thefinal permeability of the filter cake stabilized at 5.0 × 10-22 m2

(0.5 nano-darcy) and 20.0 × 10-22 m2 (2.0 nano-darcy) for thelow and high fluid loss drilling fluids respectively. Since thehigh fluid loss drilling fluid produces a filter cake that has fourtimes the permeability of the low fluid loss drilling fluid, the lat-ter fluid should be used. That is, the drilling fluid must be condi-tioned to have low fluid loss during cementing. Thickness mea-surements of the filter cake as a function of time allow the calcu-lation of the permeability of the filter cake, which reduces thecement slurry’s filtrate.

Another means of calculating filter cake thickness in real timeis based on the relationship that Newtonian and non-Newtonianfluids will exhibit an increasing resistance to shear as the slotbetween a rotating sleeve and a stationary cylinder decreases. Thisis the basic principle for the development of the rotary viscometer,but the slot on a rotary viscometer remains at a fixed distance.However, the equation that relates the rotary velocity to the torqueon the inner bob of a viscometer as the fluid’s rheology changescould allow the calculation of the slot thickness if the sleeve’storque is known.

The equation that will allow the calculation of filter cake thick-ness in the Dynamic Fluid Loss Cell (DFLC) is the modifiedReiner-Riwlin Equation (2) for Bingham-Plastic fluids whichrelates torque exerted on a cylinder to the gap between the cylin-der and a rotating sleeve. This equation is given below (seeAppendix A for derivation):

...............................(2)

By combining Equations (1) and (2) and the measured datafrom the DFLC tests, the filter cake’s permeability can be determined.

With the use of the DFLC the permeability of two filter cakeswere determined. The DFLC allows the dynamic deposition of thefilter cake on a 50.80 mm (2 in.) diameter by 63.50 mm (2.5 in.)long permeable core. The differential pressure across the core washeld constant at 2.76× 103 kPa (400 psi) with temperature of26.7˚ C (80˚ F) and 65.6˚ C (150˚ F). The quality of filtrate ismeasured on a Melter balance and recorded. The other valuerecorded with time is the torque needed to rotate the sleeve aboutthe core. The development of the equation that relates torque of arotating sleeve about the core to a fluid’s rheology is much likethe development of equations for a rotary viscometer. However, inthis case, the torque is measured on the rotating sleeve and not onthe inner bob as with a viscometer.

Experimental Set-upThe experimental studies involve the preparation of a long per-

meable core and the deposition of filter cake under dynamic con-ditions. Two dynamic fluid loss tests were conducted in order todetermine the filter cake permeability. The following equipment isrequired to conduct a dynamic fluid loss cell test: the DFLC appa-ratus, one DFLC core, and selected drilling fluid type.

DFLC Apparatus

Figure 1 shows the DFLC used in this study. This cell allowsthe dynamic deposition of the filter cake on a 50.8 mm (2 in.)diameter by 63.5 mm (2.5 in.) long permeable core, Figure 2. Ituses a sleeve rotating about the core to develop shear rate on thecake. Both the core and the sleeve are in a vertical position wheninstalled in the autoclave cell. The drilling fluid is transferred tothe core cell under pressure so as not to surge the filtrate in thecore. This assures that the pressure gradient is in one directioninto the center of the core. Depositing a dynamic filter cake simu-lates the fluid flow conditions in an actual well. A dynamic filtercake has been shown to be constant after a given time. That is, thecake is eroded as fast as it is being deposited. In general, dynamicfiltration rates are higher than static filtration rates.

DFLC Core

The man-made cores consisted of a mixture of epoxy with a 2:1mixture of 20 – 40 US mesh sand and 200 mesh sand respectively.A 50.8 mm (2 in.) internal diameter piece of pipe was placedinside a 127 mm (5 in.) casing in order to create a 50.8 mm (2 in.)hole running the length of the permeable section. The eposandwas then placed and compacted by hand in the annulus of the per-forated 127 mm (5 in.) casing and 50.8 mm (2 in. pipe). Stepswere taken to carefully pack the sand so that the permeability ofthe core would be consistent. The permeable section was thenplaced inside an oven and baked for 24 hours at 110˚ C (230˚ F).After baking period, the permeable and non-permeable sectionwere welded together to form the core.

Drilling Fluid

Two fluid types were prepared according to API standards(6) asthe candidate fluids. The two types used bentonite in fresh wateras the base generic fluid, which was prepared by pre-hydrating aknown amount of bentonite in fresh water. The bentonite suspen-sion was allowed to age overnight before use. Necessary chemicaladditives were then added to the bentonite suspension in order toobtain fluids with high and low filtrate losses. The mixtures werestirred for at least 30 minutes after the addition of each chemicalcomponent. The basic drilling fluid properties such as yield point,plastic viscosity, and API fluid loss were measured. Below is thechemical composition and properties of the drilling fluids. Thechemicals were added in the order listed.

+ ( )* lnYP

PVr Rb sΩ Τ=

( )−( )

41 12 2

π * **

L PVr Rb s

2 Journal of Canadian Petroleum Technology

FIGURE 1: Dynamic fluid loss cell.FIGURE 2: Permeable core/sleeve/autoclave combination used inthe dynamic fluid loss cell.

High Fluid Loss Drilling Fluid

Fresh water + 57.14 kg/m3 (20 lbm/bbl) bentonite + 71.43kg/m3 (25 lbm/bbl) SAND + 0.286 kg/m3 (0.1 lbm/bbl) EXTEN-DER + 0.572 kg/m3 (0.2 lbm/bbl) caustic soda. Its yield point,plastic viscosity and API fluid loss were 77 lbf/100 sq.ft, 28 cp.,and 18 cc/30 min/100 psi respectively.

Low Fluid Loss Drilling Fluid

Fresh water + 28.57 kg/m3 (10 lbm/bbl) salt + 57.14 kg/m3 (20lbm/bbl) bentonite + 8.71 kg//m3 (1.90 lbm/bbl) polymer + 0.43kg/m3 (0.15 lbm/bbl) caustic soda + 80 kg/m3 (28 lbm/bbl) barite+ 7.71 kg/m3 (2.7 lbm/bbl) Impermex. Its yield point, plastic vis-cosity and API fluid loss were 20 lbf/100 sq.ft, 18 cp., and 7 cc/30min/100 psi respectively. Appendix B lists the step-by-step proce-dure for the DFLC test(7).

Example Calculation of Filter CakePermeability

The permeability of the filter cake is determined by usingEquations (1) and (2). Measured data from the DFLC test are asfollows:

Q = 4.0× 10-8 m3/s (0.04 cc/sec)Torque (T) = 1,600,000 dynes-cm

Yield point (YP) = 25 lbf/ 100 ft2

Plastic viscosity (PV) = 25 cp.

Using Equation (A-16) and with trial and error, a value for tc of0.035-cm is found. Equation (16) is then solved for permeabilityk, knowing the value for the cake thickness. The permeability k,in this case is 3.2× 10-8 m2 (0.0032 md).

Results and DiscussionFigures 3 and 4 show the plot of filter cake permeability versus

time for the low and high-fluid loss drilling fluids respectively.The results given in these figures show that the permeability ofthe filter cake stabilizes at 5.0× 10-22 m2 (0.5 nano-darcy) and20.0 × 10-22 m2 (2.0 nano-darcy) for the low and high-fluid lossdrilling fluids respectively. The stabilized permeability of the twofluids indicates that both should initially control the filtrate of thecement. However, depending on the well’s geometry and forma-tion pressure, any filtrate loss can initiate gas migration. Since thehigh fluid loss fluid produces a filter cake that has four times thepermeability of the low fluid loss fluid, the low fluid loss fluidshould be utilized during cementing operation. In either case, thepermeability is on the order of nano-darcy, which is also the mag-nitude of the permeability of the set cement.

ConclusionsA methodology is developed to determine the permeability of a

filter cake deposited under dynamic conditions. This methodologycan be used to determine the optimum range of filter cake thick-ness and permeability for reducing the effects of short-term andlong-term fluid migration.

A low-fluid loss drilling fluid should be maintained duringcementing operations. This fluid will produce a thin filter cakethat will reduce the cement slurry’s filtrate as compared to thehigh-fluid loss drilling.

AcknowldegementThe authors would like to thank the School of Petroleum and

Geological Engineering, at the University of Oklahoma andHalliburton Energy Services in Duncan for encouragement to pub-lish this paper.

NOMENCLATUREDFLC = Dynamic fluid loss cellh = height, cmk = permeability, darcyL = length of DFLC core, cmN = DFLC’s sleeve rotation, rpmPe = pressure at re, atm.Pw = pressure at rw, atm.PV = plastic viscosity, poiseQ = flow rate, cc/secr = radius, cmrb = radius of the DFLC core, inchesre = external radius, cm Rs = radius of the DFLC sleeve, inchesT = torque of the DFLC sleeve, lbf-inYP = fluid’s yield point, dynes/cm2tc = filter cake thickness, cm˚ F = temperature degrees, Fahrenheit

Greek Symbols

γ = shear rate, sec-1

µ = filtrate viscosity, assumed to be 1 cp.µp = plastic viscosity, cp.τ = shear stress, psiτy = yield point, lbf/100 ft2

Special Edition 1999, Volume 38, No. 13 3

FIGURE 3: Cake thickness and permeability vs. time for low fluidloss drilling fluid.

FIGURE 4: Cake thickness and permeability vs. time for highfluid loss drilling fluid.

Ω = angular velocity, radian/sec

SI Metric Conversion Factors1 cp.× 1.000 E+00 = mPa.s1 darcy× 1.000 E-12 = 10-12 m2 (1µm2)1 inch× 2.540 E+01 = mm1 psi× 6.8948 E+00 = kPa˚ F (˚ F-32)/1.8 = ˚ C1 lbm× 4.5359 E-01 = kg1 ft × 3.048 E+02 = mm

REFERENCES1. RAVI, K.M., BEIRUTE, R.M., and COVINGTON, R.L., Erodability

of Partially Dehydrated Gelled Drilling Fluid and Filter Cake; SPEPaper 24571, October 1992.

2. CROOK, R.J., HAUT, R.C., and KELLER, S.R., ProblemAssociated with Deviated-Wellbore Cementing; SPE Paper 11979,October 1983.

3. SUTTON, D.L., and RAVI, K.M., New Method for DeterminingDownhole Properties That Affect Gas Migration and AnnularSealing;SPE Paper 19520, October 1989.

4. HABERMAN, J.P., DELESTATIUS, M., HINES, D.G.,DACCORD, G., and BARET, J.F., Downhole Fluid-lossMeasurement From Drilling Fluid and Cement Slurries; Journal ofPetroleum Technology, August 1992.

5. SUTTON, D.L., SABINS, F.L., and FAUL, R., Preventing AnnularGas Flow;Oil and Gas Journal, December 10 and 17, 1984.

6. Baroid Manual: Principles of Drilling Fluid Control;PetroleumExtension Service, The University of Texas at Austin, Austin, TX,12th Edition, p. 201, 1969.

7. GRIFFITH, J.E., Thickness Optimization of Drilling Fluid FilterCakes for Cement Slurry Filtrate Control and Long-term ZonalIsolation; MS Thesis, University of Oklahoma, Norman, 1994.

Appendix A—Development of theEquation to Determine Permeability ofFilter Cake

The development of the needed equation assumes a Bingham-Plastic model, which is defined by:

.....................................................................................(A-1)

where,τ = shear stressτy = yield pointµP = plastic viscosityγ = shear rateThe torque T, of the sleeve relates the shear stress in the fluid at

any radius between the sleeve radius r and the stationary bobusing the following equation.

.....................................................................................(A-2)

where r is the radius of the rotating sleeve. Solving for τ gives:

........................................................................................(A-3)

Also, the shear rate due to slippage between fluid layers isgiven by:

.............................................................................................(A-4)

By substituting Equations (A-3) and (A-4) into Equation (A-1),the following results:

...................................................................(A-5)

Assuming no slip occurs at the surfaces of the DFLC’s sleeveand core, then the angular velocity is zero at rb (core + filter cakeradius), and Ω at Rs (sleeve radius), the following integration canbe performed:

................................................(A-6)

which results in :

......................................................(A-7)

where,Ω = angular velocity, radians/sec.T = torque, dyne-cm.L = DFLC core and holder height, cm.rb = radius of core plus the filter cake thickness, cm.Rs = inside radius of the sleeve, cm.YP = yield point of drilling fluid, dynes/cm2PV = plastic viscosity of drilling fluid, cp.Equation (A-7) is also known as the Reiner-Riwlin Equation

for a modified Bingham-Plastic Fluid(8). Substituting the value of(2πN/60) for Ω in Equation (A-7) where N is the speed of rotationof the outer cylinder in rpm, and changing YP to lbf/100 ft2 andPV to cp., then Equation (A-7) results in:

....................................................(A-8)

where, 1 dynes/cm2 = 1/0.02089 * lbf/100 ft2. Simplifying for thefollowing DFLC geometry of :

L = 6.35 cmrb = 2.54 cm. + Filter cake thickness (tc) in cm.Rs = 3.18 cmN = 300 rpm for the testTherefore,

....................................................(A-9)

.............................(A-10)

.....................................(A-11)

Equation (A-11) is difficult to isolate for tc, thus tc is deter-mined by trial and error based on the YP, PV, and T measuredfrom the DFLC.

The filter cake’s permeability with tangential shear forces offluid flow is found by using Darcy’s Equation for steady statefluid flow.

10250 688

1 2 54 0 0989

0 065632 54 3 18

2= ( )+( ) −[ ]

+ +( )[ ]

Τ.

* . .

.* ln . .

PVt

YP

PVt

c

c

104 6 35

1 2 54 1 3 18

0 065632 54 3 18

2

2 2= ( ) +( ) − ( )[ ]+ +( )[ ]

Τπ * .

* . .

.* ln . .

PVt

YP

PVt

c

c

30030

41 1

30

0 02089

22 2= ( ) −( )

+ ( )

*

* **

*

. * ** ln

Τπ

π

L PVr R

Y

PVr R

b s

b s

2

60 41 1

0 02089

2 2ππ

N

L PVr R

YP

PVr R

b s

b s

=( )

−( )+ ( )

Τ* *

*

. ** ln

Ω Τ=( )

−( )+ ( )

41 12 2

π * **

* ln

L PVr R

YP

PVr R

b s

b s

0 32Ω Ω Τ

dLPV

dr

r

YP

PV

dr

rrb

Rs

rb

Rs

= − ∫∫∫ π

d

dr Lr PV

YP

PV r

Ω Τ= −×2 3π

γ = rd

dr

Ω

τπ

=( )

Τ2 2L r

Τ = ( )τ π2 rL r

τ µ γ τ= +p y

4 Journal of Canadian Petroleum Technology

.................................................................................(A-12)

For the DFLC, the permeability of the core is approximately2,500 md, which is much greater than the final permeability of thefilter cake. Also, the flow through the filter cake is in series withthe flow through the core. These two facts allow us to assume thatthe permeability measured in Darcy’s equation is the permeabilityof the filter cake.

Darcy’s equation is simplified for this test by knowing the val-ues for the geometry and pressure drop. It is simplified as follows:

h = 6.35 cmrw = 2.54 cmµ = filtrate viscosity, assumed to be 1 cpPe = 27.21 atm (400 psi)Pw = 0 atmQ = flow rate in cc/sec.

...............................................................(A-13)

Which further simplifies to :

.....................................................................(A-14)

or

............................................................................(A-15)

Equation (A-15) is used to calculate the filter cake permeabilityusing the filter cake thickness (tc) calculated from Equation (A-11) and Q measured on the Metler Balance of the DFLC.Substitution for re which equals the sum of the radius of the core(2.54-cm) and the tc value found from Equation (A-11) givesEquation (A-16).

..............................................................(A-16)

In this final equation, Q is in cc/sec, tc is in cm and k is indarcy.

Appendix B—Procedure for the DynamicFluid Loss (DFLC) Test

The aim of this test was to measure the permeability of the highand low fluid loss filter cake. The following are the step-by-stepprocedure:

1. Prepare core by mixing epoxy-sand design and hand packinto core mold. Bake core for 24 hr. at 110˚ C (230˚ F).

2. Remove cores from mold and allow to cool to room temperature.

3. Saturate core with tap water and determine the permeabilityof the core to water.

4. Place core into DFLC’s stirring cell and fill cell with water.5. Pressurize stirring cell to 2.76× 103 kPa (400 psi) and rotate

sleeve at 300 rpm. Keep sleeve rotating throughout the test.6. Open the filtrate line and remove all air in core and filtrate

line. Close filtrate line.7. Place beaker on Metler balance and direct filtrate line into

the beaker.8. Transfer into stirring cell selected drilling fluid from stand-

by cell. Balance pressure at 2.76× 103 kPa (400 psi). Watchdump cell for drilling fluid. When drilling fluid appears atdump cell, isolate stirring cell from stand-by and dump cells.

9. Initialize balance and open filtrate line.

10. Record torque on sleeve and filtrate collected each minuteuntil filtrate change is less than 5.0× 10-4 kg (0.5 g) perminute.

11. Record torque and filtrate every five minutes and thereafterfor a total time of two hours. Release pressure and clean-upDFLC.

Provenance—Original Petroleum Society manuscript, Effect ofDrilling Fluid Filter Cake Thickness and Permeability onCement Slurry Fluid Loss, (97-136), first presented at the 48thAnnual Technical Meeting, June 8 – 11, 1997, in Calgary,Alberta. Abstract submitted for review November 26, 1996; edito-rial comments sent to the author(s) April 6, 1998; revised manu-script received January 18, 1999; paper approved for pre-pressJanuary 20, 1999; final approval November 8, 1999.M

kQ tc=

+( )[ ]* ln . .

.

2 54 2 54

172 78

kQ re=

( )* ln .

.

2 54

172 78

Qk

re

= ( )172 782 54

.ln .

∴ = ( )( )( ) ( )Q

k cm atm

cp r cme

6 35 27 21

1 2 54

. .

ln .

Qkh P P

r re w

e w

=−( )

( )µ ln

Special Edition 1999, Volume 38, No. 13 5

Authors’ Biographies

James Griffith is the global technicaladviser for deep-water technology at theHalliburton Energy Services, Inc.,Technology Centre in Duncan, Oklahoma.Before joining Halliburton, he worked as aproduction engineer for Chevron USA andas a drilling engineer for an independentproduction company. James has BS andMS degrees in petroleum engineering fromthe University of Oklahoma, and an MBAfrom Oklahoma City University.

Samuel Osisanyais an associate professorof petroleum engineering at the Universityof Oklahoma, Norman, Oklahoma, wherehe teaches drilling engineering, drilling flu-ids, well completion and stimulation, hori-zontal well technology, and emerging tech-nology. Formerly, he was an assistant pro-fessor at Montana Tech University wherehe taught system analysis and surface pro-duction operations; and a visiting lecturerat the University of Ibadan, Nigeria from

1980 – 1983. His research interests include wellbore stability, wellcompletion and stimulation, formulation of drilling and comple-tion fluids, cementing and drilling optimization. Dr. Osisanya haseight years of industrial experience with Mobil, Shell, Gulf (nowChevron) and Dresser Magcobar. He holds a BS degree from theUniversity of Ibadan, Nigeria, and MS and Ph.D. degrees from theUniversity of Texas at Austin, all in petroleum engineering. He isa member of the SPE Technical Committee on Well Completions1997 – 1999. He is a registered professional engineer in Texas. Heis a member of SPE of AIME, American Association of DrillingEngineers (AADE), and American Association of EngineeringEducators (ASEE). He has authored and co-authored more than 30papers in SPE, Journal of Canadian Petroleum Technology,andASEE.