Effect of Drilling Fluid Filter Cake Thickness and Permeability on Cement Slurry Fluid Loss

J. GRIFFITH
Halliburton Energy Services, Inc.

S.O. OSISANYA
University of Oklahoma

Abstract
Excessive cement filtrate loss is known to cause formation fluid influx and migration through the setting cement. The filter cake deposited by the drilling fluid controls or limits the cement slurrys filtrate loss. The effectiveness of a particular filter cake to limit cement slurrys filtrate loss depends on its permeability. A series of dynamic fluid loss (DFL) tests were performed on a 50.8 mm (2 in.) diameter by 63.5 mm (2.5 in.) long permeable man-made cores during which filtrate volume was measured as a function of time for a constant shear stress. Two drilling fluid types, one with high fluid loss and the other with low fluid loss were used for the DFL tests. An equation was developed to determine 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 fluids stabilized in flow rate and thickness in less than 15 minutes. The final 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 the low and high fluid loss drilling fluids respectively. Since the high fluid loss drilling fluid produces a filter cake that has four times the permeability of the low fluid loss drilling fluid, the latter fluid should be used. That is, the drilling fluid must be conditioned to have low fluid loss during cementing. Thickness measurements of the filter cake as a function of time allow the calculation of the permeability of the filter cake, which reduces the cement slurrys filtrate.

removal of filter cake. Therefore, the annulus is partially filled with cement and filter cake. Initially, zonal isolation is achieved due to the cement and filter cake possessing near zero permeability(1). However with time, the polymers and chemicals in the filter cake degrade allowing the permeability of the filter cake to increase, which compromises the annular seal. This leads to further degradation of the filter cake, primarily from gas influx into the permeability of the filter cake. To provide long-term zonal isolation, the composite system of cement and filter cake must seal the space between the casing and the borehole from migrating formation fluids. The annular seal must last over the economics life of the well. Ideally, the seal should last forever to prevent pollution of the potable water by deeper formation fluids. By combining the two phenomena of a filter cake controlling the cement slurrys 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 losses controlling short-term fluid migration balanced against a maximum thickness to provide long-term sealing of the annulus.

Theory
Useful equations to determine the permeability of the drilling fluids filter cake is Darcys equation for steady state flow: Q= kh( Pe Pw ) ln(re rw )
..................................................................................(1)

Introduction
The drilling fluid consists of a mixture of solids, liquids (water or oil), and chemicals, with the liquid being the continuous phase. The solids may be active solids such as bentonite and polymers or inactive such as barite. To stabilize the wellbore, the drilling fluid attempts to seal the borehole by the solid and polymer bridging on the formation face. The deposition of the solids occurs only if a pressure differential is established away from the wellbore. Since the solids do not readily enter the formation pore spaces, a layer of high-density cake deposits on the borehole wall. The thickness of the cake increases until the cakes permeability approaches zero. This can occur under dynamic or static fluid conditions. The solids and fluid loss polymers control the final thickness of the cake development. There are situations where the filter cake is not completely removed during the cementing process(1-5). For example, when cementing some casing strings, especially the surface strings that protect the potable water sands, shear rates are low, filter cake build-up is the greatest, and drilling conditions limit mechanical
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flow rate, cc/sec permeability, darcy height of the core, cm pressure at re, atm. pressure at rw, atm. filtrate viscosity, assumed to be 1 cp. radius of the core, cm radius of the core plus the thickness of the filter cake, cm This equation allows the calculation of the filter cakes permeability to filtrate or water if the filter cakes thickness is known. Values of permeability of the high and low fluid loss drilling fluids 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 the test is completed, but that does not allow the development of a relation of permeability versus real time.
Journal of Canadian Petroleum Technology

where, Q k h Pe Pw rw re

= = = = = = = =

PAPER: 97-136

FIGURE 1: Dynamic fluid loss cell.

FIGURE 2: Permeable core/sleeve/autoclave combination used in the dynamic fluid loss cell.

Another means of calculating filter cake thickness in real time is based on the relationship that Newtonian and non-Newtonian fluids will exhibit an increasing resistance to shear as the slot between a rotating sleeve and a stationary cylinder decreases. This is 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 torque on the inner bob of a viscometer as the fluids rheology changes could allow the calculation of the slot thickness if the sleeves torque is known. The equation that will allow the calculation of filter cake thickness in the Dynamic Fluid Loss Cell (DFLC) is the modified Reiner-Riwlin Equation (2) for Bingham-Plastic fluids which relates torque exerted on a cylinder to the gap between the cylinder and a rotating sleeve. This equation is given below (see Appendix A for derivation):
= * 1 rb2 1 Rs2 (4 * L * PV )

DFLC Apparatus Figure 1 shows the DFLC used in this study. This cell allows the 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. It uses a sleeve rotating about the core to develop shear rate on the cake. Both the core and the sleeve are in a vertical position when installed in the autoclave cell. The drilling fluid is transferred to the core cell under pressure so as not to surge the filtrate in the core. This assures that the pressure gradient is in one direction into the center of the core. Depositing a dynamic filter cake simulates the fluid flow conditions in an actual well. A dynamic filter cake has been shown to be constant after a given time. That is, the cake is eroded as fast as it is being deposited. In general, dynamic filtration rates are higher than static filtration rates. DFLC Core The man-made cores consisted of a mixture of epoxy with a 2:1 mixture of 20 40 US mesh sand and 200 mesh sand respectively. A 50.8 mm (2 in.) internal diameter piece of pipe was placed inside 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 eposand was then placed and compacted by hand in the annulus of the perforated 127 mm (5 in.) casing and 50.8 mm (2 in. pipe). Steps were taken to carefully pack the sand so that the permeability of the core would be consistent. The permeable section was then placed inside an oven and baked for 24 hours at 110 C (230 F). After baking period, the permeable and non-permeable section were welded together to form the core. Drilling Fluid Two fluid types were prepared according to API standards(6) as the candidate fluids. The two types used bentonite in fresh water as the base generic fluid, which was prepared by pre-hydrating a known amount of bentonite in fresh water. The bentonite suspension was allowed to age overnight before use. Necessary chemical additives were then added to the bentonite suspension in order to obtain fluids with high and low filtrate losses. The mixtures were stirred for at least 30 minutes after the addition of each chemical component. The basic drilling fluid properties such as yield point, plastic viscosity, and API fluid loss were measured. Below is the chemical composition and properties of the drilling fluids. The chemicals were added in the order listed.
Journal of Canadian Petroleum Technology

YP * ln(rb Rs ) PV ...............................(2)

By combining Equations (1) and (2) and the measured data from the DFLC tests, the filter cakes permeability can be determined. With the use of the DFLC the permeability of two filter cakes were determined. The DFLC allows the dynamic deposition of the filter 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 was held constant at 2.76 103 kPa (400 psi) with temperature of 26.7 C (80 F) and 65.6 C (150 F). The quality of filtrate is measured on a Melter balance and recorded. The other value recorded with time is the torque needed to rotate the sleeve about the core. The development of the equation that relates torque of a rotating sleeve about the core to a fluids rheology is much like the development of equations for a rotary viscometer. However, in this case, the torque is measured on the rotating sleeve and not on the inner bob as with a viscometer.

Experimental Set-up
The experimental studies involve the preparation of a long permeable core and the deposition of filter cake under dynamic conditions. Two dynamic fluid loss tests were conducted in order to determine the filter cake permeability. The following equipment is required to conduct a dynamic fluid loss cell test: the DFLC apparatus, one DFLC core, and selected drilling fluid type.
2

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

High Fluid Loss Drilling Fluid Fresh water + 57.14 kg/m3 (20 lbm/bbl) bentonite + 71.43 kg/m3 (25 lbm/bbl) SAND + 0.286 kg/m3 (0.1 lbm/bbl) EXTENDER + 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 (20 lbm/bbl) bentonite + 8.71 kg//m3 (1.90 lbm/bbl) polymer + 0.43 kg/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 viscosity and API fluid loss were 20 lbf/100 sq.ft, 18 cp., and 7 cc/30 min/100 psi respectively. Appendix B lists the step-by-step procedure for the DFLC test(7).
FIGURE 4: Cake thickness and permeability vs. time for high fluid loss drilling fluid.

Conclusions
A methodology is developed to determine the permeability of a filter cake deposited under dynamic conditions. This methodology can be used to determine the optimum range of filter cake thickness and permeability for reducing the effects of short-term and long-term fluid migration. A low-fluid loss drilling fluid should be maintained during cementing operations. This fluid will produce a thin filter cake that will reduce the cement slurrys filtrate as compared to the high-fluid loss drilling.

Example Calculation of Filter Cake Permeability

The permeability of the filter cake is determined by using Equations (1) and (2). Measured data from the DFLC test are as follows: 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 of 0.035-cm is found. Equation (16) is then solved for permeability k, knowing the value for the cake thickness. The permeability k, in this case is 3.2 10-8 m2 (0.0032 md).

Acknowldegement
The authors would like to thank the School of Petroleum and Geological Engineering, at the University of Oklahoma and Halliburton Energy Services in Duncan for encouragement to publish this paper.

NOMENCLATURE
DFLC h k L N Pe Pw PV Q r rb re Rs T YP tc F = = = = = = = = = = = = = = = = = Dynamic fluid loss cell height, cm permeability, darcy length of DFLC core, cm DFLCs sleeve rotation, rpm pressure at re, atm. pressure at rw, atm. plastic viscosity, poise flow rate, cc/sec radius, cm radius of the DFLC core, inches external radius, cm radius of the DFLC sleeve, inches torque of the DFLC sleeve, lbf-in fluids yield point, dynes/cm2 filter cake thickness, cm temperature degrees, Fahrenheit

Results and Discussion

Figures 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 of the filter cake stabilizes at 5.0 10-22 m2 (0.5 nano-darcy) and 20.0 10-22 m2 (2.0 nano-darcy) for the low and high-fluid loss drilling fluids respectively. The stabilized permeability of the two fluids indicates that both should initially control the filtrate of the cement. However, depending on the wells geometry and formation pressure, any filtrate loss can initiate gas migration. Since the high fluid loss fluid produces a filter cake that has four times the permeability of the low fluid loss fluid, the low fluid loss fluid should be utilized during cementing operation. In either case, the permeability is on the order of nano-darcy, which is also the magnitude of the permeability of the set cement.
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Greek Symbols p y = = = = = shear rate, sec-1 filtrate viscosity, assumed to be 1 cp. plastic viscosity, cp. shear stress, psi yield point, lbf/100 ft2
3

= angular velocity, radian/sec

d YP = dr 2 Lr 3 PV PV r ...................................................................(A-5)

SI Metric Conversion Factors

1 cp. 1.000 1 darcy 1.000 1 inch 2.540 1 psi 6.8948 F ( F-32)/1.8 1 lbm 4.5359 1 ft 3.048 E+00 E-12 E+01 E+00 E-01 E+02 = = = = = = = mPa.s 10-12 m2 (1m2) mm kPa C kg mm

Assuming no slip occurs at the surfaces of the DFLCs sleeve and core, then the angular velocity is zero at rb (core + filter cake radius), and at Rs (sleeve radius), the following integration can be performed:

0 d

2 LPV

Rs

rb

dr YP r 3 PV

Rs

rb

dr r ................................................(A-6)

which results in :
= +

REFERENCES
1. RAVI, K.M., BEIRUTE, R.M., and COVINGTON, R.L., Erodability of Partially Dehydrated Gelled Drilling Fluid and Filter Cake; SPE Paper 24571, October 1992. 2. CROOK, R.J., HAUT, R.C., and KELLER, S.R., Problem Associated with Deviated-Wellbore Cementing; SPE Paper 11979, October 1983. 3. SUTTON, D.L., and RAVI, K.M., New Method for Determining Downhole Properties That Affect Gas Migration and Annular Sealing; SPE Paper 19520, October 1989. 4. HABERMAN, J.P., DELESTATIUS, M., HINES, D.G., DACCORD, G., and BARET, J.F., Downhole Fluid-loss Measurement From Drilling Fluid and Cement Slurries; Journal of Petroleum Technology, August 1992. 5. SUTTON, D.L., SABINS, F.L., and FAUL, R., Preventing Annular Gas Flow; Oil and Gas Journal, December 10 and 17, 1984. 6. Baroid Manual: Principles of Drilling Fluid Control; Petroleum Extension Service, The University of Texas at Austin, Austin, TX, 12th Edition, p. 201, 1969. 7. GRIFFITH, J.E., Thickness Optimization of Drilling Fluid Filter Cakes for Cement Slurry Filtrate Control and Long-term Zonal Isolation; MS Thesis, University of Oklahoma, Norman, 1994.

(4 * L * PV )

* 1 rb2 1 Rs2

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

YP * ln(rb Rs ) PV

where, = angular velocity, radians/sec. T = torque, dyne-cm. L = DFLC core and holder height, cm. = radius of core plus the filter cake thickness, cm. rb = inside radius of the sleeve, cm. Rs YP = yield point of drilling fluid, dynes/cm2 PV = 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 (2N/60) for in Equation (A-7) where N is the speed of rotation of the outer cylinder in rpm, and changing YP to lbf/100 ft2 and PV to cp., then Equation (A-7) results in:
2 N = * 1 rb2 1 Rs2 60 (4 * L * PV )

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

Appendix ADevelopment of the Equation to Determine Permeability of Filter Cake

The development of the needed equation assumes a BinghamPlastic model, which is defined by: = p + y
.....................................................................................(A-1)

YP * ln(rb Rs ) 0.02089 * PV

where, 1 dynes/cm2 = 1/0.02089 * lbf/100 ft2. Simplifying for the following DFLC geometry of : L = 6.35 cm = 2.54 cm. + Filter cake thickness (tc) in cm. rb = 3.18 cm Rs N = 300 rpm for the test Therefore,
300 = +

where, = shear stress y = yield point P = plastic viscosity = shear rate The torque T, of the sleeve relates the shear stress in the fluid at any radius between the sleeve radius r and the stationary bob using the following equation.
= (2 rL )r .....................................................................................(A-2)

(4

30 *
2

* L * PV

* 1 rb2 1 Rs2

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

30 * Y * ln(rb Rs ) 0.02089 * * PV

10 = +

(4

* 6.35 PV

* 1 (2.54 + tc ) 1 (3.18)
2

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

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

=

YP * ln (2.54 + tc ) 3.18 0.06563PV

(2 L)r 2 ........................................................................................(A-3)

10 = +

(250.688PV )

* 1 (2.54 + tc ) 0.0989
2

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

Also, the shear rate due to slippage between fluid layers is given by:
=r d dr .............................................................................................(A-4)

YP * ln (2.54 + tc ) 3.18 0.06563PV

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

Equation (A-11) is difficult to isolate for tc, thus tc is determined by trial and error based on the YP, PV, and T measured from the DFLC. The filter cakes permeability with tangential shear forces of fluid flow is found by using Darcys Equation for steady state fluid flow.
Journal of Canadian Petroleum Technology

Q=

kh( Pe Pw ) ln(re rw )

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

For the DFLC, the permeability of the core is approximately 2,500 md, which is much greater than the final permeability of the filter cake. Also, the flow through the filter cake is in series with the flow through the core. These two facts allow us to assume that the permeability measured in Darcys equation is the permeability of the filter cake. Darcys equation is simplified for this test by knowing the values for the geometry and pressure drop. It is simplified as follows: h = 6.35 cm rw = 2.54 cm = filtrate viscosity, assumed to be 1 cp Pe = 27.21 atm (400 psi) Pw = 0 atm Q = flow rate in cc/sec.
Q = k (6.35cm)(27.21atm) (1cp) ln(re 2.54cm)

10. Record torque on sleeve and filtrate collected each minute until filtrate change is less than 5.0 10-4 kg (0.5 g) per minute. 11. Record torque and filtrate every five minutes and thereafter for a total time of two hours. Release pressure and clean-up DFLC. ProvenanceOriginal Petroleum Society manuscript, Effect of Drilling Fluid Filter Cake Thickness and Permeability on Cement Slurry Fluid Loss, (97-136), first presented at the 48th Annual Technical Meeting, June 8 11, 1997, in Calgary, Alberta. Abstract submitted for review November 26, 1996; editorial comments sent to the author(s) April 6, 1998; revised manuscript received January 18, 1999; paper approved for pre-press January 20, 1999; final approval November 8, 1999.

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

Authors Biographies
James Griffith is the global technical adviser for deep-water technology at the Halliburton Energy Services, Inc., Technology Centre in Duncan, Oklahoma. Before joining Halliburton, he worked as a production engineer for Chevron USA and as a drilling engineer for an independent production company. James has BS and MS degrees in petroleum engineering from the University of Oklahoma, and an MBA from Oklahoma City University. Samuel Osisanya is an associate professor of petroleum engineering at the University of Oklahoma, Norman, Oklahoma, where he teaches drilling engineering, drilling fluids, well completion and stimulation, horizontal well technology, and emerging technology. Formerly, he was an assistant professor at Montana Tech University where he taught system analysis and surface production operations; and a visiting lecturer at the University of Ibadan, Nigeria from 1980 1983. His research interests include wellbore stability, well completion and stimulation, formulation of drilling and completion fluids, cementing and drilling optimization. Dr. Osisanya has eight years of industrial experience with Mobil, Shell, Gulf (now Chevron) and Dresser Magcobar. He holds a BS degree from the University of Ibadan, Nigeria, and MS and Ph.D. degrees from the University of Texas at Austin, all in petroleum engineering. He is a member of the SPE Technical Committee on Well Completions 1997 1999. He is a registered professional engineer in Texas. He is a member of SPE of AIME, American Association of Drilling Engineers (AADE), and American Association of Engineering Educators (ASEE). He has authored and co-authored more than 30 papers in SPE, Journal of Canadian Petroleum Technology, and ASEE.

Which further simplifies to :

Q = 172.78 k ln(re 2.54)

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

or
k= Q * ln(re 2.54) 172.78

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

Equation (A-15) is used to calculate the filter cake permeability using the filter cake thickness (tc) calculated from Equation (A11) 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) gives Equation (A-16).
k= Q * ln (2.54 + tc ) 2.54 172.78

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

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

Appendix BProcedure for the Dynamic Fluid Loss (DFLC) Test

The aim of this test was to measure the permeability of the high and low fluid loss filter cake. The following are the step-by-step procedure: 1. Prepare core by mixing epoxy-sand design and hand pack into 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 permeability of the core to water. 4. Place core into DFLCs 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 standby cell. Balance pressure at 2.76 103 kPa (400 psi). Watch dump cell for drilling fluid. When drilling fluid appears at dump cell, isolate stirring cell from stand-by and dump cells. 9. Initialize balance and open filtrate line.
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