Rheological Measurements on Clay Suspensions and Drilling

Rheological Measurements on Clay Suspensions and Drilling Fluids at High Temperatures and Pressures

K. H. HILLER

ABSTRACT

A rotational viscometer has been designed which permits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described.

The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensions at high temperatures and pressures, are presented. Data are also presented for the flow behavior of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order TO obtain a reliable estimate of the pressure losses in the mud system.

INTRODUCTION

The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of claywater drilling muds with temperature have been reported by Srini-Vasan and Gatlin.' The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.' Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids.

The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.'· 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro-

Original manuscript received in Society of Petroleum Engineers office Dec. 26. 1962. Revised manuscript received April 18. 1963. Paper presented at Texas U.-SPE Drilling and Rock Mechanics Conference. Jan. 23-24. H63, in Austin. Tex. SPE 489

'References given at end of paper.

CALIfORNIA RESEARCH CORP. LA HABRA, CALIf.

duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress T and the rate of shear D is given by the following equation:

T=,u,,'D+cp (1)

where fLp is the plastic viscosity and cp the yield point. If cp = 0, the equation for simple Newtonian flow, T = fLD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known.

For this reason a high-pressure, high-temperature rheometer has been designed to measure the plastic viscosity ill" the yield point cp, and the static gel strength Sg at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed.

DESCRIPTION OF EQUIPMENT

MECHANICAL FEATURES

A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress T at any given rate of shear D. This is possible only if T and D are approximately uniform throughout the entire she~red sample. A Couette apparatus is the most conve~·llent method of realizing this condition, as has been pOlllted out by Grodde. 5

The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fig. 2, which represents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1) and it is shown in detail in Fig. 3. For measurements of 'dynamic flow properties, the rotating cup is driv~n by a Yz-hp electric motor, which operates through a Vickers

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hydraulic transmiSSIOn and drives a shaft that enters the pressure cell from the side. For dynamic measurements tne input drive clutch is engaged, while the electromagnetic preload and follow-up clutches are disengaged (Fig. 1). For measuring the static gel strength S!I' the input drive clutch is disengaged and the follow-up clutch is engaged. Now the rotating cup can be turned slowly by manually turning the preload and follow-up arm. The direct-reading scale indicates the angle through which the cup has been rotated. This angle, less the angle through which the torsion system has been rotated, is a measure of the strain in the sample.

The torsion system is suspended from the upper part of the pressure cell by a fine wire that offers only negligible resistance to torsion. When the cup is rotated the sample is sheared in two annular spaces. The dimensions of these annular spaces and the location of the fluid sample are shown in Fig. 3. A torque is exerted on the torsion system when the sample is sheared. This torque is compensated by the torsional resistance of the torque tube shown in Fig. 2. For the small angles of twist encountered in this instrument, the angular deflection is proportional to the applied torque, and is a measure of the shearing stress exerted on the sample. The angular deflection is imparted to a small illuminated mirror, which is rigidly attached to the torsion system with a fine wire. The deflection of the small mirror is transmitted by means of mirrors onto an illuminated scale and can be read with an accuracy of 0.01 degree.

When the preload clutch and the follow-up clutch are both engaged, while the input drive clutch is disengaged, the torsion system and rotating cup are rigidly connected. When the preload and follow-up arm is turned through a certain initial angle and the preload clutch is released, the restoring moment of the torque tube tends to bring the torsion system back to zero deflection. In a nonthixotropic fluid the deflection declines logarithmically with time, while in a thixotropic fluid the decline curve deviates from the logarithmic shape. This method of characterizing thixotropy goes back to Pryce-Jones." It will not be referred to again in this paper and is mentioned here only

~

®

®

'''''i<c \ \ \ \

A DIRECT READING SCALE B PRELOAD AND FOLLOW-UP ARM C SUSPENSION FOR TORSION SYSTEM D ILLUMINATED SCALE E OSCILLOSCOPE F LOW-FREQUENCY SIGNAL GENERATOR G PRELOAD CLUTCH H FOLLOW-UP CLUTCH I SIGNAL PICK-UP COILS

J = INPUT DRIVE CLUTCH K = VARIABLE SPEED TRANSMISSION L = MOTOR M = HEATER CONTROL N = THERMOCOUPLES o = SAMPLE CUP P = TORQUE TUBE Q = MIRROR R = HYDRAULIC OIL PUMP

FIG. l--SCIIL\TATIC ])IAl;HUI UF rilE HICll-PRl:SSCRE, HIGII

TE~IPERATURE RHEO~IETEH.

780

in order to give a complete description of the capabilities of the instrument.

It has already been pointed out that one of the variables measured by the instrument is the deflection a of the torque tube. The other variable is the number of rotations per minute n of the cup, measured by the following method: two small magnets are attached to an aluminum disc which is mounted on the drive shaft. Electric impulses are caused in 15 small coils when the fields of the moving magnets cut the stationary coils. The electric signals are fed into the Y-input of an oscilloscope, while the output of a low-frequency signal generator is fed into the X-input. The frequency of the generator is matched to the fre-

~ PRESSURE CELL THERMOCOUPLES

IIII!IIIl INTERNAL fRAME TORQUE TUBE

~ TORlIONSYSTEM INDICATING MIRROR

~ ROTATING CUP

~ CEll HEATERS

FIG. :?~C()"STHCCTW, OF THE ROl'ATI-'iC Cu' A'iD TORSIO:\ SYSTDI.

I'll;. 3---1)1 UE'iSllL,S OF ROTATl:\C CI-P "\ND

SA.\lPLE SPACE.

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quency of the impulses received from the coils by observing Lissajous figures on the screen of the oscilloscope. This method of measuring the shaft rotational speed has proved accurate to within 0.1 rpm of cup rotation up to 1,000 rpm, the limit of the instrument.

The entire pressure cell is filled with a hydraulic oil, which is carefully dried and de-oxygenated to reduce corrosion. Two air-operated hydraulic Sprague pumps supply pressure up to 10,000 psi. There is a constant small leakage past the drive shaft, which is not packed. The oil is preheated before it enters the pressure cell, in order to reduce the heat loss caused by the constant loss of oil. Heaters surround the sample space inside the pressure cell (Fig. 2). Their output is controlled by a Leeds & Northrup Model C Micromax controller operating from the output of either of two themocouples within the pressure cell. The maximum operating temperature is 350F. The entire outside of the cell is wrapped with heating tape to counteract the rapid heat loss at high temperatures. The power input into this heating tape is controlled with a Variac, which is regulated by hand according to the readings of a third thermocouple placed between the heating tape and the outside of the pressure cell. The temperature difference between the two thermocouples within the cell is no more than 2F at 350F after temperature equilibration.

The sample space and rotating cup are made of No. 316 stainless steel, which does not contaminate the samples. A mercury seal, shown in Fig. 3, prevents the mixing of the sample with the hydrau lic fluid. The torque transmitted to the torsion system through the mercury seal is negligible compared to that transmitted through the sample.

OPERATION OF THE EQUIPMENT The rheometer can be charged with a sample only when

the sample cup is removed from the pressure cell. This is done by first unscrewing the large lock nut shown in Fig. 2 and in the photograph (Fig. 4). The lock nut is lowered with the aid of a hydraulic elevator shown in the photograph (Fig. 4), which also reveals the ball bearings that permit easy turning of the nut. After removal of the nut, most of the torsion system and part of the internal frame shown in Fig. 2 can be removed from the pressure cell. The removable part of the system is fastened to the remainder by means of a lock which is not shown in the figures.

FIG. 4-FI(():,(T VIEW OF THE HICH-PRESSl:RE, f-hGII-TUIPERAT L: HE RHEO~IETER Rr-:ADY FOR A

TEST.

Jl: LY, 1')63

The exact volume of the sample, 65 ml , is measured into the sample space by means of a large hypodermic needle . Mercury is placed into the circular groove, which forms the stationary part of the mercury seal. When the assembly, filled with mercury and sample, is inserted into the pressure cell , the rotating cup dips into the sample and displaces so much fluid that the entire sample space is filled , and the sample makes contact with the mercury seal in the proper position. Trapped air is allowed to escape through properly placed relief holes of very small diameter that can be closed after the charging operation has been completed.

Under pressure , the sample is compressed and mercury tends to spill over the lip separating the annular sample space from the mercury seal. The volumes are so calculated that even for relatively compressible oil-base muds the quantity of mercury that spills over is so small that, after sinking to the bottom of the sample space, it does not reach to the lower lip of the rotating cup (Fig. 3) . Thus, the area of the shearing surfaces exposed to the sample is not changed. After the large nut has been replaced, hydraulic oil is pumped into the pressure cell. The instrument is now ready for operation.

THEORY OF FLOW IN THE RHEOMETER

The theory of flow in a rotational viscometer has recently been discussed extensively in the literature" 7; therefore, the equations necessary for an understanding of the operation and calibration of the instrument will be presented without discussion or derivation ,

The behavior of a Bingham body in a rotational viscometer is described by the Reiner and Riwlin equation. ' For a simple Couette viscometer this equation can be written

271" n K , T = 60. K , . fL. + K:' </> .

(2)

where T is the torque exerted cn the spring in dynecentimeter, n is the number of rotations per minute of the rotating cup, p..p is the plastic viscosity in poise and </> is the yield point in dynes per square centimeter. K, and K , are constants defined by

Kl=4;rl'h(~" - ~,,)' (3)

R. ) K2 = In R~-' (4

where R, is the inner radius, R , is the outer radius and h is the height of the annular space in which the sample is sheared. Eg. 2 applies only when

T>2r.h· R/ · </> , (5)

as has been pointed out in the literature." S At smaller values of T plug flow occurs, i.e. , some of the material between the cylinders moves as a rigid body . . In the rheometer, the condition of Eq. 5 is fulfilled for normal drilling fluids under most conditions at reasonable rotational speeds. Eq. 2 has to be modified for the rheometer, because the sample is sheared in an outer and an inner annular space. The modified Reiner-Riwlin equation becomes then

T=-- --+-- It + - - +--2-rrn (I 1) (K"" K" .. ) 60 Kw ) K,(o) P K

"" Kl(,, '

(6)

where K,(i) and K 2(,) are the constants defined by Eqs. 3 and 4 for the inner annulus, and Kl( o) and K" v) are those for the outer annulus. The dimensions which determine KW h K,,, ), K t( Q) and K" . ) are given in the Nomenclature.

The dimensions of the viscometer cup are such that K,ti ) = K,(,,) = K,. The torque T is related to the angular

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deflection of the torsion cup by the relationship T = K,' (1',

,where K, is the spring constant of the torque tube shown in Fig. 2 in dyne-centimeter/degree, and a is the deflection of the mirror in degrees. Substituting for T in Eq. 6 and solving for .fL" one obtains

K, . 60 . a K, . 60 . q, fL" = 27.' n' K

(7)

The experimental variables are the mirror deflection a and the speed of rotation n. One can rewrite Eq. 7 as follows:

fL" B a = An +A' q" (8)

where

A = K,. 60 K 27.

(9)

and

B = 60 ·K. 2iT

(10)

Eq. 8 represents a straight line. From the slope of the straight line one obtains fL", and from its intercept one can calculate ,q,. The constants A and B are obtained by calibration.

It is preferable to rewrite Eq. 8 in terms of the mean shearing stress Tm and the mean rate of shear Dm. The mean rate of shear in an annulus is given by the following equation:'

D = 47. . R, . R, . n on (60). (R,' - R,') (11 )

The dimensions of the two annuli in the rheometer are such that Dm is equal for both of them: D",(o) = Dm(i) = Dm. Now we substitute Eq. 11 in Eq. 8 and, after rearrangement, obtain

A 60· Vi' (R,' - R,') B a = 47. . B . R, . R, . D m + q,; . (12)

and, remembering that from Eqs. 4 and 10

B = (In R'). 60 , R, 2 ....

we get

A (R,' - R,') fLl' , B'a= g,'DmTq,

2R, . R, . In R: (13 )

RoO' - R' The expression - 'is very close to 1.0 for

g, 2R, . R, . In R:

ratios of R,fR, that are close to unity, as can be shown by developing the logarithm in a power series and dropping higher terms. Then

A B' a = Vi" Don + q, (14)

But (A/B) . a is then equal to the mean shearing stress T m , as can be seen from Eq. 1, and by plotting (A/B)'a= T m against D m one obtains JLp directly from the slope of the straight line and .cp from the intercept with the stress axis. In this paper, most consistency curves have been plotted in terms of shearing stress in Ib/lOO sq ft and shearing rate in sec-" which are not dependent on the instrument constants.

782

INSTRU,vIENT CALIBRATION The constant A of Eq. 8 can be calculated either from

the results of a mechanical calibration or by means of calibration fluids of known viscosities. By mechanical calibration with dead weights, the spring constant K, of the torque tube was obtained as K, = 14.4 X 10' dynecm/degree. K is determined by the dimensions of the sample cup. The value of A can then be calculated from Eq. 9, which yields A = 271.5, when fL" is given in poise, a in degrees, and n in revolutions per minute.

The constant A has also been determined by calibration with Newtonian oils of known viscosity. These calibrations were done by measuring the mirror deflection at a given speed of rotation, then reducing the speed to zero and allowing the sample to come to temperature equilibrium again. The flow curves of these Newtonian oils were straight lines through the origin, according to

fL" a=A' n,

which is obtained from Eq. 8 if q, = O. The viscosity of the oils is strongly dependent on temperature. The fact that straight lines were obtained shows that not enough heat was generated in the sample during viscosity measurements to affect the results. The average value of A obtained by calibration with various National Bureau of Standards viscosity calibration oils was A = 240. The instrument was also calibrated at 212F and 8,000 psi with a fluorocarbon oil (Hooker Fluorolube S), whose viscosity was known under these conditions from tables prepared by the ASME Pressure Viscosity Project." The value of A was the same within the limits of accuracy with which the viscosity of the oil was known.

Two sources of error limit the accuracy with which A can be determined: an uncertainty of ± IF in the temperature of the sample and the presence of end effects. A variation of ± IF in the sample temperature leads to an uncertainty of ±5 per cent in the viscosity of these oils and to a corresponding uncertainty in A. End effects lead to a lower value for A than is obtained by mechanical calibration' because in Eq. 9 the effect of any liquid shearing the top of the cylinder or any areas below the edge of the rotating cup has been neglected. The lower value A = 240 is therefore more likely to be correct and is known with an accuracy of ± 5 per cent. The precision with which individual measurements can be made is better than 1 per cent over a range of 20 to 1,000 cp and is determined largely by the accuracy with which the scale can be read. The uncertainty in the constant A is reflected in a corresponding error in the absolute values of the plastic viscosity and yield point, although it does not affect the observation of relative changes caused by varying temperature and pressure.

The constant B can be calculated only from the dimensions of the instrument, because standards for Bingham plastics do not exist. From Eqs. 4 and 10 it is obtained as

B = 60 'In R'(i I = 0.821. 27. Rt(o)

To obtain q, from the intercept in Eq. 8 in the customary units of Ib/l00 sq ft, one has to multiply B by

poise' rpm the factor 4.788, so that B = 3.93 Ib/100 sq ft'

The calibration of the instrument for gel strength (Sg) measurements is also based on the known stiffness of the torque tube. The maximum shear stress in a rotating cylinder viscometer occurs at the surface of the inner cylinder and is given by

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T T max - -:------;;--=-c

270' h· R/ (15)

Since in the rheometer the gel ruptures first at the surface of the inner cylinder of the inner annulus, where T is at a maximum, the gel strength is simply determined by T"""

in the inner annulus:

S = K,,·(t Q 27o·h,·R,'c"

or in conventional units:

1056 . a: dynes sq cm '

Sg = 220.8 . a: 1 od~q ft

EXPERIMENTAL MEASUREMENTS

MEASUREMENTS ON HOMOIONIC CLAY SUSPENSIONS

The rheological behavior of simple homoionic clay suspensions was studied at high temperatures and pressures, because it was believed that an understanding of such simple suspensions would assist in the interpretation of the behavior of complicated drilling muds.

Sample Preparation

Raw Wyoming bentonite was suspended in distilled water for six months. The suspension was then diluted to 1 per cent by weight and centrifuged in a Sharples laboratory supercentrifuge. A size range of 0.2- to 0.5-micron equivalent spherical radius was retained. This material was converted to the hydrogen form by stirring it into IN hydrochloric acid and rapidly filtering out the acid. Excess electrolyte was removed by washing with distilled water and stirring the hydrogen clay rapidly with Amberlite MB-l ion-exchange resin, whereupon the resin was separated from the clay by passing the mixture through a screen which retained the resin beads. The clay suspension was immediately titrated with 1 N NaOH to a pH of 8.0 and was thus converted to a sodium clay.

To prepare suspensions of known clay content, the following procedure was followed: aliquot portions were removed from suspensions of unknown clay content and evaporated at 105C. From the weight of the dry clay, the unknown concentration could be calculated. Suspensions of given weight concentrations were prepared by adding the appropriate amount of water. Suspensions containing an excess of sodium chloride or sodium hydroxide were prepared by adding the required volumes of solutions of known electrolyte concentration to the pure sodium montmorillonite suspensions. Pure calcium montmorillonite suspensions were prepared in an analogous way by titrating the hydrogen clay with saturated Ca(OH), solution to a pH of 8.0.

Description of Flow Tests

Two representative consistency curves, describing the flow behavior of a 4 per cent suspension of pure sodium montmorillonite with an excess of 5 meqlIiter of NaOH and of a 13 per cent suspension of pure calcium montmorillonite are shown in Figs. 5 and 6. All plots exhibit straight-line behavior above a critical rate of shear. Below this critical rate of shear, plug flow is observed. The critical rate of shear is a function of the ratio 1>/ fL.: when this ratio is large, plug flow occurs at higher shear rates.' This fact is clearly brought out in Figs. 5 and 6.

The difference between the flow behavior of the two suspensions of Figs. 5 and 6 is striking. While an increase in temperature decreases the yield point of the sodium montmorillonite suspension drastically, the opposite occurs

JULY, 1963

with the calcium montmorillonite suspension. Pressure slightly increases both fL. and rp for the sodium montmorillonite and ,fL. for the calcium montmorillonite suspension at 78F, while it drastically lowers the yield point rp of the calcium montmorillonite suspension at 350F. The latter effect was checked by measuring the flow curve at 350F and 300 psi twice-once before and once after the test at 8,000 psi, with the result that the two low-pressure curves agreed with each other.

Many suspensions, especially those already flocculated at room temperature, gel at high temperatures. This hightemperature gelation can be only partly reversed by prolonged shearing, as the following example will illustrate.

(\J 60 r.: LL 0 78°F,8,000 PSI

0 50

"-ai -.J

40 a

(f) /~~8°F, 250 PSI (f) /

W 30 ~ 'l a: 'l

f-- 'l (f) ~

20 t9 Z a:

10 <{ W I (f)

RATE OF SHEAR - SEC - I

FIG. 5-CONSISTENCY CURVES FOR A 4 PER CENT SUSPENSION OF PURE SODIUM MONTMORILLONITE TO WHICH 5 MEQ/LITER OF NAOH HAVE BEEN ADDED, MEASURED AT VARIOUS TEMPERATURES

AND PRESSURES.

(\J 80

f-' LL

0 70

0 "- 60 rn -.J

(f) (f) W a: f--(f)

t9 Z a: <{ w I (f)

100 200 300 400 500

RATE OF SHEAR-SEC- I

FIG. 6-CONSISTENCY CURVES FOR A 13 PER CENT SUSPENSION OF PURE CALCIUM MONTMORILLONITE AT VARIOUS TEMPERATURES AND

PRESSURES.

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A 4 per cent sodium montmorillonite suspcnsion, brought !o a pH of 12.5 with NaOH, was heated for several hours to 350F. Before heating, Flow Curve I of Fig. 7 was measured at lOOF and 300 psi. After allowing the suspension to cool again to 100F, the sample was sheared at 480 sec-" and the shearing stress was plotted as a function of time of shearing. As can be seen from Fig. 8, the sample was thinned, and the shearing stress asymptotically approached 60 Ib/lOO sq ft. Then Flow Curve 2 was measured (Fig. 7), and it is evident that even lengthy shearing had not completely restored the suspension to the deflocculated state, because Curve 2 does not coincide with Curve l.

The association-dissociation equilibrium in montmorillonite suspensions is dynamic. Fig. 9 shows the slow

(\J 60 r lL

/' /'

/' 0 50 0

/' p'

2 /' "- /'" rri ...J 40

/' /'

/' I

(f) /

/'" /'"

(f) 30 W 0: r (f) 20

/'"

/ /

;/ t9 Z

/ d

0: 10 « W I (f) 0

0 100 200 300 400 500

RATE OF SHEAR-SEC - I FIG. 7-IRREVERSIBLE EFFECT OF HIGH·TEMPERATURE GELATION J:\"

A 4 PER CENT SUSPENSION OF PURE SODIUM MONTMORILLONITE

BROUGHT TO A pH OF 12.5 WITH AN EXCESS OF NAOH. CURVE 1:

CONSISTEl'OCY CURVE AT 100F AND 300 PSI. CURVE 2: CONSISTENCY CeRVE AT 100F AND 300 PSI AFTER THE SUSPENSIOl'O HAS BEEN

(\J

r lL 100

o o "- 90 rri ...J

I (f) (f) W 0: 70 r (f)

t9 60 ~ 0:

HEATED TO 350F FOR SEVERAL HOURS.

~ 50L-__ ...L. __ -L. __ -.l.. __ ---J~_-J I 25 50 75 100 125 (f)

TIME -MINUTES

FIG. 8-REVERSIIlLE HIGH·TEMPERATURE GELATIO:\ IN TIlE SA~If. SUSPENSIO:\ AS DESCRIBED IN FIG. 7. SUSPENSIO:\ WAS SHEARED

WITH D HELD CO:\STANT AT 480 SEC' AT 100F AND 300 PSI UNTIL

A:\ EQUILIBRIU~I SHEARING STRESS WAS ATTAINED.

784

breakdown by shearing of a sodium montmorillonite suspension flocculated with 50 meq/liter of NaCI. When the shearing was interrupted, flocculation set in again, but when the suspension was sheared again, breakdown of the flocculated particles continued along the same stress-vstime curve as before.

The rheological behavior of montmorillonite suspensions is extremely complicated, as these examples show. Therefore, the following precautions were taken for all flow measurements: the samples were always aged and hotrolled at J 60F for several days before each experiment. The individual points on each flow curve represent equilibrium readings, obtained by shearing the sample at each rate of shear long enough to get a constant reading. Often the flow curves were taken going "up" and "down", i.e.,

C\I 110

~ lL

0 100

0 ...... rn 90 ...J I ({J ({J 80 W !r f-({J 70 (j Z !r <!

60

W I ({J 50

0 200

SHUT DOWN OVERNIGHT

400 600

TIME - MINUTES

800

FIG. 9-SLOW BREAKDOWN OF THE GEL STRGCTlJRE CAUSED BY

SHEARI:'iG OF A 4 PER CENT SLURRY OF PURE SODlVM MovI'·

;\lORILLO:\ITE CONTAMI:>ATED WITH 50 ~IEQ/LITER OF NACL.

D.. o

0.

:::l

40

30

20

10

CO~STANT SHEAR RATE = 480 SEC· ' .

0' /-Lp 300PSI

o 'CP

20

15

10

OL-__ ~ ____ ~ ____ ~ __ ~ ____ ~ __ ~ 0

50 150 250 350

TEMPERATURE OF

(\J

I-' lL

o o "m ...J

FIG. 10-E~·FECT OF TDIPERATURE A:\D PRESSGRE Ol'O THE YIELD

PonT cp A~D PLASTIC VISCOSITY flp OF A 4 PER CE:'iT SGSPENSIO:\

OF PI'RE SODW:\1 :YION'nIORILLONITE TO WHICH AN EXCESS OF

5 ~IEQ/LlTF.R OF NAOH HAS BEE~ ADDED.

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increasing and decreasing the rate of shear. Equilibrium had been reached when both curves coincided. Care was laken to assure the same temperature history for all samples, and no sample was exposed to a temperature higher than that at which its flow curve was measured. except when irreversible high-temperature gelation was studied. Flow curves were usually exactly reproducible when nat much time intervened between measurements. Prolonged shearing or heating of the samples usually shifted the flow curves. The complicated nature of clay suspensions limits the reproducibility of the measurements,

TABLE 1 - PLASTIC VISCOSITY jJ.p, YIELD POINT </J, AND GEL STRENGTH So OF A 4 PER CENT SUSPENSION OF PURE SODIUM MONTMORillONITE TO WHICH AN EXCESS OF 5 MEQ/liTER OF NoOH HAS BEEN ADDED,

MEASURED AT VARIOUS TEMPERATURES AND PRESSURES.

r/> Sg llb!100 sq It)

t (OF). P (ps;) jJ.p (ep) (lb/l00 sq It) 1 min ~ 30 min

78 300 39.6 19.6 2 2 8000 41.3 21.2 2 2

212 300 16.8 6.5 2 2 8000 18.6 8.0 a a

302 300 11.0 2.3 a a 8000 11.6 3.9 a a

350 300 9.4 1.7 0 0 8000 12.S 3.7 a a

TABLE 2 - PLASTIC VISCOSITY jJ.p, YIELD POINT </J, AND GEL STRENGTH Sg OF A 4 PER CENT SUSPENSION OF PURE SODIUM MONTMORillONITE TO WHICH AN EXCESS OF 50 MEQ/liTER OF NoOH HAS BEEN ADDED,

MEASURED AT VARIOUS TEM'PERATURES AND PRESSURES.

<p So (lb/l00 sq It)

~ P (ps;) jJ.p (ep) (lb/l00 sq It) 1 min 10 min 30 min

78 300 43.S 3.7 2.2 35.0 8000 42.3 4.3 2.2 7.0

212 300 14.3 8.2 18.0 26.0 40.0 8000 19.4 4.5 9.0 9.0 15.0

302 300 10.8 52.5 240.0 290.0 265.0 SOOO 4.S 35.0 88.0 100.0 100.0

TABLE 3 - PLASTIC VISCOSITY jJ.p, YIELD POINT <p, AND GEL STRENGTH Sg OF A 4 PER CENT SUSPENSION OF PURE SODIUM MONTMORillONITE TO WHICH 5 MEQ/liTER OF NoCl HAS BEEN ADDED, MEASURED AT VARIOUS

TEMPERATURES AND PRESSURES.

r/> Sg (lb/l00 sq It)

t (0 F) P (psi) jJ.p (ep) (lb/l00 sq It) 1 min 10 min 30 min

7S 300 36.8 13.8 2 8000 38.0 15.6 2

100 300 30.4 10.0 212 300 13.7 5.5 a a

8000 17.5 5.3 a a 302 300 11.9 5.2 a 2

8000 15.6 5.5 a a 350 300 12.5 10.6 4 46

8000 22.6 10.6 4 13 27

TABLE 4 - PLASTIC VISCOSITY jJ.p, YIELD POINT </J, AND GEL STRENGTH So OF A 13 PER CENT SUSPENSION OF PURE CALCIUM MONTMORillONITE,

MEASURED AT VARIOUS TEMPERATURES AND PRESSURES.

r/> Sg (lb/l00 sq It)

t (OF). P (psi) fLn (cp) (lb/l00 sq It) 1 min 10 min. 30 min

7S 300 23.3 3.1 a a SOOO 26.4 3.1 a a

100 300 20.S 7.5 2 2 212 300 29.5 64.0 2 3

SOOO 37.8 56.1 2 2 302 300 52.0 111.0 79 114

SOOO 42.6 84.3 22 37 350 300 19.2 62.2 46

8000 19.2 34.2

TABLE 5 - PLASTIC VISCOSITY jJ.p, YIELD POINT <p, AND GEL STRENGTH So OF A 13 PER CENT SUSPENSION OF PURE CALCIUM MONTMORillONITE, TO WHICH 5 MEQ/liTER OF CoCl, HAS BEEN ADDED, MEASURED AT

VARIOUS TEMPERATURES AND PRESSURES

1) Sg (lb/l00 sq It)

tJ2L P _lJ>Sil. /lJ'lco'L. (lb/l00 sq It) 1 min 10 min

78 300 15.S 20.S 22 27 SOOO 17.6 lS.9 2; 27

100 300 12.6 25.0 27 31 212 300 10.8 53.0 62 S4

SOOO 13.8 50.0 75 77 302 300 28.2 60.3 75 123

SOOO 17.4 58.0 59 102 350 300 28.2 59.2 84 112

8000 24.0 52.5 40 53

JULY, 1963

and even small differences in the history of samples lead to noticeably different flow behavior.

The data obtained with homoionic montmorillonite suspensions are summarized in Tables I through 5 and Figs. 10 through 12. In these figures the plastic viscosities and yield points, which have been derived from the slopes and intercepts of the straight-line portions of individual flow curves, are plotted as a function of temperature. The accuracy with which the slopes and intercepts can be obtained varies somewhat with each sample, depending on the scatter of the individual measurements. In samples that are not very thixotropic the accuracy is very good, while in thixotropic samples it may be no better than ±5 per cent. In samples that are very thixotropic and have very high gel strengths, as in the sample of Fig. 14, accurate plastic viscosities and yield points can no longer be obtained. However, none of the montmorillonite suspensions was of this nature. Smooth curves were drawn through the data points in Figs. 10 through 12 where this was possible. In some cases the observed changes in plastic viscosity and yield point were so abrupt that the curves were drawn with discontinuities which are probably not real and could be avoided by obtaining more data points clustered around a narrow temperature range.

Discussions oj Results on Clay Suspensions

Two main types of behavior are evident: in suspensions of sodium montmorillonite that are well dispersed and have a low gel strength, both /-'p and ¢ decrease with increasing temperature and increase slightly with increasing pressure. This type of behavior is found with sodium montmorillonite suspensions which have been dispersed by the addition of 5 meqjliter of NaOH and 5 meqjliter of NaCI (Tables 1 and 3, Fig. 10), although in the latter case some flocculation sets in at 350F. This type of deflocculated suspension, containing very small concentrations of electrolyte, has been described by van Olphen. 'o

A completely different type of behavior is found for the sodium montmorillonite suspension that has been flocculated by excess electrolyte (Table 2 and Fig. 11),

40

30

20 a.

::l

10

50

. / \ /

\ / \ /

------- ,/

, .0f.L /\'--0

P 8,OOOPSI / \ o~ / \ . ~ / \

__________ D / •

i:---~----"""

150 250

TEMPERATURE OF

60

50

(\J

40 f-' lL

0 30 0

"-m ...J

20 I

-e.

10

350

FIG. II-EFFLcr OF TEMPERATCRE AND PRESSCRE 0:\ THE YIELD

POINT ¢ AND PLASTIC VISCOSITY J.Lp OF A 4 PER CENT SUSPENSION

OF PURE SODIUM MONnIORILLONITE TO WHICH AN Excr.ss OF SO ME(l/J.ITER OF NAOH HAS BED' ADDED (pH = 12.5).

785

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and for calcium montmorillonite suspensions (Tables 4 and 5, Fig. 12). These suspensions tend to be thixotropic, especially at high temperatures. The yield point¢ increases with increasing temperature and, especially at high temperatures, decreases with increasing pressure, as does the static gel strength So. This latter effect can reduce ¢ to one-half and So to one-fourth of its original value for a pressure increase from 300 to 8,000 psi (Table 4). The gel strength So and yield point ¢ show in general a parallel behavior, but no simple relation exists between them. The plastic viscositY{tp decreases with increasing temperature for the flocculated sodium montmorillonite suspension (Table 2, Fig. 11) and shows a more complicated behavior for the calcium montmorillonite sus-

0.. o

30

20

10

TEMPERATURE 0 F

FIG. 12-EFFECT OF TEMPERATURE AND PRESSURE ON THE YIELD POINT ¢ AND PLASTIC VISCOSITY fLp OF A 13 PER CENT SUSPENSION

OF PUllE CALCIUM MONTMORILLONITE TO WHICH 5 MEQ/LITER OF CACL2 HAVE BEEN ADDED.

(\J ",rt,

f-' 6C ov, ~,o

LL v0 0 '\'\ 0 50 r;;> "'- ?, ai

rt,e..,

.J " '00 rt,

~'\ 1

40 '-(9 0 &'" \,0

(f) o? ,'v'<J (f) 0° ". W 30 '0' 6(. 0::

ov, , e..,'X '

I-' '00 IX":) ":l

(f) "

&",,?'! 20 l') 0'X

Z oCJ " 0:: o~,

4 10 ,00 W I (f)

100 200 300 400 500

RATE OF SHEAR-SEC -I

FIG. 13-CONSISTENCY CURVES OF A PROPRIETARY SODIUM-BASED DRILLING FLUID "A" CONTAINING A CHROME-LIGNOSULFONATE, CHROME-LIGNITE DISPERSANT (pH = 9.0, WEIGHT = 15.7 LB/GAL).

786

pensions. In the case of the pure calcium montmorillonite, {tp decreases slightly, then reaches a maximum at 300F and abruptly decreases again (Table 4). The calcium montmorillonite suspension with added CaC!, shows a slight initial decrease in ,{tp with increasing temperature, followed by a much smaller rise and no decrease at high temperatures (Table 5, Fig. 12). Pressure has little effect on{tp at low temperatures, where only small increases are observed. At high temperatures {tp is in some cases lowered by an increase in pressure, following the behavior of the yield point ¢.

(\J

I-' 400 LL o o "'-ai .J 300

I (f) (f) W 0:: 200 I-' (f)

l') Z 0:: 100 4 W I (f)

100 200 300 400 500

RATE OF SHEAR-SEC-I

FIG. 14--CONSISTENCY CURVES OF A PROPRIETARY SODIUM-BASED DRILLING FLUID "B", IDENTICAL WITH FLUID "A" OF FIG_ 13

EXCEPT FOR A HIGHER CLAY CONTENT AND LESS WEIGHTING MATERIAL (pH = 8.4, WEIGHT = 11.6 LB/GAL).

2500

2000

W (f)

0 1500 D...

f= Z W 118 11

0 1000

c. c. 0

:::l 500

IIA"

50 150 250 350

TEMPERATURE 0 F

FIG. IS-ApPARENT VISCOSITY OF THE DRILLING FLUIDS OF FIGS. 13 AND 14 AS A FUNCTION OF TEMPERATURE AT CONSTANT PRESSURE OF 1,000 PSI, CONSTANT RATE OF SHEAR OF 120 SEC-

1 AND

CONSTANT RATE OF TEMPERATURE INCREASE OF 2 F/MIN.

JOURNAL OF PETROLEUM TECHNOLOGY

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The effect of increasing temperatures on the dispersed suspensions of the first type can be explained by a simple weakening of the strength of the bonds between particles by thermal energy. This effect explains the decrease in cp. The plastic viscosity ftp also decreases at higher temperatures for all sodium montmorillonite suspensions, probably because of a partial destruction of the hydration shell. These observations are in agreement with previous investigations,'" which have revealed decreases of ftp with increasing temperature.

The calcium montmorillonite suspensions consist of thicker particles formed by parallel association of unit layers, which explains the fact that much higher concentrations of clay are required to observe a yield point." These thicker particles are dispersed at high temperatures, which causes jJ-p as well ascf> to increase.

The effect of high temperatures on montmorillonite suspensions can be attributed to the complicated interplay of several causes, among which the following are prominent: reduction of the degree of hydration of the counterions, changes in the electrical double-layer thickness, increased thermal energy of the clay micelles, reduction of the viscosity of the suspending medium and increased dispersion of associated clay micelles. All these processes take place simultaneously, and an interpretation of the observed results is possible only in those cases where some of the effects are predominant, so that they can be identified.

Pressure normally would be expected to increase both P'P and cf> slightly, because it leads to a compression of the suspending medium and some increase of its viscosity. According to the Einstein equation, both these effects contribute to an increase in the resistance to flow of a solid suspension,' although this equation does not hold quantitatively for colloidal suspensions of very unsymmetrical particle shapes. In general, slight increases in ftp and cf> with increasing pressure are observed with dispersed suspensions of relatively low yield point and gel strength.

The considerable decrease in cf> and So with increased pressure observed for the calcium montmorillonite and flocculated sodium montmorillonite suspensions at high temperatures is unexpected. Grodde' is the only author who has pointed out that the gel strength may decrease slightly with pressure, but he gives no data. A high yield stress in solid suspensions is generally attributed to anisometry of particles," The suspensions in which we observe reductions in yield stress with pressure consist probably of flocculated lamellae, where face-to-face, edgeto-face and edge-to-edge attraction accounts for the structural viscosity, not heterocoagulation with its attendant card house structure," Foster, Savins and Waite" have suggested that increased cation hydration increases the degree of asymmetry and the amount of water bound to the particles. It is possible that at high pressure the hydration is reduced, which would cause an increase in symmetry and a lower yield point. On the other hand, if one accepts the lyosphere theory, which explains structure formation by the mutual interaction of extended hydration shells," the proposed diminution of the hydration shell easily explains the observed reduction of cf> and Su' This theory would account for our data most convincingly. Of the other factors that influence the balance of attractive and repulsive forces between the suspended particles, the van der Waal's attractive force cannot be influenced by pressure. The electric double layer, however, which is responsible for the repulsive forces, could be affected by pressure-although how this could happen is not clear. A

JUI,Y. 1963

unique explanation for the lowering of cp and So by pressure cannot be given based on our data alone without further supporting and independent evidence.

TEST RESULTS ON DRILLING FLUIDS

Results of rheological measurements on a few representative drilling fluids are presented in Figs. 13 through 20. Some were field samples, others were prepared especially for these tests.

Chrome Lignite-Chrome Lignosulfonate Mud

Figs. 13 through 15 represent flow tests on two chrome lignite-chrome lignosulfonate mud samples that were chemically identical, except that Sample A contained more barite and less bentonite than Sample B. Sample A gelled very little at 350F and 8,000 psi, while the yield point of Sample B increased so much that low shear-rate measurements were complicated by slip and very long relaxation times caused by extreme thixotropic behavior. At 100F and 1,000 psi, the two samples differed very little. Fig. 15 shows the continuous change of the apparent viscosity with temperature at a constant shear rate of 120 sec-' for Samples A and B. The apparent viscosity is defined as ft,pp = TID and depends on D for non-Newtonian fluids. It is plotted when rapid temperature-viscosity profiles are taken by raising the temperature at a constant rate and rotating the rheometer cup at a constant rotational speed. Fig. 15 shows that Sample B begins to gel rapidly at 250F because of the high concentration of swelling clay.

High-pH, Lime-Lignite Mud

The behavior of this lime-base mud (Fig. 16) is qualitatively similar to that of the calcium montmorillonite suspension of Table 5 and Fig. 12. The plastic viscosity goes through a minimum at about 200F, while cp increases continuously. The magnitude of the increase in cp is much larger than in the calcium montmorillonite suspension, because the concentration of solids is higher in the lime-base mud, and the high pH causes irreversible reactions between Ca(OH), and clay.

N f-' 200 u.. o o "-ai ..J 150

I (f)

~ 0:: 100 f-(f)

~ rr 50 « W I (f)

100 200 300

RATE OF SHEAR-SEC- I

FIG. 16-COl'iSISTENCY CURVES AT VARIOUS TEMPERATURES A:>D PRESSURES FOR A HIGH-pH, LIME-LIGNITE DRILLING FLUID

CONTAINING EMULSIFIED OIL.

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Calcium Surfactant Mud In contrast to the lime-base mud, the calcium sur

factant (DMS) mud of Fig. 17 is completely stable at 350F and 8,000 psi. Its rheological behavior varies with temperature in a way qualitatively similar to the behavior of the dispersed sodium montmorillonite suspension of Table I and Fig. 10, except that in the case of the DMS mud cp goes through a shallow maximum at 200F. It may be assumed that the colloidal structure of the calcium surfactant (DMS) mud is similar to that of the dispersed sodium montmorillonite suspension.

Gyp Q-Broxin Mud The gyp Q-Broxin mud of Fig. 18 resembles the cal

cium montmorillonite suspensions whose properties are described in Tables 4 and 5 and Fig. 12 insofar as both ¢ and So increase considerably with increasing temperature.

~ 40 r---------------------------------, f-' LL o o '- 30 ai -.J

I (f) (f) 20 W (t f-(f)

() 10 Z (t <! W I (f)

100 200 300 400 500

RATE OF SHEAR-SEC - I

FIG. I7-CONSISTENCY CCRVES AT VARIOUS TEl\IPERATlJRES A'\'D

PRESSURES FOR A CALCIUM SURFACTANT DRILLING FLnD

~

f-: LL 50

o o '- 40

(f) (f) W

30

(t 20 f-(f)

() Z (t <! W I (f)

10

00.5 LE/GAL).

100 200 300 400 500

RATE OF SHEAR- SEC - I

FIG. IS-CONSISTENCY CURVES OF A GYP·Q·BROXIN DRILLING

FLUID AT VARIOUS TEMPERATURES MiD PRESSURES.

788

However, the decrease in ,flp at 300F corresponds more to the behavior of the sodium montmorillonite suspensions and probably reflects the influence of the lignosulfonate on the colloidal structure.

Oil-Base Mud

The oil-base mud of Fig. 19 approaches Newtonian behavior, especially at high temperatures. Its plastic viscosity decreases strongly with increasing temperature; however, this decrease is partially offset by a considerable increase inflp with pressure (Fig. 20). This behavior can be explained by the greater temperature and pressure dependence of the viscosity of the suspending medium, oil, compared to that of water. The large changes Offtp and ¢ with temperature and pressure, indicated in Figs. 19 and 20 for a representative oil-base mud, point out that exact rheological data could be obtained for these samples only

C\I 140

I-' LL o 120 o '-

~ 100

I (J) (J) 80 W a: r-(J) 60

t9 Z a: 40 « W I (J) 20

100 200 300

RATE OF SHEAR-SEC - I

FiG. I9-CONSISTENCY CURVES OF OIL· BASE DRILLING FLUID AT

VARIOUS TEMPERATURES AND PRESSURES.

:\J 120 I-' LL o 100 o '-oj -.J 80

(J) (J) 60 W a: r-(J) 40

t9 Z a: 20 <! W I (J)

100 200 300

RATE OF SHEAR- SEC - I

FIG. 20-EFFECT OF PRESSURE ON THE VISCOSITY OF OII.·BA:;I:

DRILLING FLTTID AT 200F.

.I0IJR:\',\I. OF PETROI.EITM TECII"IOI.O(;Y

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in an instrument permIttmg measurements both at high temperature and high pressure.

CONCLUSIONS

The flow properties of clay suspensions and of drilling fluids differ considerably under bottom-hole conditions from those measured under ordinary conditions, and the magnitUde of these differences is not generally predictable. The example presented in Fig. 15, in which two chemically similar drilling fluids show entirely different flow behavior at high temperature but not at low temperature, is convincing evidence of the need to make pilot tests on drilling fluids under conditions equivalent to those in the borehole.

The data presented in this paper show, however, that certain generalizations concerning the effects of temperature and pressure on the flow behavior of drilling fluids are possible. These generalizations are based on the qualitative relationship that exists between rheological behavior and colloidal structure. Certain parallels exist between the behavior of homoionic clay suspensions on the one hand and drilling fluids on the other hand. If one identifies the type of colloidal suspension to which a drilling fluid belongs, qualitative predictions of the temperature and pressure variations of its flow properties are possible based on the data presented in this paper.

The data can be applied also to quantitative calculations of friction losses in drill pipe and annulus according to the procedures described by Melrose and co-authors.' These authors have solved the problem of computing the pressure drop for the flow of a Bingham plastic fluid in an annulus and have presented graphical representations of the solution. The rheological properties should be known under down-hole conditions to make accurate use of the graphical procedures presented in the paper of Melrose, et al.

The data can be applied also in calculating start-up pressures after periods of interrupted circulation and in computing the suspending ability of the quiescent drilling fluid. Both of these characteristics are dependent on the static gel strength S9' which has been found to vary considerably with temperature and pressure.

NOMENCLATURE

A = instrument constant (Eq. 9); A = 240 poise· rpm

degree

B = instrument constant (Eq. 10); B = 3.93 poise' rpm

Ib/lOO sq ft

D = rate of shear, sec-'

D", = mean rate of shear (Eq. 11); D",

hCi) = length of inner annulus surface; h(i) = 7.112 cm

h(o) = length of outer annulus surface; h(o) = 10.015 cm

Kl( i) == --- --.,-- - --" -1 (1 1) 47Th, R-'(i) R-'(l)

.JIILY. 191i;1

1.2 . n sec-'

K = K,(o) + K ,(,) K'(i)'K,(o)

K, = spring constant K, = 14.4 . 10' dyne-cm/degree

T = torque, dyne-cm n = rotational velocity, rpm

R,(,) = inner radius of inner annulus, R'(i) = 1.746 cm R,c i) = outer radius of inner annulus, R,( i) = 1.905 cm R,(o) = inner radius of outer annulus, RI(o) = 2.064 cm RI(o) = outer radius of outer annulus, R,c", = 2.202 cm

Sa = gel strength, lb/ 100 sq ft a = mirror deflection, degrees }L = viscosity (Newtonian), poise (or cp)

p,p = plastic viscosity, poise (or cp) }Lopp = apparent viscosity, poise (or cp)

cp = Bingham yield point, lb/ 100 sq ft T = shear stress

T", = mean shear stress Tmax = maximum shear stress

REFERENCES

1. Srini-Vasan, S. and Gatlin, C: "The Effect of Temperature on the Flow Properties of Clay.Water Drilling Muds", Trans., AIME (1958) 213, 59.

2. Gurdzhinian, L. D.: "Effect of Temp,eratures on the Rheolog· ical Properties of Clay Suspensions", Neft i Gaz (1959) 2, No. 7,91.

3. Grodde, K. H., "Rheologie kolloider Suspensionen, insbeson· dere der Bohrspuelungen", Erdoel & Kohle (1960) 13, No.1, 11.

4. Melrose, J. C, Savins, J. G., Foster, W. R. and Parish, E. R.: "A Practical Utilization of the Theory of Bingham Plastic Flow in Stationary Pipes and Annuli", Trans., AIME (1958) 213, 316.

5. Grodde, K. H.: "Ein Absolut·Rheometer vom Couette·Typ", Kolloid Z. (1954) 139,91.

6. Pryce·Jones, J.: "Studies in Thixotropy", Kolloid Z. (1952) 129, 96.

7. Savins, J. G. and Roper, W. F.: "A Direct·Indicating Vis· cometer for Drilling Fluids", Drill. and Prod. Prac., API (1954) 7.

8. Reiner, M.: Deformation, Strain, and Flow, Interscience Pub· lishers, Inc., N. Y. (1960).

9. ASME Pressure Viscosity Project, Unpublished data obtained at Harvdrd U. (1950·1951).

10. Van Olphen, H.: "Forces between Suspended Bentonite Par· ticles", Proc., Fourth Nat. Conf. on Clays and Clay Min., Nat. Acad. Sci. (1956) 204.

11. Van Olphen, H.: "Forces between Suspended Bentonite Par· ticles Part II-Calcium Bentonite", Proc., Sixth Nat. Conf. on Clays and Clay Min., Nat. Acad. Sci. (1959) 196.

12. Street, N.: "Viscosity of Clay Suspensions", World Oil (Dec., 1958) 151.

13. Foster, W. R., Savins, J. G. and Waite, J. M.: "Lattice Ex· pansion and Rheological Behavior Relationships in Water· Montmorillonite Systems", Proc., Third Nat. Conf. on Clays and C!t:y Min., Nat. Acad. Sci. (1955) 296. ***

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Documents

Rheological Measurements on Clay Suspensions and Drilling