Rheological Design of Cementing Operations

KNOX A. SLAGLE

ABSTRACT

Hydraulic analysis of the wellbore has become increas­ingly important for designing cementing operations and selecting equipment, materials and techniques to comple­ment modern well-completion practices. Non-Newtonian fiuid technology has advanced beyond the point where former empirical methods of analysis adequately define the hydraulic system and fluid properties.

In view of these factors, this paper describes a series of rheological calculations which have been found prac­tical, through field usage, for assistance in selecting a cementing program. A relatively simple laboratory method using standard viscometric equipment is suggested for de­termination of the rheological properties of slurries, and data are presented on some of the more common cement­ing compositions. A criterion for divergence from laminar­flow characteristics has been proposed. Usefulness of the calculations is indicated by examples of cementing opera­tions where they have been used.

INTRODUCTION

With the changing aspects of well-completion practices during the past few years, it has been increasingly im­portant to have a relatively simple method of analyzing the flow conditions existing in the well during cementing operations. This is particularly true in view of the im­proved economics toward which most of the changes have been directed. Rheological characteristics of slurries used for cementing should be a major consideration in the trend toward smaller casing sizes, either single or multiple strings.

Receiving increased attention is the practice advocated in 1948 by Howard and Clark' of attaining turbulent flow with the fluids circulated during a primary cementing operation. While there may still be a difference of opinion concerning this technique, most available information indicates that superior primary-cementing results are gen­erally obtained when high displacement rates are em­ployed. Fluid properties of the slurry to be used must be available, as well as calculation methods, to determine what flow rates should be attained and the probable con­sequences in terms of frictional pressure and horsepower utilization. It would certainly be inappropriate to attempt high displacement velocities if sufficient pressure might be developed to create lost circulation.

Since cementing slurries are non-Newtonian fluids, it

Original manuscript received in Society of Petroleum Engineers office Sept. 9, 1961. Revised manuscript received Jan. 9, 1962. Paper presented at 36th Annual Fall Meeting of SPE, Oct. 8-11, 1961, in Dallas.

'References given at end of paper.

MARCH, 1962 SPE 152

HALLIBURTON CO. DUNCAN, OKLA.

is not possible to define their rheological or fluid proper­ties by the single factor of viscosity and then make cal­culations for the quantities just described. Because the shear stress-shear rate ratio is not constant, it becomes necessary to establish at least two parameters for adequate fluid-flow calculations. It is not the purpose of this paper to delve into the mathematical development of non-New­tonian technology, nor to discuss the arbitrary classifica­tion system under which a single fluid may resemble two or three different classes depending upon experimental conditions. Rather, the intention is to present a useful series of calculations based on a concept applicable to both Newtonian fluids and to the preponderance of non­Newtonian fluids encountered in the oil-producing industry.

Development of this approach was begun some 32 years ago; and has most recently been brought to fruition by Metzner'-' and his co-workers at the U. of Deleware. Some non-Newtonian fluids encountered in the petroleum industry, other than cementing slurries, have also had the benefit of this method of analysis."" The two para­meters required to define the fluid are usually denoted by the symbols n' and K' and, for the purposes of this discussion, are called "flow behavior index" and "consis­tency index", respectively. These two slurry properties per­mit calculation of the Reynolds' number and the "critical" velocity, or the velocity at which departure from laminar flow begins.

EXPERIMENTAL DETERMINATIONS

The two principal instruments used for rheological studies are the pipeline (capillary-tube) viscometer and the rotational viscometer. When conveniently possible, a capil­lary-tube viscometer (where the pressure drop and flow rate of the material can be measured) is the better method for rigorous determination of the flow behavior index and consistency index for non-Newtonian fluids. With pressure-drop data at various flow rates, it is then possible to prepare a logarithmic plot of shear rate as the abscissa­shear stress as the ordinate. For fluids which do not exhibit time-dependency, these data will usually produce a straight line. The flow behavior index n' represents the slope of this line, while the consistency index K' becomes the intercept of this line at unity shear rate in accordance with the mathematical derivations associated with this concept of rheology.

Due to the difficulties anticipated in maintaining a uni­form, pumpable cement slurry for the time interval re­quired to obtain measurements from the pipe viscometer, the n' and K' data reported herein were obtained using a direct-indicating rotational viscometer (Fig. 2). The

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instrument was of the type described by Savins and Roper," but was equipped to operate at six rotational speeds (600, 300, 200, 100, 6 and 3 rpm). With this instrument, the shear stress is obtained by dividing the dial reading by 100; the shear rate is a function of the speed of rotation and the dimensions of the rotor and bob. For the standard instrument, shear rate equals 1.703 X rpm. As with the pipe viscometer, a logarithmic plot of shear rate vs shear stress yields essentially a straight line where the slope and intercept at unity shear rate again are the desired slurry properties.

Complexity of the chemical reactions occurring when cement and water are initially mixed makes it extremely important that slurry preparation methods be standardized in order that reasonably reproducible data be obtained with the rotational viscometer. The following steps have been found most satisfactory.

1. Mix the slurry initially with a high-speed mixer, as described in API RP lOB, "Recommended Practice for Testing Oil-Well Cements and Cement Additives".

2. Transfer slurry to atmospheric-pressure thickening­time Tester A of API RP lOB for 5 to 15 minutes of slow­speed mixing.

3. Pour the slurry into the sample cup of the viscometer, raise the cup into the operating position and start the instrument at 600 rpm.

The slow-speed mixing period is required to minimize the initial gelling characteristics of freshly mixed slurries which complicate viscometric measurements.

Each step in handling the slurry should involve a mini­mum time delay since thixotropic or gelling tendencies of a much lower magnitude still exist and could interfere with measurements. Another part of the procedure which also tends to depress thixotropic interference is the practice of taking the initial viscometer reading after 60 seconds at the highest speed (600 rpm), then decreasing speed (300, 200 and 100 rpm) and taking resultant dial readings at 20-second intervals. These data are used to prepare the flow curve on logarithmic co-ordinates as described earlier to obtain n' and K'.

The readings at 6 and 3 rpm are not normally used in this analysis. It is believed that erratic readings are obtained at these rotational speeds because of the extreme shear-rate gap between 100 and 6 rpm. This was apparently sub­stantiated by brief experimental data obtained on a rota­tional viscometer capable of infinitely variable speed. It was found that all points below 600 rpm, including the readings at very low shear rates, produced a basically straight line on a logarthmic shear rate-shear stress plot.

The data presented in Table 1 were obtained using this procedure at room temperature. This table includes some of the average n' and K' values discussed later for 17 sources of cement, as well as the values for several slurries prepared with a cement of median viscous properties.

The most recent addition to cement slurry rheology liter­ature has been presented by Ish-Shalom and Greenberg" This work, done at the Portland Cement Assn. lab, utilized a different rotational viscometer. When comparable slur­ries were tested, re-evaluation of their viscometric data in terms of n' and K' shows very similar slurry properties to those of Table 1 within the limits imposed when test­ing cements from different manufacturing plants.

The Fanning friction factor-Reynolds' number correla­tion proposed for cementing slurries in the turbulent region is that marked "non-Newtonian" in Fig. 1. The Newtonian curve is the standard correlation for such fluids in com-

324

TABLE I-SLURRY PROPERTIES OF API CLASS A CEMENT

P Additive n' K' (lb/gai)

None' 0.30 0.195 15.6 Calcium Ligno5Ulfonate* 0.33 0.104 15.6 Bentonite-4o;.* 0.10 0.95 14.1 Bentonite-8o;.' 0.10 0.90 13.1 Bentonite-12o;.' 0.10 0.76 12.6 Bentonite--12% plus Calcium lignosulfonate--O.6 % * 0.14 0.124 ~2.6 Saturated Salt Water 0.20 0.180 16.2 Diatomaceous Earth-20o;.' 0.20 0.312 12.4 Latex Cement 0.44 0.039 14.5 Pozzolan X Cement-O% Bentonite* 0.30 0.166 15.2 Pozzolan X Cement-2% Bentonite* 0.10 0.81 14.1 Pozzolan X Cement plus Calcium lignosulfonafe 0.23 0.155 14.1 Pozzolan X-lime 0.35 0.120 14.0 Pozzolan X-lime plus Calcium ligno5ulfonate 0.43 0.057 14.0

* Average data for 17 sources of API Class A cement.

API Class C-Sulfate Resistant Cement None 0.43 0.03 14.1

13.0 12.5

Benton ite--4 %

Bentonite--8% 0.10 0.30 0.10 0.30

merical pipe, while both types of fluids are accommodated in the laminar region by f = 16/NRe • The extensive data represented by the non-Newtonian curve were obtained using 1,000 ft of 2-in. tubing which was approximately one-half test section and the remainder calming sections. Three triplex plunger pumps commonly used in the oil field were employed to provide power for measurements in the turbulent region approaching a Reynolds' number of 200,000. It should be noted here that these data were obtained with bentonite-water suspensions and with emul­sions, both of which are discreet-particle systems as dif­ferentiated from gelatinous fluids, for which an entirely different correlation is necessary. The not unreasonable assumption must be made that cement and the predominant number of additives will produce suspensions of indepen­dent particles which are adequately described by this cor­relation. Only one cement slurry has been tested in this manner and through a rather limited range of Reynolds' numbers. Excellent agreement was obtained both with the friction-factor correlation and with the comparison of viscometric and pipeline slurry properties. Metzner and Reed' also reported essentially the same friction factor­Reynolds' number plot in their resume of published data on various non-Newtonian fluids.

VARIATIONS IN CEMENTS

One of the major sources of deviation which can be introduced into any system of rheology dealing with ce­menting slurries is that of the variable properties of cement. This study involved the measurement of n' and K' for the API Class A cement from 17 sources (each cement being mixed in 20 different slurry compositions, or

I

'" ~ .0 l!

I

,"'

I

I"'

I ~ .... 2:N I

z o ;:: <.)

ii: f---- + LAMINAR FLOW

---i{ I

u..

'" Z Z z l!

I--

I .00 10'

-hREGI?NI I

I

i

I I I

! ! I I

i' Iii I

i i I

10'

REYNOLDS NUMBER - N

I I

R,

, I" I i ;

I , N£WT01W):;;-

j----. -i--

NON-NEWTONIAN

II IT ' r-- ,-t+

iii ~tl 10'

FIG. I-REYNOLDS' NUMBER-FRICTION FACTOR CORRELATION.

10'

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a total of 340 fluids), always tested in duplicate and often - in triplicate. Geographical distribution of the cements in­

cluded four from the Southwest, two from the Midwest, six from the Gulf Coast, three from California and two from the Rocky Mountain area. Generalization of the cement characteristics indicated that Gulf Coast cements were more viscous than average, cements from the South­west and Midwest had median viscous properties, while California and Rocky Mountain cements were less viscous. It was found that no apparent correlation existed between viscous properties and surface area or fineness of the cements tested.

Further generalization showed the more-viscous neat cements to have minimum n' values and maximum K' values, while the less-viscous cements tend toward maxi­mum n' values and minimum K' values. These factors also influence the calculations described later, with the more­viscous cements yielding higher "critical" velocities and frictional pressure drop.

Actual ranges in rheological properties for different ce­ments mixed with the API recommended water ratio (46 per cent) were n' from 0.19 to 0.42 and K' from 0.638 to 0.049, as compared to the average values of 0.30 and 0.195, respectively. The average values reported in Table 1 were obtained from a shear stress-shear rate plot after averaging the basic viscometric measurements. The ex­tremes of n' and K' caused fluctuations in calculated "crit­ical" velocity of approximately ± 35 per cent. Somewhat higher variations existed in Reynolds' number calculations, particularly in the region beyond laminar flow. Friction­pressure drop calculations were more seriously affected in the laminar-flow region, while in the transition-turbulent region the deviation between cements was about ± 15 per cent.

Additives such as pozzolans, bentonite and diatomaceous earth generally tended to minimize variations in cements due to the decrease in cement content of the slurry. With these additives, n' and K' ranges were not as widespread and "critical" velocity deviations were usually ± 20 per cent or less. Chemical additives such as calcium lignosul­fonate usually caused the opposite effect and created larger deviations. An extreme variation of 100 per cent in calculated "critical" velocity occurred with the ligno­sulfonate, but was attributable primarily to two cements which reacted at marked variance to the other 15 cements.

FLOW EQUATIONS

There is no particular complication involved in calcu­lations for this system of rheology when compared to usual Newtonian formulas. The fluid properties n' and K' appear only in the Reynolds' number formula. This equation, with the constant required to permit use of standard oiI-produc­tion-industry dimensional units and with rearrangement of terms for easiest calculation, becomes

N _ 1.86V'-·' p Re - K' (96/D)n. (1)

For Newtonian fluids n' 1 and K' is proportional to viscosity so that this relationship reduces to

NRC = 927.6 DV p (2) JL

Another useful expression for some phases of these calcu­lations is the relationship between Fanning friction factor and Reynolds' number in the transition and turbulent region for the non-Newtonian correlation of Fig. 1.

f = 0.00454 + 0.645 (NRe)-'<O (3)

MARCH, 1962

The friction pressure-drop formula

P 0.039 LpV'f

!:::.. ! = --D-=-'-- (4)

is the usual equation associated with this calculatIon, with a constant being inserted to correct for the dimensional units used.

One extremely interesting finding during establishment of the friction factor-Reynolds' number correlation was the rather pronounced divergence from laminar flow which occurred at N Re = 2,100. Although this does not represent an abrupt change to turbulent flow and in reality the tran­sition region probably is quite broad, these disperse fluids did not yield the fluctuations often obtained in the transi­tion region with Newtonian fluids. In view of this, a minimum criterion for turbulent flow was established at this Reynolds' number and rearrangement of Eq. 1 yields a minimum "critical" velocity.

V,"" = 2,100 K' (96/D)n. 1,129 K' (96/D)n. 1.86 p p

(5)

Also of use is the expression for hydraulic horsepower. HHP = 0.0245 PwQ (6)

P w = !:::..P, + Ph. - Ph' • (7)

Calculation of hydrostatic pressures can be determined rather easily when fluid densities are available in the form of pressure gradients as recommended by APr for reporting mud weight (Table 2).

One of the major problems of wellbore hydraulic analy­sis which has not been discussed is that concerning calcu­lations in annular sections. There presently exists only limited information for this type of flow channel and, while methods have been proposed for this situation, they are largely unsupported by published experimental proof or data. In view of this inadequacy, it becomes contingent upon us, as on many previous authors, to use the old standby-hydraulic radius or "equivalent diame­ter". D. is described as four times the cross-sectional area of the channel divided by the wetted perimeter of the channel; for a concentric circular annulus, this reduces to

D. = Do - DI (8)

Admittedly, there is a certain undefined error introduced by use of this term, particularly in thin annuli, but correc­tion must await the development of a more practical analysis than now exists. Also for many of the pipe size­hole size relationships encountered in well-completion practice, the matter may be rather academic since the effect of the annulus often appears to be minimal in the over-all hydraulic analysis, with the exception of calcu-

Ib/gal

8.33 8.5 9.0 9.5

10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

TABLE 2-PRESSURE GRADIENT

Density Ib/eu ft

62.4 63.6 67.3 71.0 74.8 78.5 82.3 86.0 89.8 93.5 97.2

101.0 104.7 108.5 112.2 115.9 119.7 123.4 127.2

Gradient (psi/l,OOO ftl

433 442 468 494 520 546 572 598 624 650 676 702 728 754 780 806 832 858 884

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lating velocities for approaching turbulent flow. Even in this latter situation, the error may not be acute because of the almost equal reported efficiency' of upper laminar and transitional or turbulent flow in removing circulatable mud from the hole.

FIELD EXAMPLES

The following are not hypothetical field situations; they represent some of the actual calculations which have been used to set up cementing operations. Where data were available on performance of the job, they have been included.

NUMBER 1

Set 2V2 -in. tubing in 8¥! -in. hole at 3,800 ft. Use 12 per cent gel cement with 0.3 per cent calcium lignosulfonate to bring top of cement to 1,800 ft.

Problem: Can turbulence be approached in the annulus? What flow rate can be obtained with 3,000-psi pressure limitation? What hydraulic horsepower could be utilized?

Slurry Properties: n' = 0.14, K' = 0.28, and p = 12.6 Ib/ gal.

Flow Channels:

2%·in. Tubing Annulus

D = 2.441 in. D, = 8.75 - 2.875 = 5.875 in . Area = 0.372 sq ft Area = 0.0325 sq ft

"Critical" Velocity in Annulus:

3·26

V ' .86 = 1,129(96/ 5.875) °14 (0.28) c 12.6 = 37.1 ,

Vc = 7.00 ft/second.

Q __ 7.00 (60) (0.3725) -----:~;---'- = 27.9 bbl/ min.

5.61

FIG. 2-ROTATIONAL VISCOM ETER.

Frictional Pressure Inside Tubing @ 27.9 bbl/min: 27.9 (5.61)

V = 60 (0.0325 ) = 80.3 ft/ second.

1.86 (80.3)' " (12.6) N Re = 0.28 (96/2.441)014 = 177,610.

From Fig. 1, f = 0.0044, P _ 0.039(3,800) (12.6) (80.3) 2(0.0044 )

Cl f - 2.441

= 21,704 psi.

Obviously, it is impractical to consider annular turbulence as a possibility.

Solution of the second phase was most simply achieved by trial-and-error methods. Eq. 1 using the known factors reduced to

N Re = 50.0 VUH•

Substitution of this in Eq. 3 gave 1= 0.00454 + 0.0416 V ' 3

which, when introduced into Eq. 4, yielded

ClPf = 3.473 V' + 31.82 y O' .

Assuming hydrostatic heads and frictional pressure in the annulus would tend to balance each other . during the major portion of the mixing and displacement tim.e, espe­cially since the mud properties are not known, then ClPf

= P lY = 3,000 psi, the maximum permissible pressure. The trial-and-error solution under this assumption gave

V = 27.75 ft/ second in the tUbing.

Q = 27.75 (6~.~iO.0325) = 9.65 bbl/min.

HHP = 0.0245 (3,000) (9.65) = 709 hp.

NUI\1BER 2 Set 4Vz -in., 9.5-lb casing in TVs -in. hole at 3,307 ft. Use

Pozzolan X cement with 0 per cent bentonite (104 cu ft). Calculate: Displacement rate to approach turbulent flow

in annulus. Hydraulic analysis for comparison with pres­sures recorded during the actual operation.

Slurry Properties:

Fl ui d Properties

n' K' p

Pressure Gradient

Slurry

0.30 0.166

15.2 Ib/gol 790 psi /1 ,000 ft

Drilling Mud '

0.29 0.066

9.7lb/gal 505 psi/1 ,000 ft

' Properties measured on location while circulating prior to cementing.

Flow Channels:

4'h·in. Casing Annulus

D = 4.09 in. De = 3.375 in. Area = 0.0912 sq ft Area = 0.2278 sq ft

"Critical" Velocity lor Slurry in Annulus:

V 1.10 = 1,129(96/3.375)°30(0.166)

c 15.2 = 33.7.

Vc = 7.91 ft/ second. 7.91 (60)(0.2278)

Q = 5.61 = 19.3 bbl/min.

Actual displacement rate during job = 16.5 bbl/min, which calculates to

V (Pipe ) 16.5 (5.61) = 16.92 ft/second. 60 (0.0912) 16.5 (5 .61)

V (Annulus) =6.77 ft/second . 60 (0.2278)

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Frictional Pressure-Drop Calculations: Cement in pipe,

N - 1.86 (16.92)" (15.2) - 5 R. - 0.166 (96/4.09)0'0 - 8,0 0,

/ = 0.0057, e:..P = 0.039 (1,000) (15.2) (16.92)' (0.0057)

, 4.09

= 236.6 psi/1 ,000 ft. Cement in annulus,

N _ 1.86 (6.77)'7 (15.2) Rc - 0.166 (96/3.375)030

/ = 0.0099,

1,610,

0.039 (1,000) (15.2) (6.77)' (0.0099) e:..p, = --------,,---c==--------

= 79.7 psi/1,000 ft.

Drilling mud in pipe, NRe = 13,650,

/ = 0.0054,

3.375

e:..Pf = 143.0 psi/1,000 ft. Drilling mud in annulus,

NRe = 2,710, / = .0071,

e:..P, = 36.5 psi/1 ,000 ft.

Hydraulic Analysis with All Slurry Inside Casing:

104 cu ft of slurry in 41h-in., 9.5-lb casing. Height of cement column = 104/0.0912 = 1,140 ft. Height of mud in pipe = 3,307 - 1,140 = 2,167 ft.

Total llP,

1.140 X 236.6 = 270 psi 2.167 X 143.0 = 310psi 3.307 X 36.5 = 121 psi

701 psi

1.140 X 790 = 901 psi 2.167 X 505 = 1,094 psi

3.307 X 505 = 1 ,670

1,995 psi

P w = 701 - 1,995 + 1,670 = 376 psi.

Actual P IV on pressure recorder at this stage of the job was 350 psi.

Hydraulic Analysis Just Be/ore Bumping Top Plug:

28 cu ft of slurry in 4Yz -in casing (L = 307 ft) . 76 cu ft of slurry in annulus (L = 334 ft).

Total llP f

0.307 X 236.6 = 73 psi 3.000 X 143.0 = 429 psi 0.334 X 79.7 = 27 psi 2.973 X 36.5 = 109 psi

638 psi

0.307 X 790 = 243 psi 3.000 X 505 = 1,515 psi

0.334 X 790 = 264 psi 2.973 X 505 = 1,501 psi

1,758 psi

P w = 638 - 1,758 + 1,765 = 645 psi.

Recorded P w was 650 psi before top plug landed.

NUMBER 3

1,765 psi

Set 7-in. casing in 8*-in. hole at 13,150 ft. Caliper showed portions of the hole washed-out to 9* and 11 in. Use Pozzolan Y cement, 0.4 per cent calcium lignosulfo­nate and 121h Ib of gilsonite / sack (total 350 sacks), with 1,000 gal of chemical wash ahead of cement slurry.

MARCH, 1962

Problem: Calculate rate to approach annular turbulence.

Slurry Properties: n' = 0.24, K' = 0.25, and p = 13.9 lb/gal.

Annular Flow Channel:

Hole Size 0, Area (in.) (in.) (sq ft)

8% 1.75 0.1503 9% 2.75 0.2512

11 4.00 0.3927

Annular Calculations for "Critical" Velocity:

Hole Size (in.)

8% 9%

11

V. (ft/second)

9.55 9.00 8.52

Actual displacement rate during job

Q (bbl/min)

15.3 24.2 35.8

21.5 bbl/min.

Attainment of a higher rate was not attempted due to the limited number of 2-in. lines possible between the cementing units and the wellhead, and due to the proba­bility of lost circulation being induced at the extreme rates.

Calculated Values at 21.5 bbl/min in Annulus:

Hole Size V llP, (in.) (ft / second) N"c (psi /1 ,000 ftl

8% 13.37 3,790 365 9% 8.00 1,720 117

11 5.12 855 66

These data were for the first stage of a two-stage job with the stage collar located at 10,727 ft. Indicated cement top from a sonic bond log was 10,800 ft. Upper stage was cemented at 24 bbl/min using a similar slurry except that calcium lignosulfonate percentage was reduced to 0.2. This well was successfully completed in two formations and perforated in two other formations without communi­cation between zones. Indicative of the value of high displacement rates was the correlation between caliper log and sonic bond log, where the lower sound-transmission values were recorded in the section of the hole nearest bit size. Similar comparisons have also been obtained on other wells, particularly when displacement rates ap­proached turbulence.

These examples represent the predominant usage of the techniques and data discussed herein; further elaboration for other jobs on which these calculations have been used, and for which data are available, would be largely repeti­tion. Problems encountered using high displacement rates for cementing casing have mainly been caused by restric­tions to the flow. The principal of these restrictions has been the manifolding arrangement available between ce­menting units and the top of the casing. Under normal operating conditions this represents some 500 to 1,000 equivalent ft of 2-in. tubing, and relatively high llP, may be encountered here. This situation has been combated on at least one occasion by bringing the discharge line of each cementing pump into a manifold and proceeding from this manifold to the 13%-in. cementing head with two 4-in. lines.

Generally, the restriction in floating equipment has not apparently been significant because its equivalent length represents a very small percentage of the total depth of casing. It is quite obvious that advanced planning by the well owner is necessary to organize a job of this type to insure sufficient tankage, water supply and proper mani­folding of equipment, as well as to establish what type of slurry could be used to the greatest advantage.

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CONCLUSIONS

A relatively simple method has been suggested to permit hydraulic well bore analysis for cementing operations, whereby it is possible to calculate several factors which influence primary cementing practices. Using these criteria, it is then possible for the well owner to select the most satisfactory arrangement of equipment and (to a lesser degree) the cementing composition to obtain a pre­conceived performance during the operation within reason­able limits of engineering accuracy. The essential data not usually available are the slurry rheological properties which affect flow performance. A substantial number of more-common slurries have been measured and these properties determined, in some cases on API Class A cement from 17 different manufacturing plants. A simpli­fied method using standard cementing-laboratory facilities will yield these data on other cementing compositions rather rapidly.

As with other non-Newtonian fluid systems, work of this nature on cementing slurries is continuing. It is anticipated that improvements will be made in all areas of rheological analysis, but there is no indication thus far that gross inaccuracies exist in this sl'ggested simplified analysis.

328

NOMENCLATURE

NRe = Reynolds' number, dimensionless V = average or bulk velocity, ft/second

volumetric flow rate/cross-sectional area of flow channel

p = fluid density, lb/gal n' = fluid-flow behavior index, dimensionless K' = fluid consistency index, lb-sec'" /sq ft D = diameter of flow channel, in.

fJ. = Newtonian fluid viscosity, cp f = Fanning friction factor, dimensionless

fl.P, = frictional pressure drop, psi L = length of flow channel, ft

Vc = bulk critical velocity, ft/sec HHP = hydraulic horsepower

P IV = wellhead pressure, psi Q = bulk flow rate, bbIjmin

P". = hydrostatic pressure-annulus, psi P he = hydrostatic pressure-casing, psi De = equivalent diameter-annulus, in. D. = outside diameter-annulus, in. D I = inner diameter-annulus, in.

REFERENCES

1. Howard G. C. and Clark, J. B.: "Factors to be Considered in Obt~ining Proper Cementing of Casing", Oil and Gas Jour., (Nov. 11, 1948).

2. Rabinowitsch, B.: "Uber die Viskositat and Elastizitat von Solen", Phys. Chem. (1929) 145A, No.2, 1.

3. Metzner, A. B. and Reed, J. C.: "Flow of Non-Newtonian Fluids-Correlation of the Laminar, Transition and Turbulent Flow Regions", AIChE Jour. (1955) I, No.4.

4. Metzner, A. B.: "Recent Developments in the Engineering Aspects of Rheology", Rheologica Acta (1958) No. 2-3.

5. Dodge, D. W.: "Turbulent Flow of Non-Newtonian Fluids in Smooth Round Tubes", PhD thesis, U. of Delaware (June, 1958) .

6. Melton, L. 1. and Saunders, C. D.: "Rheological Measure­ments of Non-Newtonian Fluids", Trans., AIME (1957) 210, 196.

7. Savins, J. G.: "Generalized Newtonian (Pseudoplastic) Flow in Stationary Pipes and Annulus", Trans., AI ME (1958) 213,316.

8. Savins, J. G. and Roper, W. F.: "A Direct Indicating Vis­cometer for Drilling Fluids", Paper No. 90l-30-A presented to API Div. of Production (1954).

9. Ish-Shalom, Moshe and Greenberg, S. A.: "The Rheology of Fresh Portland Cement Pastes", Paper presented at Fourth Int. Symp. on Chern. of Cement (Oct. 2-7, 1960) in Wash­ington, D. C.

10. "Mud Pressure Gradient", Pet. Eng. (Jan.,1958). ***

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