DRILLING PRACTICE '

This section contains six (6) papers on drillinipractice, as follows:

"The Flow Properties of Drilling Muds" By R W. Beck, - ' Stanolind Oil and Gas Company, Tulsa, Okla.

(Removed, as of May 1, 1946, to Creole Petroleum Company, Maracaibo, Venezuela) and

W. -F. Nuss and T. H. Dunn, Stanolind Oil and Gas Company, Tulsa, Okla.

(Presented a t Southwestern District Meeting, Fort Worth, Texas, March 1947)

"Factors Influencing the Selection of Mud Fluid for Completion of Wells" By H. E. Radford,

Shell Oil Company, Inc , Ventura, Calif. (Presented a t Pacific Coast District Meeting, Los Angeles, Calif, May

1947)

"Deep Contract Drilling in Oklahoma" By Jack H. Abernathy,

Big Chief Drilling Company, Oklahoma City, Okla (Presented a t Mid Continent District Meeting, Amarillo, Texas, May

1947)

"Economic Trends in Contract Drilling'" By J. E. Warren,

Carl B King Drilling Company, Midland, Texas (Presented a t Twenty-seventh Annual Meeting, Chicago, Ill., Novem-

ber 1947)

"New Developnients in Diamond Coring" By R. W. Stuart,

Stanolind Oil and Gas Company, Fort Worth, Texas (Removed, as of April 1947, to Hallhurton 011 Well Cementmg Company, Duncan, Okla , removed, as of December 1947, to Diamoad Oil Well Drllllng Company, Midland, Texas)

(Presented a t Southwestern District Meeting, Forth Worth, Texas, March 1947)

"Hard-Rock Drilling in the Permian Basin" By David Johnston,

Humble Oil and Refining Company, Midland, Texas (Presented a t Southwestern District Meeting, Forth Worth, Texas,

March 1947)

THE FLOW PROPERTIES OF DRILLING MUDS + R. W. BECK,* W. F. N U S S , ~ AND T. H. DUNN t

ABSTRACT

INTRODUCTION

The known equatlons for the flow of plastic flu~ds are appl~ed specifically to drilhng-mud problems, and the applicab~lity of these equations for various size pipe 1s ver~fied esper~mentally. Laboratory and field ~nstru-

I t IS generally known In the petroleum Industry that drilhng muds have a more complex flow behavlor than true flulds, yet ~t IS st111 common practlce to express the flow propertles of muds In terms of a slngle vls- coslty value.

The necessity for complete data on flow properties of drllhng flulds has been recognlzed, but lack of a convenient method of determlnlng such propertles has hltherto prevented development of mud-flow data for routlne application to drllllng problems Knowledge of the flow characterlsbcs of drilllng flulds 1s of ad- vantage In almost all phases of drilhng operations. Some of the more Important appllcat~ons relate to loss of mud lnto drllled formations, and selection and deslgn of muds and mud-circulating systems In order to ob-

ments developed for determ~nat~on of drilhng-mud flow character~stics are described, and the calibration of these lnstrunlents by comparison with results of pipe-flow tests IS ~ncluded.

tam optimum rates of clrculatlon to remove blt cuttlngs and Increase drllllng rates.

The flow propertles of true flulds are accurately de- fined, In the reglons of vlscous and turbulent flow, by Polseullle's law and by the Fanning equatlon, respec- tlvely These two equatlons require a knowledge only of the vlscoslty and denslty, which are easlly deter- lnlnable characterlstlcs of a true fluld I t IS unfortunate that most drilling muds are not true flmds, but are Instead plastlc rnaterlals whlch obey the laws of plastic flow

Although the difference between plastic flow and the flow of true flulds was recognlzed a t an early date, a satisfactory quantitative expression for plastic flow was not developed untll about 1920, when E. C. Blng- ham '" published hls book, Fluzdzty and Plastzczty. Bing- ham's equatlon was found to be applicable and useful to lndustrles deallng wlth ceramics, paints, sewage dis- posal, and soil physlcs. Evans and Reid of the Burma 011 Company, L td , comprehended the Importance of mud-flow propertles in the applications of the B~ngham equatlon to certain drilling-mud problems Also Greg- ory: Ambrose,' Looms,' Pigott," ' and a number of other ~nvestlgators recognized the anomalous character

* Stanolincl 011 nnd Gas C o , Tulsa, Okln , r en~ored , n s of ALay 1. 1946, to Creole Petrpleu;n Co , AIaraca~bo. Venezuela

t Stanohnd 011 a n d Gas Co . Tulsa. Okln $ Presented, by Alr Nr~ss , n t t he slJrlng m r e t ~ n g of the F?:outh-

western D ~ s t r ~ c t , D ~ v ~ s ~ o n of F'roAuct~on, F o r t Wortll, l e s a s . Mnr 28. 1947. presidlup. George H Fnncher, Unlverslty of -. Terns. K u s t ~ n , T e i a s

a F ~ g r ~ r c s refer to REFERENCES on p 21

of drilhng mud, but, unfortunately, llttle advantage has been taken of such available ~nformation m solving drllllng problems Wllhelm, Wroughton? and Loeffel in 1939 studled the varlat~on of cement-slurry viscosity wlth rate of shear, and Caldwell and Babb1tt8 In 1941 published a paper relating to the flow of sludges and other suspensions In plpe, glvlng equations whlch were verlfied experimentally

Notwthstanding the slgnlficant amount of past work conducted on plastlc flow, there appeared to be a n unfortunate gap between theory and ~ t s general appll- catlon to drllllng problems lnvolvlng the flow of dr~ll ing mud. The lnvestlgatlon described herem was under- taken for the purpose of developing a slmple method of determining the flow characterlstlcs of drllllng flulds and applying the lnforlnation to .drilling problems

Theory of Plast~c Flow

The d~fferentlatlon between plastlc rnaterlals and true flulds was expressed In 1859 by Clerk Maxwell In his Tkeonj of Heat lo

"If the form of the body IS found to be permanently altered when the stress exceeds a certaln value, the body 1s said to be plastlc, and the state of the body when the alteratlon IS just golng to take place IS called the llmit or perfect elastlclty. If the stress, when it 1s maln- tamed constant, causes a straln or displacement In the body whlch increases continually wlth tlme, the sub- stance is sald to be vlscous

"When thls continuous alteratlon of 'form is only produced by stress exceeding a certaln value, the sub- stance 1s called a (plastic) solld, however soft ~t may be. When tho very smallest stress, ~f continued long enough, wlll cause a constantly lncresslng change of torm, the body ,yust be regarded as a liqu~d, however hard it may be

A graphlc illustration of the differences between plastlc flow and true fluld 1s shown 111 Flg 1, whlch represents flow In a cyllndr~cal plpe. For a true fluld the pressure dlfferentlal during streamline flow IS pro- portlonal to the velocity, resulting In a stralght line passlng through the ongln, the slope of whlch IS a direct ~uncbon of the vlscoslty Under condltlons of plastlc flow the pressure dlfferentlal less a constant 1s propor- tlonal to the velocity, the constant berng a direct func- tion of the inltlal shearlng stress, or yleld value, of the plastlc material. The slope of the plastlc curve 1s pro- portlonal to the reciprocal 6f the moblllty as Blngham

defines it, or to the coefficient of ngidi ty of the material a s defined by Caldwell and Babbitt The vlscosity of the plastlc f l u ~ d a t any glven veloclty 1s proportional to the slope of a line from a p o ~ n t on the plastic-flow curve corresponding to the given veloclty through the origln Thus it can be seen t h a t the vlscosity wlll be a n inverse functlon of the velocity.

In drlll plpe or annulus, the shearlng force on the material 1s greatest a t the plpe wall, and decreases wlth distance from the wall A t low velocltles; the shear- m g force at some pomt inside the tube may become in- sufficient to overconle the yield value of the plastic The nlaterial mslde this radius will then flow a s a solid plug, causing the downward trend a s the plastic-flow curve approaches zero velocity

At h ~ g h e r velocities the flow of plastlc material be- comes turbulent, a s does t h e flow of a t rue fluld The veloclty a t which this occurs 1s known a s the critical veloclty and, above the critical velocity, drilling lnuds be- have 111 the same manner a s t rue hqulds-1 e , the pres- sure dlfferentlal is a functlon of a hlgher power of the velocity

The symbols and definit~ons used herein a r e a s follows

A = shearing stress ( a t the pipe wall), poundals per square foot.

a = yield value, o r shearing stress necessary to overcome the lnternal frlctlon, poundals per square foot

D plpe or tublng dlameter, feet Dl = outside diameter of annulus, feet

T R U E L I Q U I D F L O W

Y ~ e l d Value X

'%

Flow

t VeIocr ty + Pressure Vs. Velocity Relat~onsh~p In True Liquld Flow

and In Plastic Flow.

FIG. 1

I Dz = outside diameter of drlll pipe, feet f = F a n n ~ n g friction factor g = acceleration of giavity, 32 2 f t per sec per sec L = pipe or tubing length, feet m = hydraulic radlus of the annulus, feet n = rlgldity of the mud, pounds per 'second per foot. P = pressure drop, pounds per square foot

AP = pressure drop, pounds per square ~ n c h . R = plpe or tubing radius, feet

Re = Reynolds number p = fluid density, pouilds per cubic foot

t p = shearing stress, pounds per scluare foot t y = yleld value, pounds per square foot u = viscosity, pounds per second per foot -- - " A volume ra te of flow, cubic feet per second t - V = mean flow veloclty, feet per second

1 V. = critical veloclty, feet per second.

La~nlnar Flow of Plart~c illatenals

Blnghain showed t h a t the conlplete l a m ~ n a r flow curve of p l a s t ~ c materials in plpe could be expressed a s fol- lows

In thls equation, the shearing forces, A and a, a r e in absolute unlts To convert to more useful g rav l ta t~ona l unlts, let

A t --, tp=shearlng stress [pounds per square foot]. (2) ,- g

, t,= yield value [pounds per scluare foot] (3)

1 Then

The mean flow veloclty is

I t can be shown tha t

D P t, = (6)

Where P 1s the pressure gradient, In pounds per square foot, L 1s the pipe length, and D the pipe dlameter

Substituting thls value of t, In equatlon (5) :

The last term IS necessary t o obtaln accurate values only when V 1s small, f o r larger values ~t may be omitted with negllglble error The equabon then becomes

DAP determ~ned froin plpe-flow data by plotting -- a s the , 4L

8V ordinate, and - a s the absclssa The yield value is gD

Expressing P In the more common u ~ n t s of pounds per square inch

~p = <. ?ff!! 27D 9gD' (10)

The yield value ( t , ) and i l g i d ~ t y (n.) of a mud can be

then equal to 2 of the Intercept of the straight-llne por- tion of the curve on the t , asls, and the rlgldlty is equal to the slope of the straight-line portion of the curve

If the yleld value and n g i d ~ t y a r e known, the com- plete plastlc-flow curve for any slze plpe can be obtained with equatlon (7) , aild the approximate curve can be obtalned with equations (8) , (9) , o r (10)

vibration, drill-stem ro ta t~on , etc , therefore, turbulence will usually occur a t the lowest c r l t~ca l veloclty Under these circumstances equation (12) wlll probably give results a s sa t~s fac tory a s those obtained by the mole elaborate equatlon (15)

The apparent viscosity of a mud flowing 111 any size of plpe a t any veloc~ty below the critical veloclty call be obtained by ecluatlng Poiseuille's equation

wlth equation (9), thus obtaining a n expression for the apparent viscosity (71) in terms of yleld value and r l g i d ~ t y

It has been expenmentally determined by several in- vestigators t h a t the critical velocity fo r inuds normally occurs a t a Reynolds number of 2,000 to 3,000 The c n t ~ c a l velocity may be located by subs t i tu t~ng the fo rego~ng value for zc, setting the new form of Reynolds number equal to 2,000 and to 3,000, aild solving

Turbulerrt Flow of Plastrc Materials

The flow of drilling inuds above the critlcal velocity is turbulent or hydrauhc, and resembles t h a t of t r u e flulds Caldwell and Babbitto stated t h a t the f a m l i a r friction-factor vs Reynolds-number char t nlay be used with the Fannlng ecluat~on, viz , ecluation (14), f o r tur- bulent flow of sludges and such similar suspensions, prov~ded the viscos~ty of the dispersion mediunl 1s used

I11 the espeninents described later In this paper it was found t h a t computatioils fo r d r ~ l l i n g inuds. based on , ~ ~~ ~ - -

this method, resulted 111 pressure drops lower t l ~ a i l ob- served values Inasmuch a s the correct f r l c t ~ o n factor vs Rey?olcls-number relationship had been established with water in the writers' experiment fo r 2-in -ID pipe, it was possible to compute the effective turbulent vis- cosity fo r the muds used in these tests These viscosities vaned from 2 5 to 12 centipoises, instead of being equal to the v~scosity of water , also, Plgott a has shown turbulent vlscoslties of 3 and 5 centipo~ses, respect~vely, fo r 2 common muds However, it developed tha t a reas- onably good correlation could be drawn between the turbulent viscosity and the r~g&ty , a s shown in F lg 2- even though the da ta points exhuhlbit a somewhat scat- tered pattern

The Reynolds number, a s ordinarily expressed f o r llydraulic fluids, IS

D2t,pg V - 1,00011+1,000

e - n2+ a9000 (where Reynolds number = 2,000) PD

D2t,pg 1,50On+1,500

n2+ - V, = ' 49500 (where Reynolds nun~ber = 3,000)

PD

A more accurate calculation of the critical veloclty under u n ~ f o r m flow conditions nlay be made by use of the Fannlng equat~on

F o r drilling muds, however, the data from F i g 2 sug- gest t h a t thls should be altered to the following em- plrical relat ionsh~p

with ecluatloll (9 ) The resultlng Is a quadratic with respect to V,

fo r calculatioils of crltical velocity-pressure re la t~ons and deteiininat~on of the Fani~i i lg friction factor Good

f D2t,pg 8n+8 d n2+ v, =

fDp (I5)

results were obtalned by uslng this relationship ~n the Fanning equation for calculations of turbulent-flow pressure difFei-entials F l g 3 shows the fnction factor

Inasmuch a s the Fanmng f r lc t~on factoi, f , is dependent 011 the velocity, the solut~on of this equation must be made by t r ~ a l and error

In actual practlce the flow coiidltions of drilllng mud a l e not unlform, due to the use of rkciprocatlng pumps,

"S Re~nolds-llulnber relatlonshll) for flow In several types of PlPe and In annull Curves 1 and 11 were taken directly froni Walker, Lewis, McAdams, and Gllliland Curves 111 and 1V were est~inated from Pigott's data

All of the equat~ons given here a r e applicable t o

annular flow, provlded the value Int,, In whlch TIL 1s the hydrauhc radlus, 1s used ~n place of D

Apparatus for Measuring Mud-Flow Constants

Conslderatlon of the advantages and disadvantages of varlous Instruments for determmn~ng the necessary mud-flow constants for use in plastlc-flow equat~ons leads ~mmed~ate ly to d ~ s c a r d ~ n g actual pipe-flow meth- ods P~pe-flow tests requlre relatively large-scale ap- paratus and large mud samples They are time-con- suinlng and requlre more than one operator Capillary tube methods were cons~dered, ~liasmuch a s the method 1s fundamental, and has been well developed, both in the field of t rue llqulds and for plast~c-flow measure- ments Unfortunately, thls method is not ent~rely s u ~ t -

RIGIDITY, n

Correlation between Turbulent Vlscos~ty and Rigidity as Determined in the Author's Esperin~ent for 2-In.- ID Tublng.

FIG. 2

Friction Factor Vs Reynolds-Number Chart for Calcula- tion of Turbulent-Flow Pressure Drops.

FIG. 3

I

f

able for use with drilling muds because of the coarseness of a large part of the suspended phase of the mud. Falllng-ball viscos~nleters were obv~ously unsuited to drl l l~ng muds, because the opac~ty of the mud prevents vlsual observation of the rate of fall of the spheres

I I I Lowest values for drawn brass orgbss tub~ng

II For clean ~nhrna l flush tubular goods

IU For full hole dr~ l l plpe or annul1 In cased hole

IP For annul1 In uncased hole

I A third method, wh~ch showed the most prormse, In- volved the use of a rotational vlscos~meter

A number of 'rotational viscosiineters a re avallable commerclally, however, none of these 1s colnpletely sulted for drilling-mud determinations Instruments of the McMichael type, in whlch the outs~de cup rotates, must operate a t low speeds to prevent the centrifugal force from throwlng out the fluid These slow speeds do not allow measurements in the complete flow range " The Stormer type 1s capable of operation over satisfactory speed ranges, but its baffled cup produces heterogeneous flow cond~tions wh~ch are not well suited to mud-flow deter~ninatlons Also, the short running time of the Storiner does not allow the p las t~c substance to attaln equ~llbrium flow condit~oiis prior to comple- tion of the test

A lnodlfied Stormer vlscos~lneter which uses a speclal unbaffled cup, descnbed by Caldwell and Babb~tt: is more nearly satlsfactory , however, it also suffers from the last named d~sadvantage W~lhelm and Wroughton ' descr~bed a motor-dnven concentric-cylinder vlscoslme- ter, wh~ch was not avallable commerclally, and wh~ch was of somewhat colnplicated des~gn

Inasmuch a s none of the commercial v~scosimeters was found satlsfactory for the study of plastic flow of muds, ~t was necessary to develop an instrunlent s u ~ t - able for thls work The rotational vlscosimeter devel- oped for drilling-mud flow studies is shown In Fig 4 * It consists of a covered cyllndrlcal cup, A, a rotor, B, a drill-press mechanlsm for holding and turnlng the rotor, C, and a mechanlsm, D, whch supports the cup and measures the torque ~mparted to ~t by balancing the torque against the weight of a reeled cham, E. In order to reduce frict~on, the we~gh t of the cup 1s sup- ported by a cylindrical float in a nlercury bath

To milumlze end effects, the cup and rotor were made long 111 relat~on to dlalneter The rate of rotation of the rotor 1s controlled through a range of 0 to 836 rpm, by means of a Graham vanable-speed t ransmss~on. Tests a re made by r ead~ng the length of cham necessary to balance the instrument a t several revolutions-per- minute values

T h ~ s v~scosimeter gave good results In numerous tests, and was found to be satisfactory for mud testing

To verify the accuracy of the rotational viscoslmeter in measurlllg mud-flow properties, the vlscosimetric flow constants for a number of d n l l ~ n g f lu~ds were coin- pared wlth the flow constants obtalned In plpe-flow sys- tems which used two sizes of plpe These systems are shown in Flg. 5 and 6

Patent appl~ed for by R W Beck

The Rotat~onal Vlscoslmeter Usecl for Drlll~ng Muds.

FIG. 4

S M A L L SCALE PIPE FLOW A P P A R A T U S

20'of 375 1 D Plpe Between

,, .. A By-pass Valve

" 0 Choke Valve C 8 D C ~ t y Water Pressure

to Flush Manometer L ~ n e s Three Mercury Manometers

In Ser~es - Can be used Indl- v~dually or Collect~vely to Measure

0 to I00 p s l

Schematic D~agran~ of 3!-ln.-ID Pipe-Flow Test.

FIG. 5

Seven different muds were prepared and tested on the large- and sinall-scale pipe-flow setups, and on the rota- tional viscosiineter These muds were especially pre- pared to have a relatively wide range of yleld values and rigiclities, their composition is given in Table 1. Cali- bratioil of the rotational viscosinleter was accomplished by plotting the curves of the intercept and the slope of the torque-revolutions-per-n1111ut.e curves for the vis- cosiineter against the mud-yield values and rigidities, respectively, as determined in the small pipe-flow ap- paratus Fig 7 shows flow constants as determined in the sinall pipe-flow apparatus. Flg 8 shows flow curves which were obtalned from the viscosiineter for the same muds The latter are sin~ple plots of the revolutioi~s per mlnute of the rotor against the length of the chain necessary to balance the instruillent F lg 9 and 10 show the calibration of the vlscosimeter

Mud Flow Measur~ng Tank

Pressure Mud Return L ~ n e Mud Input L ~ n e Gauges \ I Y

Schematic D~agran~ of 2-111 -ID Plpe-Flow Test.

FIG. 6

av/s D

Plot of Flow Data In 20 Ft of %-In. Pipe for Determi- nation of Mud-Flow Constants.

FIG. 7

14 DRILLING

TABLE 1

Mud Compos~t~o~l

Mud No 1 6 5 per cent bentonite slurry denslty = 8 66 lb per gal.

Mud No 2 4 5 per cent bentonite slurry density = 8 58 lb per gal

Mud No 3 4 5 per cent belltoil~te slurry, weighted with barium

sulfate cleiisity = 10 93 Ib per gal

Mud No 4 4 5 per cent bentonite slurry, weighted \vith barium

sulfate dens~ty = 12 39 Ib per gal

Mud No 5 4 5 per cent bentonite slurry, weighted with barium

sulfate and treated wlth 0 25 Ib of sodium-acid pyrophosphate per barrel

density = 12 30 lb per gal

Mud NO G 25 3 per cent El Paso clay slurry density = 10 0 lb per gal

Mud No 7 26 3 per cent El Paso clay slurry density = 9 G G lb per gal

60

fn a 50

z I- Z 3 40 1- I-

2 30 ' 1 Z

20 U

10

'0 100 200 300 400 500 600 700 REVOLUTIONS PER MINUTE

Plot of Rota t~o~~a l Viscosimeter Data for Detern~inatio~i of Mud-Flow Co~lstants.

FIG. 8

PRACTICE

Fig 11 shows the flow curves, a s deternllned experi- nientally in the large-scale plpe apparatus A coinpari- son w t h curves from small plpe and viscosinleter data indicates that the constants for each mud, a s deterinined by the three methods, a re 111 substantial agreement. The fact tha t the dlanleter of the larger plpe is 5 4 tlnles that of the smaller is good evidence that the Bingham yield value and rlgldity are indepeiident of pipe diameter

Fig 12 and 13 show the calculated and observed pres- sure drop vs velocity curves for 2 of the 7 i l~uds 111 the 2-111 tubing The other five inuds showed comparable correlatioiis between computed and observed pressnre- drop velocity curves The average deviation of visco- slineter values for the same pipe was 3 per cent I t can be seen readily from these data tha t the accuracy ob- tamable with the rotational vlscosiineter approaches the accuracy of the pipe-flow apparatus Using the flow constants for each of the seven inuds as determined

3

.- 2.

g 2 J

> a

D J Y

E I

0 0 5 10 I5 20 25 30 35 40 45 50

VISCOMETER INTERCEPT, cm

Correlat~oli of Rota t~o~~a l V~scos~meter Curbe 111tercept and Y~eld Value, Based on P~pe-Flow Data.

FIG. 9

03

C

02 - e I? a

01

o VISCOMETER SLOPE

Correlation of R o t a t ~ o ~ ~ a l V~rcosil~leter Curve and R~g id~ ty as Determined from Pipe-Flow Data.

FIG. 10

Plot of Flow Data In 500 Ft of 2-In. T I I ~ I I ~ ~

FIG. 11

Pressure-Veloc~ty Relat~onshlp as Determined in P~pe-Flow Tests and as Calculated fro111 V~scosuneter DHta for Mud No. 2.

FIG. 12

VELOCITY, FT PER SEC. Pressure-Veloc~ty Relationship as Determined in P~pe-Flow Tests and as Calculated from Vlscos~meter Data for

Mud No. 3.

FIG. 13

f rom the small pipe a n d the viscosimeter, t h e computed flow curves shown on these g raphs were obtained a s follows :

1. The critical velocity f o r each of t h e muds i n 2-in. pipe was computed f r o m equation (12) .

2. The pressure drops f o r each of the muds at 3 differ- en t velocities below the critical were computed f r o m equation (9) .

3. F o r each mud the Reynolds number w a s calculated at 2 velocities above the critical by means of equa- tion ( lG) , and the corresponding friction factor was determined f rom curve 111 of the friction- factor-Reynolds-number cha r t shown in Fig . 2. The pressure drops a t t h e 2 velocities above t h e critical were then calculated by equation (14) .

4. The flow curve fo r wa te r in t h e 2-in. tubing was placcd on each g raph fo r orientation purposes.

The calculated curves a r e based 011 da ta f rom t h e rotational viscosirneter and pipe-flow tests through 20 f t of 2-in.-ID pipe. The observed curves were plotted f rom pipe-flow tes ts through 500 f t of 2-in.-ID tubing. Most of these curves agree very closely, showing clearly t h a t the pipe-flow constants used in BinghamJs equation of ~ ~ l a s t i c flow a r e independent of pipe diameter. 41so .the agreement between observed and computed flow da ta in the turbulent r ange indicates t h a t the Reynolds number fo r drilling muds, a s calculated i n equation ( lG) , i s es- sentially correct.

Simplified Ficld Instrument

Upon completion of th is portion of the investigation, the rotational viscosimeter w a s used in a nearby field to determine and control the flow properties of muds on some 20 wells. Although good results were obtained i n this survey, i t w a s evident t h a t use of t h e rotational viscosimeter a s a field ins t rument would lead t o difficul- ties in packing and shipping, and in finding t ra ined personnel a t t he well to operate the instrument. A number of different types of simpler appara tus f o r the determination of yield value a n d rigidity were designed a n d tested f o r reliability and ease of operation under field conditions. The instrument which proved best under such conditions consisted of a funnel-type visco- simeter wi th a brass efflux tube of 0.185-in. inside diameter by 6-in. length, extending horizontally f rom the base of t h e funnel. Inasmuch as i t i s necessary t o determine the volume r a t e of flow vs. the head, t h e body of the funnel is made of lucite plastic so t h a t the fall ing mud meniscus may be observed. The brass tube is mounted horizontally at t h e base of the funnel to elimi- na te excessive fluid head. The side of each funnel i s marked off in 1-in. intervals; a n d the volume, in milli- liters, a s well a s the mean hydrostatic head of each head interval, i s determined. This funnel viscosimeter i s shown in Fig. 14.

I n the operation of the funnel the efflux tube i s plugged with a cork, and the funnel i s filled to above the top interval mark. The cork is then removed, a n d the t ime a t which the mud meniscus passes t h e first and each successive head mark i s recorded.

The volume r a t e of flow and the average head of water fo r each interval a r e then determined. The vol- ume r a t e of flow fo r each interval, in milliliters per sec- ond, is then plotted a s the abscissa against the average head, in inches of wa te r fo r the interval, a s the ordinate. The resulting curve is a typical flow curve, which may exhibit either turbulent or plug-type flow, a s well a s laminar flow. Typical curves taken with the funnel viscosimeter a r e shown in Fig. 15. The laminar-flow

The Drilling-Mud Funnel Viscosimeter.

FIG. 5.4

O 0 I I I 5 I0 15

I 20

VOCUME RATE OF FLOW, CCk PER SEC.

Typical Flow Curves Obtained from the Mud Funlie1 Viscosimeter for Various muds.

FIG. 15

Ih. HEAD AXIS INTERCEPT

Corrclatiort nf Fu1l1tc.1-Viscnsimetor Curve Ir~tcrcept and Mud-Yield Valuc.

FIG. 16

portion can be recognized a s the straight portion of the curve which has a lowcr slo1)e than either plug or turbulent-flow regions.

Thc funnel viscosimeter has been calibl-atcd a s a relative, ra ther than a n absolute, viscosimeter because of the difficulty of correcting for the end effects of the short flow channel, and because of thc minor prcssure drops which take place in the funnel itself. A correla- tion between the intercept of the laminar-flow par t of the flow curvc on the head axis and the yield value of the mud, a s determined on the rotational viscosimctcr, is shown in Fig. IG . Correlation of the slope of the laminar-flow portion of the curve and the rigidity, a s determined on the rotational viscosimeter, is show~n in Fig. 17.

Several of these funnels have been used successfully in the field, but a s yet no extensive application of the instrument has been attempted. The mud-flow funnel is not so accurate a s the rotational viscosimeter, and also requires considerable amounts of mud, precluding i ts use a s a laboratory instrument.

Practical Applications o f Mud-Flow Data

As previously mentioned, a knowledge of the flow properties of drilling fluids can be applied to advantage in many drilling problems; e.g., in some Gulf Coast wells the fluid pressure in the formations is only slightly

Correlatiol~ of Ft~~inc-l-Vi*c.osi~i~(.~t.r Cnr+r Slope artd Mud Rigidity.

tween the formational and overburden pressures. An obvious solution to such a problem ~vould be to inotiify the niud propelties so a s to deci.easc the pressure drop due to annular flow. This can usually be accomplished by lowering the yicld value of the mud. By the proper application of mud-flow data it should be possible to devise progralns for mud properties, hole size, and drill pipe which will minimize lost circulation problems in areas known to be troublesome.

Typical calculations of static and circulating bottoin- hole pressure a r e shown. Dimensions of pipe and holc, and pumping rate, a r e a s follows:

Diameter of hole. . . . . . . . . . . . . .ll in. or 0.317 f t . Outside diameter of drill pipe.. .4L in. or 0.375 f t . Circulating ra te . . . . . . . . . . . . . .450 gal per min. Well depth. . . . . . . . . . . . . . . . . . .5,000 ft.

The mud characteristics a r e as follows:

Density ...... .10.0 lb per gal o r 75 lb per cu ft. Yield value t,. .0.40 lb per sq f t . Rigidity n . . .. .0.01 lb per sec per ft.

The value of h n ~ for the annulus is calulated by equation (17) :

4m = (0.917) - (0.375) = 0.542 ft.

The critical velocity is calculated by equation (12) : - ---

(0.542)? (0.40) ( 7 m ) 1,000 (0.01) +1,000

(0.01)2+ -- v, = ---- 3,000 - - . = 10.5 f t per sec.

(0.542) (75)

less than the overburden pressure and, a s a consequence, the wells will sometimes lose mud to the formation while mud is circulating, and be in danger of blowing out when circulation is stopped. This may be explained by the fact that the pressure drop, due to flow of mud in the well annulus, approximates the difference be-

The actual annual velocity a t 450 gal per min is found to be:

Therefore, the flow is laminar; and the pressure drop due to flow is calculated by means of equation (10) :

The pressure due to fluid head 1s

(5,000) (O 434) = 2,605 8 33

and the total circulat~ng bottom-hole pressure 1s

2,605+140 = 2,745 psi.

A pressure dlfferentlal of 140 psi between flowing and static bottom-hole pressure could easlly be sufficient to cause serlous trouble.

lated by ineans of equatlon (14) The pressure drop in drill holes and kelly 1s accounted for by adding 120 f t to the length of drill pipe.

The Reynolds number is calculated by equatloil (16)

Re = ( 3 2) (0 24) (10 5) (79 4) (0 07) = 9,150

Froin curve 111, Fig 3, the fr~ction factor, f , is found to be 00092, and the pressure drop from equation (14) IS

Overall Pressure Drop (4) (0 0092) (7,000) (10 5)2(79 4) = psl In connection with an actual field trial of an oil-base

(2) (32) (0 24) (144)

mud, ~t was deslred to compute the overall pressure The pressure drop in the annulus is calculated by means drop in the drllbng well. I of equat~on ( l o ) , uslng 4nt in place of D

Typical coinputations follow Tests made a t the well with the mud-flow funnel indi-

cate that the oil-base mud had a yield value, t,, of 0 0885 lb per sq f t and ripdity, n, of 0 07 lb per sec per f t The density of the mud was 10 6 lb per gal, or 79 4 lb per cu ft. Dimensions of the mud pump, hole, and drill plpe are as follows

Diameter of liner .63 ~n or 0 562 f t Diameter of piston rod .2 i in or 0 208 f t Length of stroke 18 in or 1 5 f t Diameter of hole. .... . 6 4 in or 0 533 f t Outside diameter of drill pipe 33 In or 0 292 ft. Inside dlanleter of drill pipe 2g in or 024 f t Well depth 6,880 f t Cross-sectional area of annulus . 0 156 sq f t Cross-sectional area of drill-pipe

lilside diameter . .O 045 sq f t Hydraulic radlus, m, of annulus . 0 0603 sq f t 4 . ~ 8 , annulus 0 241 sq f t

The volume of mud pumped per cycle of pumps is thus.

( 1 5) $ [ (0 562)'+ (0 562)'-

and the velocities in the drill pipe and annulus a t 24 cycles per mlnute and 85 per cent pump efficiency are

( 1 384) (24) (0 85) (60) (O 045) = 10 5 f t per sec ~n drlll pipe

384) (24) (O 85) 3 02 f t per sec in annulus (60) (0 156)

The critical veloclty ~n the drill pipe is calculated, uslng equation (12) :

The total computed pressure drop is 1,019+266 = 1,285 psi Thls conlpares well w t h the observed mud pres- sure of 1,250 psl

The observed and computed mud pressures oil this well for three other pump speeds are as shown a t top of P 21

Sllnllar tests were made for drilling wells in several widely scattered fields Total overall pressure drops in the drllhng well, as colnputed from flow properties de- termlned wlth the vlscoslmeter, agreed well w ~ t h meas- ured pressure drops Inasmuch as total pressure drops agree, there is added assurance that pressure drops wlthin var~ous parts of the circulating systein can be computed with equal accuracy

At a southern Louisiana well no data were taken as to dlmenslons of drlll collars, which generally have a smaller internal d~ameter and, hence, higher pressure loss than the same length of pipe This factor accounts for the low conlputed pressures a t that well

A summary of the field tests is given in Table 2. B

CONCLUSIONS 1 The flow characteristics of any drilling mud can

be defined In terms of two constants, viz , the yleld

- (0 208)'] = 1 384 cu f t per cycle,

value and rlg~dity, whlch are independent of the dlinen- slons of pipe through which the mud is flowing

2 I t has been verlfied experimentally that the two coilstailts necessary to define flow propert~es of muds can be deternllned with certain types of rotational or funnel viscoslmeters

3 Knowledge of the hydrodynamic properties of muds should prove a valuable tool in the solution of numerous drllling problems.

(oo70)q (0241) ' (00885)(794)(32) (1,000) (0 070) +1,000 3,000 v =

(0 241) (79 4) = 8 6 f t per sec

The actual velocity in the drlll plpe is hlgher than the critical, therefore, the flow is turbulent, whereas the actual velocity in the annulus is lower than the criti- cal velocity, resulting in laminar flow in the annulus The pressure drop in the drill plpe is, therefore, calcu-

ACKNOWLEDGMENT c

The authors express their appreclatlon to Stanolind , 011 and Gas Company for permission to prepare and present this paper -

Pulllp Speed

(Cycles Per

Minute)

16 20 24 28

Annular Velocity

Estimated (Feet Pump P e r

Efficiency Second)

Marsh Funnel \Vnter 1 ns=

Viscos~ty (I\filliliters Well (Seconds) Per SO Min)

West Texas A 108 4 4

80 4 4 75 4 8 80 5 7 93 4 0 86 3 6

Central Oklahoma B 180 6 2

195 6 0

West Texas. C 0 0136 D 35 0 0182 E 42 5 0 068

Southern Loulslana I 58

50 44 48 45 55 51 40 53 46

Drlll- Pipe

Velocity (Feet P e r

Second)

s P A P Drill

Annulus Pipe (PSI ) (PSI )

TABLE 2

1 F~eld Test Results

e (Pounds n Per Gallon) Type Mud

P e r Cent

Deviation A P A P f roin

Total Observed Observed (PSI) (PSI ) (PSI )

Calculated Ohserved Pressure Pressure Error

(PSI) (PSI) (Per Cent)

0 0156 9 1 C a u s t ~ c treated 1,193 1,100 8 5 0 0192 9 0 Caustlc treated 1,221 1,150 6 2

' 0 0136 9 1 Caustic treated 1,273 1,150 10 7 0 0182 9 2 Caustlc treated 1,345 1,200 12 1 0 0206 9 3 Caustlc treated 1,386 1,275 8 7 0 0181 9 1 Caustic treated 1,428 1,200 19 0

G 0 0046 10 7 Natural mud 411 460 10 6 0 00475 9 2 Natural mud 631 590 7 0 0088 9 3 High pH caustic-

quebracho 980 7 900 9 0 0054 10 5 Salt-water lmperlnex 403 5 435 7 3 0 0102 8 95 Emulsion-gel oil 251 2 265 5 2 0 00316 Emulsion-gel oil 797 5 790 0 9

10 0 Gel chemical 9 9 Gel chemical 9 0 Gel chemical

10 2 Gel cheinlcal 10 0 Gel chemical 10 1 Gel chemlcal 10 1 Gel chemical 10 1 Gel chenllcal 10 2 Gel cheinlcal 10 2 Gel cheinical

REFERENCES

'I;: C_' R~nglinni. Plrrrtlrty atrtl Plastrcrt!~, 3IcC;mn-H111 Book Co . New Pork ( 1 993'1

21' E?;ans ilnd A Rcld. "Drllllng Rind-Its AInn~~fac tu re a n d Testing Tratrs :1fin111g Of301 I n s t of I~rr l ro 32, 1 I19361

3 nT R Gregory, " r u m p ~ n g Clay Slurries through -I-In Pil)e," Meclr Etzg 49, bO0 (1037)

4 H A An~llrose and A C ,>oo"~n~s ' ' F l ~ ~ ~ r l ~ t ~ e s nf Tllixotropic Gels Rentonlte Sospensions, PAyarcs 4, 965 (1933)

5 R J S Pigott. "Flo~!~ ot- Flu111 in Closed Conrlult." MecR E ~ r g 55, 407 (1933)

8 R J S pigot t . "AIufI Flon in D r ~ l l ~ n g , " Drlllrrlg and Produc- trot8 Pmctrcc, 91-103 (1941)

of S~~spens io i i s tlirough Pil)es," I1rc1 E i i o q n l ,I" ' ., g D 11 Caldwell and H E Bap!)~tt , "Flow of I fnds , Sludges.

and Suspensions ~n Circular Pipe, I n d Elrg Clre111 33 [2] 249- 56 11941)

lqClerk RInswell, Theory of Heat, Clarendon Press, Oxford . Iif.:nh , ""L.11 '

11W I3 Walker, W K Lenls . W H RlcAdams. and E R G~l l~ lnn ( l . Prlttcrnles of Cl~eniical Eng~neer lng, 3rd edn , RfcGraw- H ~ l l Book C o . New Pork (19371

'2 P S Roller and C ,,K Stoddnrd. " V ~ s c o s ~ t g nnd Rigidity of Structural Suspensions, J Phys Chcm 48 f61 410 (1044)

DISCUSSION

Huebotter Lead Company, Okla ) (written) * This In-

vest lgat l~l l appears to set forth reliable 'l1stl'unlents and fOrnlulas which call be used to determine the of flow In any part of a drllling under any set of clrculatlng condltlons The continuance of this lnves- tigation should ( levelo~ a n ~nstrunlent suff iclent l~ sllnllle, rugged, and reliable, having rules, charts, o r graphs which will allow field engineers and techlllclans

'lulckly the pattern of the In a under a given set of drilllllg con(litlOns There

will naturally follow suggestecl methods to change the flow characteristics of the mud, o r the condltlons under whlch the lnud 1s being handled, so a s to overcome such difficultles a s loss of clrculatlon, poor cutting recovely, caved into the hole, high punll' pressures, and reduced drilllng rate

John E Owen (Geophys~cal Research Corporation, Tulsa, Okla ) (written) I n the work t h a t was presented here, the total pressure drop in the d r ~ l l pipe and ~n the annulus was used a s a basis for checking the cal- culated pressure drop In the annulus only Reading the data m the paper showlng the correlat~on between the calculated and the observed pressure drops, it w ~ l l be noticed that, ~f a n apprec~able error is made 111 the calculated value for the pressure drop in the annulus, t h ~ s error wlll show u p a s a smaller per cent e r ror in ~n the total pressure drop In the esalnple given the de- viation in per cent of the comi~uted total lwessure drop froin the observed pressure drop Increased in one dlrec- t ~ o n , suggesting tha t there inay be a b a s ~ c error of some kind In the calculatlons of Pressure drops either In the drill pipe or 111 the annulus, O r both Tha t these devla- tlons a r e small may be the result of compensating effects in the calculations The importance of the pressure drop in the annulus may ~ u s t l f y , and c e r t a l n l ~ sug- gest, maklng direct measurements on the pressure drop in the drilling annulus In a test well a bottom-hole pressure gage can be located a t the bottom of t h e s t r ing of drlll pipe, flow tests may be made, and pres- sure drops in the annulus recorded Such a test, made In a few cases, would either confirm the nlethod of t h ~ s paper o r serve a s a b a s s fo r closer calculat~ons

I n the paper just presented, all calculatlons a r e made a s though rotatlon of the drill plpe does not affect plastlc flow It appears likely tha t turbulent flow s ta r t s a t a lower value of critical velocity than is deterinlned by calculations in which the bounding walls a r e sta- t?onary, r e l a t ~ v e to each other By the use of a bottom- hole pressure gage, this can readily be determined

Froln a sonleu~hat different angle thls paper has fu r ther interest, fo r there is reported here some ex- per~inental woik establishing a correlation between v ~ s c o s ~ t y d a t a taken with a inodified Stormer vls-

Presented Iby George R Gmy, Enrod Sales D ~ \ l s ~ o u , Nn- tlonnl Lend Co , Houstun, Texas

cos~meter and a inodified Marsh-funnel In some es- perllnental work done several years ago and reported 111 '4, Inst Minzrtg Me t Eng.grs Tech Pttb N o 1373, the writer of these comments established a correlat~on betxveen vlscoslty data taken with all unlnodlfied Storiner vlscosllneter and a standard Marsh-funnel, and found methods for calibrating both these instruments In such a way that use u,ould allow the deterlnlnatlon ,,f

absolute vlscosltles of anlllng muds ~h~ wri ter feels that the work that has beell reported the paper Just presented with value, be by call- bratlng 111 a siinllar manner both the lnodlfied Storiner and the Marsh-funnel the true llqulds of &fleepent weights and vlscosltles, In order tllat tlley, too, call be used for absplute vlscoslty d e t e r n l l l l a t ~ o l ~ ~ The effect of the weight of fluids used has usually not received suficlellt either the callbPatlon o r t h e use of vlscosllneters, and the present work is no exception It is, however, a valuable con tnbut~on t o the knowledge of the characterlstics and properties of drilling muds

George E Cannon (Humble Oil and Refinlng Com- pany, Houston, Texas) Heretofore ~t h a s been rela- tively slmllle to calculate the pressure loss in the drill-

pipe the other fixed portions of the clrculat- systeln ~h~~ will be of much value In calculatil1g

the pressure loss in the annulus There is one t l ~ l n g t h a t I notlced 111 the d ~ s c u s s ~ o n ,

collcernl,g several of the curves ( F ~ ~ 12 13) , where you get Illto the turbulent flow range, at solne 300 to 500 f t per nlln a large of the drilling ,, the ~ ~ l f coast the drllllng rate appears to be proportlollal to the rate of clrculatlon The llmltlng factor, then, occurs when you hi t turbulent flow, and rather dlscouPaglng to see that solne of the nluds are to go onto the turbulent flow range earller than alltlclpated jve have pumps avail- able a t the present time to reach such ~e l0c l t l es I

If the aut]lor would care to that a little

Mr Nuss I do not belleve the c r~ t ica l velocity was qulte r ight In most of these lnuds s o m e t h ~ n ~ between 180 and 400 f t per nlln IS the crltlcal velocity, fo r vely t h ~ c k muds the veloclty would be higher, but more pressure loss would be requ~red .If the crltlcal veloclty 1s the I inl~t ing factor, the only way to get around tha t is to use a thln mud, whlch would require less pressure drop in turbulent flow We have found t h a t most muds a r e pu~llpecl well above c r i t~ca l veloclty inslde the drill s t n n g The mud characteristics, drill- s t r ing d~inens~ons, ancl pump capaclty a r e the llinitlng factors, ra ther than the crltical velocity

Also, isn't it possible t h a t the fact t h a t drilling rates seem proportional to lnud velocltles 1s due Inore to the all-around better equlpme~$ on the rigs where better pumps capable of higher mud velocltles are