9
.. . IADCISPE lADC/SPE 14786 The Use of a Drilling Model in Simulation, Optimization, and Fwrnation Description by S.C,Malguarnera, NL Technology Systems/NL Industries Inc. MemberSPE . Copyright1986, lADC/SPE 1986 DrillingConference This psper waa prepared for presanlation al the 1986 lADC/SPE DrillingConference held in Dailaa, TX, February 10-12, 1986. This paper was selected for presenlafion by an IADCLSPEProgram Committee followiri~review of informationcontainedin an abstractsubmittadby Ihe author(s).Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers or InternationalAa.wciationof Drilling Contractorsand are subjectto corracticmby Ihe author(a).Th; material, as preaentad,does not neceaearily reflectany positionof the :#DC or SPE, itsof- ficers, or members. Papera presanled al lADC/SPE maetings are subject to publicationby Editorial Committees of the IADC anti SPE. Permissionto copy is restrictedto an abetract of not more than 3rXlwords. Illustrationsmay not be copied. The abstract shouldcontainconspicuousacknowladgmenl of where c-d bv whom the pafw is presented. Write PubticationaManager, SPE, P.O. Box 633S36, Richardson, TX 76063-3636. Telex, 730989 SPEDAL. ABSTRACT A system of equationsconstitutinga drilling model has been developedwith the capabi1ity to handle al1 bit, mud and formation types. This model has been used in three application programs: o DRLSIM. A bit run time simulation o DRLOPT. An optimization program which pre- dicts terminationmechanismsand cost per foot for a range of operatingconditions. o FORMDES. Foot-by-footdrilling data is used to produce drilling resistance,pore pressure and fracturegradientlogs. INTRODUCTION Drilling Models Although the term ‘DrillingModel’ has been much used in the literature,there is a great deal of ambiguityassociatedwith it. A drillingmodel is much more than a single rate of penetrationequa- tion describing a relationship between measured parameters of the drilling process. A true drilling model is a system of equations, some of which may be differential, which quantitatively explains the interaction of the most important parametersof the drillingprocess. By necessity, some of these relationshipsmay be empirical. Drilling models should not be judged as right or wrong because of our present lack of understanding of the process based on first principles.However, . they may be judged as to their usefulness. If a model is useful, then it is a worthwhileaddition to engineeringpractice. The uses of a comprehen- sive drilling model would include simulation of bit runs on computers allowing alternative prac- tices to be evaluated, detection of drilling .- problems, formation correlation and drilling optimization. Previous Wrk Over the last thirty years, there have been vari- ous periods of activity In developing drilling models. It is not w intention to exhaustively review these previous efforts, since the model discussed in this paper Is not based on any speci- fic previouslyexisting result. In general, these efforts have centered on trying to relate some of the more obvious measurable of the drilling process to rates of penetration. They have generally had the form of an algebraic relationshipbetween weight-on-bit,RPM, bit size and some constants which need to be determined through some type of field test. Almost all considered roller cone type b+~s only. some of them includedthe effects of cutter wear, few con- sidered hydraulic effects [1], and most proved of limited use in helping to make better decisions in drillingoperations[2-10]. These efforts were generally based on laboratory observations, and that is about as far as any verificationwent. For the most part, there was not enough interest in their further development to warrant.the effort of extensive field verifi- cation. The problem also existed as to how to test a drilling model, It is really not enough to just coma up with the same average rate of pene- tration over a several hundred foot bit run, since several different rock layers would generally be passed through. Unfortunately, about the only drilling data recordedin the fieldwas the single line entry of a typical bit ‘eccrd. These could lie for years in a file room .:i:twt ever being examined. However, over the last five years, substantial improvements ha’e .)eenmade in both the volume and accuracy I?+cr:;ling data. Some -.. 5

[Society of Petroleum Engineers SPE/IADC Drilling Conference - Dallas, Texas (1986-02-09)] SPE/IADC Drilling Conference - The Use of a Drilling Model in Simulation, Optimization, and

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. . .

IADCISPE

lADC/SPE 14786

The Use of a Drilling Model in Simulation, Optimization, andFwrnation Description

by S.C, Malguarnera,NL Technology Systems/NL Industries Inc.

MemberSPE

.

Copyright1986, lADC/SPE 1986 DrillingConference

This psper waa prepared for presanlation al the 1986 lADC/SPE DrillingConference held in Dailaa, TX, February 10-12, 1986.

This paper was selected for presenlafionby an IADCLSPEProgram Committeefollowiri~review of informationcontainedin an abstractsubmittadby Iheauthor(s).Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers or InternationalAa.wciationof DrillingContractorsand are subjectto corracticmby Ihe author(a).Th; material, as preaentad,does notneceaearily reflectany positionof the :#DC or SPE, itsof-ficers, or members. Papera presanled al lADC/SPE maetings are subject to publicationby Editorial Committees of the IADC anti SPE. Permissiontocopy is restrictedto an abetract of notmore than 3rXlwords. Illustrationsmay notbe copied. The abstract shouldcontainconspicuousacknowladgmenlof where c-d bv whom the pafw is presented. Write PubticationaManager, SPE, P.O. Box 633S36, Richardson, TX 76063-3636. Telex, 730989SPEDAL. ‘

ABSTRACT

A system of equations constitutinga drillingmodel has been developed with the capabi1ity tohandle al1 bit, mud and formation types. Thismodel has been used in three application programs:

o DRLSIM. A bit run time simulation

o DRLOPT. An optimization program which pre-dicts terminationmechanismsand cost per footfor a range of operatingconditions.

o FORMDES. Foot-by-foot drilling data is usedto produce drilling resistance,pore pressureand fracture gradientlogs.

INTRODUCTION

Drilling Models

Although the term ‘DrillingModel’ has been muchused in the literature,there is a great deal ofambiguityassociatedwith it. A drillingmodel ismuch more than a single rate of penetrationequa-tion describing a relationship between measuredparameters of the drilling process. A truedrilling model is a system of equations, some ofwhich may be differential, which quantitativelyexplains the interaction of the most importantparametersof the drilling process. By necessity,some of these relationshipsmay be empirical.

Drilling models should not be judged as right orwrong because of our present lack of understandingof the process based on first principles.However, .they may be judged as to their usefulness. If amodel is useful, then it is a worthwhileadditionto engineeringpractice. The uses of a comprehen-sive drilling model would include simulation ofbit runs on computers allowing alternative prac-tices to be evaluated, detection of drilling

.-

problems, formation correlation and drillingoptimization.

Previous Wrk

Over the last thirty years, there have been vari-ous periods of activity In developing drillingmodels. It is not w intention to exhaustivelyreview these previous efforts, since the modeldiscussed in this paper Is not based on any speci-fic previouslyexisting result.

In general, these efforts have centered on tryingto relate some of the more obvious measurable ofthe drilling process to rates of penetration.They have generally had the form of an algebraicrelationshipbetween weight-on-bit,RPM, bit sizeand some constants which need to be determinedthrough some type of field test. Almost allconsidered roller cone type b+~s only. some ofthem includedthe effects of cutter wear, few con-sidered hydraulic effects [1], and most proved oflimited use in helping to make better decisions indrilling operations[2-10].

These efforts were generally based on laboratoryobservations, and that is about as far as anyverificationwent. For the most part, there wasnot enough interest in their further developmentto warrant.the effort of extensive field verifi-cation. The problem also existed as to how totest a drilling model, It is really not enough tojust coma up with the same average rate of pene-tration over a several hundred foot bit run, sinceseveral different rock layers would generally bepassed through. Unfortunately, about the onlydrilling data recordedin the field was the singleline entry of a typical bit ‘eccrd. These couldlie for years in a file room .:i:twt ever beingexamined. However, over the last five years,substantial improvements ha’e .)eenmade in boththe volume and accuracy I?+cr:;ling data. Some

-..5

. . .

2 DRILLINGMODEL IN SIMULATION,OPTIMIZATIONAND FORMATIONDESCRIPTION lADCfiPE14786

operating companies have foot-by-foot dri~1ingdata measured on all their rigs. This data isavailable on magnetic tape or other mass storagedevices for automatic use in interpretativepro-grams. Thus, it seems worthwhile to re-examinethe subject w- drilling models in making drillingdecisionsat this t~me [11-14].

Approach

The approach taken in this work was to formulateasystem (if~quations which describe the quantita-tive interactionsof the most importantparametersof the rotary drilling process. These equationsare based on both laboratc”y and field observa-tions. Their functional form is shown in Figure1. The equations were then incorporated intocomputer progralisto provide bit run simulation,operating condition optimization, or formationdescriptiondependingon the program’sinput.

The model behaves in accordance with observeddrilling practices. For example, it predictsslower rates of penetrationwith oil based mud ofthe same mud weight as water based mud. It drillsfaster in over-pressuredzones, slower in depletedzones. Details of the model’s capabilities,andexamples of its applications, will be given indetail in later sections.

IU)DEL CAPABILITIES

Bits

The four types of bits nmst commonly used intoday’s drilling practice, milled tooth, insert,natural diamond and polycrystallinediamond, canbe handled by the model. Each bit used by themodel is individuallydescribed through interact-ive questions,so that differencesbetween brandscan be modeled. For roller cone bits, threebearing types are availabie: standard lollerbearings, sealed roller bearings,and sealed jour-nal bearings. Bit material propertiesand cuttergeometry are also included.

Mud Properties

Three nud system types are availablein the model:fresh water, salt water and oil based. Theologi-cal propertiesand mud weight effects are includedin the model’s computations.

Hydraulics

Hydraulic effects on the rate of penetrationdueto flow rate, jet number, jet size, and extendedjets (if used) are included. Some of these Capa-

bilitiesare based on previousstudies (15-21).

Mechanical Conditions

Weight-on-bitand rotary speed are the most impor-tant mechanical parametersincluded in the model.In using the model for bit run simulation, ameasure of the variations in these parameters isneeded in order to provide more realisticpredic-tions of the drilling process by includinguncer-tainty in the nndel’s output.

..

Lithology

Any type rock car be modeled. For bit ,>unsimula-tion purposes, th.,rock can be characterizedbythe output of the model using foot-by-footdrillingdatd from an offSet well. If this is notavailable, approximate values for drilling resis-tance are calculated from the input of certainrock properties. The use” is ;ead through thisprocess by interactivequestions. Any number oflayers of arbitrary thickness can be modeled.However, the resolution of the results in thesimulation k!ll be strongly dependent on thesimulation time step. Thus, using many “,hinlayers for modelingmay prove klsteful.

An arbitrarypore pressure distribution,includingboth over-pressured and depleted zones, can beaccommodated. In bit run simulation, the porepressure can be input at any desired intervalas aseries of values in ppgo

KXIEL LIMITATIONS

The model described in this paper has no capabil-ity to describe dynamic phenomena,nor are dynamiceffects accounted for in the rate of penetrationequation. The model makes no directionalpredic-tions; it drills straight ahead in the directionof the weight-on-bit. Thus, it can be used insimulating a straight inclined borehole, but itwill be unable to predict deviations from theincline direction. A computer is needed to usethe model, although it can run on micro- or mini-computers and does not require long computationaltimes. It will give outputs as long as correctlyformatted inputs are entered. However, outputsobtained with arbitrary data far removed fromtypical drilling practice must be viewed withcaution.

APPLICATIONS

The subject drilling mdel has been used in threedifferent application p-ograms. Bit run simula-tion is accomplishedby the DRLSIM program. Mini-mum cost drilling optimization is done by theDRLOPT program. A descriptionof the lithologieswhich have been drilled, as well as the porepressure and fracture gradient, are computed bythe FORMDES program. The details of each programwill be described separately. Figure 2 shows abrief comparisonbetween the inputs and outputs ofthese programs.

DRLSI14,the bit run simulationprogram, needs thefollowinginputs:

. Operating conditionsincludingmud properties,hydraulic,and mechanicalparameters.

- Bit description including type, geometry andbearings.

Lithology including rock drilling resistanceand pore pressuredistribution.

Uncertaintiesin the above parameters. ThiSis given as a mean value and a standard

. .

‘4 sALVATOM C. MALGUARNERA IADC/SPE 14786-1.

deviation, thus characterizinga Gauss!an or T~~ user must input the allowable range for WOBrandom distributionof the given parameter. afluRPM. These ranges are then divided into a

fixed number of equal intervals, usually eight.The outputs of DRLSIM are given as functions of Each combinationis then used in simulatinga bitdrilling time. The mean or most probable value run. No uncertaintiesare used in these simula-and the 95% confidence limits for the following tions, so there is only one result per comblna-quantitiesare provided: tion. The bit run terminates under the same

conditionsused in the DRLSIM prog,’am. The cost0. Depth of each run is saved and sorted to provide the. Rate of Penetration- % of Cutter Life used

minimum cost per foot as well as a cost per foot

- % of Bearing Life usedcontour. A failure mode map as a function of WOB

% of InsertsFractured (for insert bits only)and RPM is also provided.

-Torque-On-Bit FORMDES is an applicationsprogram,which uses the

The simulation is performed using adjustabletimemodel in conjunction with fOOt-by-fGOt drilling

steps. This allows long bit runs in the order ofdata to calculate rock drilling resistance, pore

100 hours, as well as shorter runs, to be handledpressure and fracture gradient of the formationbeing penetrated.

in reasonable times. The time step is a userdefined input. The simulation can be performed FORMDES requiresthe followinginputs:any number of times, usually 50-100. During anyparticular simulation, the value of a relevant - Bit descriptionparameter i? selected from a random distribution. -This is defined by the user input values of mean -

Mud propertiesJet number and sizes

and standarddeviation,an; used in the subsequentcomputations. A given simulation will terminate and on a foot-by-footbasis:upon reaching one of the followiflguser inwtconditions: RPM

A maximum number of time steps has been ex- :WOB

. Depthceeded which is equivalent to drilling for a -fixed time period.

Cumulativerotatingtime. Rate of penetration

Flowrate. A maximum depth has been exceeded.

The most probable value of tooth wear, bearingFORMDES ~ives the followingoutputs for each depthat which data is entered:

wear or insert fractureexceeds 100%.

The result of each simulation trial is saved and -Rock drilling resistance. This can be calcu-

the statistics of the output for each time arelated as a running average over any desiredinterval.

then computedand plotted.A five foot averaged plot corre-

lates well with SP logs, and makes selection

DRLOPT is a drilling optimizationprogram, whichof major lithological changes easy. ‘ihe

calculates the outcomes of drilling under a rangeunaveraged plots correlate well with resis-tivity logs.

of specified conditions and recommends a leastcost operatingpoint within the given range. Pore pressure. This is determined frofi.

DRLOPT requiresthe followinginputs:changes in the rock drilling resistance.

Bit descriptionFracture Gradient. This is calculated from

.Allowable range of WOB, RPM

the rock drilling resistance and pore-

Lithologyand pore pressurepressure.

. HydraulicconditionsBit cost and salvage value

All of these outputs are plotted in a log format-

Rig costs and tripping speedsand scale to make comparisonwith MWD or wirelinelogs convenient.

The DRLOPT output for each combinationof WOB andRF$iiS:

Foot-by-foot drilling data is fed into the modeland an unadjusted rock drilling resistance,which

The bit run length in feet and ending depth.contains both the pore pressureeffects and inher-

The bit run durationin hours.ent rock propertiesis cal ulated. The changes in

The cutter and bearing conditions at the end

2

this parameterwith depth a fitted to a polyno-

of the bit run.mial curve which will match a known pore pressure

The average rate of penetrationduring the bitat a point near the beginnig of the bit run.Since the model contains a equation which des-

run.The cost per foot for the bit run.

tribes the effect f the fference between pore

A cost per foot matrix summarizingthe costspressure and y ros

.mud pressure on rock

for each bit run.drilling resistance, the pore pressure can be

A minimum cost per foot and associatedcondi-determined. This effect is now removed from the

tions.unadjusted rock drilling resistance to yield therock drilling resistance,which is a ,characteris-

617“..

. ..

(J DRILLINGMODEL IN SIMULATION,OPTIMIZATIONAND FORMATIONDESCRIPTIONIADC/SPE 14786

tic of the rock type and flaws present alone.Results from many Gulf Coast wells Indicate that

and 50,000 lbs. [222.41 kN] and the RPM between 50and 250. The time step used was 900 seconds,and a

sands and shales in this regionhave rock drilling maximum of 1000 time steps were allowed. A bitresistancesof 1000-200~ Psi [6.89 - 13.79 Mpal cost of $5,000, a rig rate of $1,000 per hour, andand 3000-4000 psi [20.68 - 27058 MPalascalcula-ted by this model, respectively.Knowing this,

a tripping speed of 2,000 feet per hour [169.32mm/s] were assumed. The resulting cost contours

actual drilling problems such as bit balling havebeen detected since this condition would cause

were plotted in Figure 10. The star marks thecost associated with the previously described

much higher values of rock drilling resistancetobe calculatedby the model.

simulation. The cost per foot could have beenreduced by driving the drilling conditionstowardthe upper right hand corner of the figure. This

EXAMPLES type of display illustratesthe economic impact of

The use of the model in the applicationsdiscussedchanging drilling conditions. The example shows acost minimum at a corner.

above will be illustratedby an example from a bitThis is because the

range on the drilling conditionswas too small torun in an onshore Louisiana well. The bit used allcw a local minimum to exist inside the figure.was a 9-7/8” [250.8 ITIIIIJ-22* The actual bit runbegan at 11,424 feet [3503 m] and ended at 12,000

Figure 11 shows a failure mechanism map for the

feet [3658 m]. The lithologywas normally pres-same range of drilling conditions. The plot deli-

sured sand and shale. The weight-on-bitaveragedneates the way each combinationof WOB dnd RPM canbe expected to cause bit run termination.Plots

29,000 lbs. [129 M] with a standard deviation of3,600 lbs. [13.34 kN]. The RPM averaged 110 with

such as these can be used in conjunctionwith the

a standard dev ation of 5. The flow rate was 440d

cost contours to select the most desirabledrilling conditionsfor a particularinterval.

GPM [27.76 dm /see]. Three j ts were used: 11,11,12.

?A 9.8 ppg [1174 kg/m ] water based mud Formation Description

with a funnel v;scosity of 42 seconds was used.The actual bit run lasted44 total hours includingconnections. The bit had 55 broken teeth, and the

By providing the model with foot-by-footdrilling

bearings were graded 8-5 at the end of the bitdata, it is possible to plot the five foot runningaveraged drilling resistance log shown in Figure

run. 12, An SP log for this same interval is providedfor comparison. The correlation is good. It is

$iwlation much easier to correlate these plots with offset

Figure 3 is a comparisonof the actual depth andwell logs than by using rate of penetrationplots.

the simulation’sprediction,both as a functionofdrilling tire. The agreement between the pre-

Pore pressure and fracture gradient logs, derived

dieted mean value of the simulationand the actualfrom the model’s use of foot-by-foot drilling

data is good. The variation in the magnitude ofdata, are shown in Figures 13 and 14, respec-tively.

the 95% confidence limits ‘!sdue to the differ-ences in the uncertainties associated with the CONCLUSIONSpropertiesof the different rock layers. Simula-tion results need to be carefully interpreted.For example in Figure 3, after eight hours Of

The most effective use of the drilling model des-

drilling, the depth will most probably be 11,590cribed in this paper is to use the three applica-

feet [3533 m]. However, if this same operationwastion programs in a coordinatedway. Foot-by-footdrilling data from offset wells can be used to

repeated many times, we are confident that 95% ofthe resulting depths at eight hours would be be-

create drilling resistance logs. These drilling

tween 11,570 feet [3527 ml and 1I,61O feet [3539resistance logs can then serve as input to the

m]. Only 5% of the time would the result beoptimizationprogram to s@lect the most economicalbit and operating conditions. Then, a simulation

expected to fall outsidethese limits, of the given bit run can be made. The simulation

Figures 4 through 9 show computer generated plotscan serve as a guide during the actual drilling

for the simulation of this same bit run. Theoperation, and the foot-by-footmeasured data canbe compared to the simulation predictions. Dif-

center tic mark represents the most probable ferences can indicatedrilling problemsor changesvalue, while the end tic marks delineate the 95% in lithologies. This process could be refined asconfidencelimits. more development wells are drilled in a field.

The simulationterminatedafter 40 hours of drill-The improved drilling efficiency could result in

ing due to bearing failure, as shown in Figure 6.substantialsavings in drilling costs.

The mean number of broken inserts predictedby thesimulation is about 44 (45% of the total of 96).

Orilling models like the one described in this

The wear of the inserts reaches approximately60%paper provide a systematicway to use mathematical

at the end of the simulation.modeling and computer capability:; to assist inoperational,~lanningand decision making. These

Optimizationresults can be provided rapidly, requiring only10-20 seconds of CPU time on a VAX 11-785 for a

Using this same interval, the drilling optimiza-1500 ft. bit run. Although such models are pre-

tion program was run. All the inputs were thesently in their infancy, they hold the promise ofimprovementsin accuracy and capability,which can

same as for the simulation,except the weight-on-bit was allowed to vary between 10,000 [44.48 kN]

make them as essential a tool for tomorrow’s

518

5 SALVATOREC. MALGAURNEPA IADC/SPE 14786

drilling engineer as an electronic calculator isfor today’s.

MMNCLATURE

‘bit = Bit Diameter

Djet = Jet Diameter

NW = Mud Weight

z = Depth

Pm = Mud HydrostaticPressure

‘P= Pore Pressure

= AtmosphericRock DrillingResistance‘ou = Rock DrillingResistanceat Depth

EPim = Energy Flux on the FormationFace

‘im = Fluid Jet Velocityon FormatiohFace

f = CharacteristicCutter Dimension

ROP = Rate of Penetration

RPM = Rotary Speed,“Revolutionsper Minute

T = Torque on the Bit

WOB = Weight-On-Bit

ACKNCMLED6E14ENTS

I wish to thank NL Industriesfor permission topublish this paper and Carolyn McFarland forpreparingthe mmuscript.

REFERENCES

1. Warren, T.M., “PenetrationRate PerformanceofRoller Cone Bits”, SPE Paper 13259, presented atthe 1984 SPE Annual TechnicalConference,Houston,September26-29.

2. Outmans, H.D., “The Effect of Some DrillingVariables on the InstantaneousRate of Penetra-tion”, Petroleum Transactions. AIME, Vol. 219,1960, 137-1490

3. Rowley, D.S,, Howe, R.J., and Deily, F.H.,“Laboratory Drtlling Performance of Full-ScaleRock Bit”, Journal of Petroleum Technology (Jan.1961), 71-81.

4. Eckle, J.E., and Rowley, D.S., “Effect ofSpeed on PenetrationRate”, The Petroleum Engineer(Jan. 1958), 46-48.

5. Gamier, A.J., and van Lingen, N.H., “Pheno-mena Affecting DrillingRates at Depth”, PetroleumTransactions AINE (1959), Vol. 216, 232-239.

6. Cunningham,R.A. and Eenink, J.G., “Laboratory.Study of Effect of Overburden Formation and MudColumn Pressures in Drilling Rate of PermeableFormations”, Petroleum Transactions AME (1959),Vol. 216, 9-17.

7. Gall@, E.M., and Woods, H.B., “VariableWeightand Rotary Speed for Lwest Cost Drilling”,Annual;ee;ing of AAOOC, New Orleans, September 25-27,

.

8, Young, F.S., “ComputerizedDrilling Control”,Journal of Petroleum Technology (April, 1969),483-396.

9. Wardlaw, H.W.R., “f)ptimizationof RotaryDrilling Parameters”,Ph.D. Dissertation,Univer-sity of Texas at Austin, August, 1971.

10. Warren, T.M., “DrillingModel for Soft Forma-tion Bits”, Journal of Petroleum Technology (Dec.1981), 963-970.

11. t“iillheim,K.K., and Huggins, R.L., “TheEngineering Simulator for Dri11ing (Parts 1&2)”,SPE Papers 12075 and 12010 presented at the 1983SPE Annual Technical Conference, San Francisco,October 5-8.

12. Millheim, K.K., “The Roll of the Simulator inDrilling Operations”, SPE Paper 11170, presentedat the 1982 SPE Annual Technical Conference,NewOrleans, Sept. 26-29.

13. Onyia, E.C., “Geology Drilling Log (GDL): AComputer Database System for OrillingSimulation”,SPE Paper 13113 presented at the 1984 SPE AnnualTechnicalConference,Houston, September26-29.

14. Brett, J.F., and Swmners, M.A., “PlanningandPractical Problem Solving Using an EngineeringSimulatorfor Drilling”,SPE Paper 13206 presentedat the 1984 SPE Annual Technical Conference,Houston, Sept. 26-29.

15. Maurer, W.C., “The ‘Perfect-Cleaning’Theoryof Rotary Drilling”, Jwrnal of Petroleum Tech-nology (tiOV. 1962), 1270-1274.

16. van Lingen, N.H., “Bottom Scavenging,A MajorFactor Governing Penetration Rates at Depth”,Journal of Petroleum Technology (Feb. 1962), 187-196.

17. McLean, R.H., “Velocities,Kinetic Energy, andShear in Crossflow Under Three-Cone Jet Bit”,Journal of Petroleum Technology (Dec. 1963) 1443-1448.

18. Sutko, ‘LA., “DrillingHydraulics- A Study ofChip Removai Force Under a Full-Size Jet Bit”,Society of Petroleum Engineering Journal (Aug.1973) 233-238.

19. Feestra, R., and van Leeuwen, J.J.M., “Full-Scale Experiments on Jets in Impermeable RockDrilling”, SPE reprint series No. 6a, Drilllng,1973 Rev.

20. Albertson, M.L. et al., “Diffusion of Sub-merged Jets”, ASCE Papers, Vol. 74, 1948, 1571-1596.

21. Feenstra, R., and Zijsling, D.H., “The Effectof Bit Hydraulics on Bit Performance in Relationto the Rock DestructionMechanisniat Depth”, SPEPaper 13205 presentedat the 1984 SPE Annual Tech-nical Conference,Houston,Sept. 26-29.

1---- ---- -.FilQ

z = t=(RORROTATINQTIME)

Pm = F(MW, Zl

Pp = F(POREFLUID,DEPTH)

Uo = F(ROCKTYPE,FLAWSIZEI

0 = F(u* Pp Pm, a

EFIm = F(FLOWRATE D@t,%t, MWl

vl~ = F(FLOWRATE D~t, ~i, MW)

f = F(CUllER GEOMETRY,BITTYPE,INITIALCONDITIONS,MATERIAL,ROTATINGTIM5 WOB,RPM)

ROP = F(a, Vim, EFIm, Mud Pro@las, ~It, BIT TYPE, RPM, WOB,o

T = F(RORo, hit, RPM)

% B2wIw Life U$@d = F(TYPEOF BEARING,WOB, ~t, RPM, ROTATIN13TIME)

% Cutter Life US2J s F(TYPEOF B~, CU~ER QEOM~RV AND MATERIALS,WOB,RPM, ROIATtNGTIM% ROCKTYPSI

% Irrsmfs Fraotumd s F(WOB,~Ii, RPM, ROTATINGTIME)

Fig. 1-Dfllllng model symom of qustlons.

sitD02crlptbrrop2r2tl~CorrdithsFormalIonD2sorlpffon

BltDnort@nOpsmtlngCor18tmlntsFomratiorrOobort@lorr

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