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By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.',' Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact'on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,' but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation' and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a'c' and c'b are equal to a'b cos +, and a'b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m'c' and c'b are projected as lengths from point a, rather than from point a'. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

By D. S. Rowley, F. C. Appl

Assuming that rock behavior, during cutting with a single diamond, may be approximated by that of a rigid, Coulomb, plastic material, a theory of single diamond cutting action has been developed. Using this theory, the stresses on the diamond cutting surface and the components of the cutting force have been determined. Theoretical results agree reasonably well with available experimental data. The theory of cutting of single diamonds may be used as the basis for subsequent study of the perfonnance of surface set diamond drill bits and other surface set diamond cutting tools. INTRODUCTION For more than twenty years, surface set diamond bits have been used successfully in the mining and petroleum industries to drill and core rock formations that range from medium hard to the hardest known formations. Most extremely hard rock formations cannot be economically drilled or cored by any other means. In view of the growing use and importance of surface set diamond drill bits, it is reasonable to study the way in which these tools cut, and the factors that influence wear of the diamonds. Such knowledge will contribute to better bit design and will improve operating procedures. To analyze the cutting performance of these tools it is appropriate to consider the way in which an individual diamond cuts. Once this is established, the over-all performance of the bits can be determined by considering the total effect of the individual diamonds. In recent years there has been a growing interest in rock mechanics and there now exist several publications dealing with the deformation and failure of rocks. Notable experimental work has been reported by Bredthauer,1 Handin and Hager,2, 3 and Gnirk and Cheatham.4 An extensive collection of data pertaining to rock properties at low confining pressures has been given by Wuerker.5 Cheatham and Gnirk have recently presented an excellent review of the state of knowledge regarding analytical and experimental rock deformation and failure.6 Generally rocks are extremely weak in uniaxial tension, and weak or only moderately strong in uniaxial compression. Both tensile failure and compressive failure are generally brittle in nature. This means that there is little or no deformation or "flow" of the material before shear or tensile fracture occurs. Thus, until fracture occurs, rock behaves very nearly like an elastic material in uniaxial stress. Significant changes in behavior of rock occur under conditions of triaxial compressive stress. There is generally a marked increase in compressive strength and in ductility. It has been demonstrated that the failure becomes plastic (in a macroscopic sense) at sufficiently high values of confining pressure. Sharp wedge chisel indentation studies conducted by Gnirk and Cheatham indicate that many rocks behave in a plastic manner at relatively low triaxial compressive stress states.4 If "failure" under triaxial compressive conditions is considered to be either complete rupture or macroscopic plastic flow, then the general failure characteristics of a rock can be reasonably well represented by the commonly known Mohr envelope. This certainly is not a perfect failure criterion (since the effect of the intermediate principal stress is neglected) but it has been found to be adequate for most engineering purposes. Mohr envelopes usually are constructed graphically using experimental triaxial test data. For purposes of analysis it is convenient to represent the envelope in equation form. Among the several approximate forms appearing in the literature, a parabolic form is suggested by Cheatham,7 and an exponential form is suggested by Paone and Tandanand.8 The exponential form has been adopted for this study, and based on published data, appropriate parameters have been established for 19 rock types. A typical plot of the data compared with the approximate envelope, and a summary of the rock properties and

Jan 1, 1969

By C. Dalton, H. L. McGill

The purpose of this study was to develop a method for predicting the time delay created by metering a fluid through an annular restriction with translational motion of the boundaries. This time delay is utilized to control the opening of valves in various down-hole oilfield tools and forms the basis for the "hydraulic jar". The hydraulic jar is used to give upward impact forces to tubing or other tools that become lodged down-hole. The design of these jars has primarily been by trial and error; varying the clearances, fluid viscosities and dimensions of the jar until a satisfactory time delay was achieved. Obviously, a better understanding of the fluid flow characteristics is required to produce designs that are satisfactory and to eliminate the trial-and-error approach. Previous studies of flow in annular spaces were based on constant length of the annular restriction. Any motion of the boundaries of the annular space was confined to a rotational motion, like that encountered in journal bearing design. Consideration of the effect of translational motion of one boundary with respect to the other was necessary in applying this previous work to a time delay device. A prediction method was developed that takes into account this relative translational motion. Equations were developed to predict the relative velocity, the flow rate, and the time delay in a concentric annular space. The effect of eccentricity also was included. Experimental data were obtained and closely correlated with the prediction method. This correlation is presented graphically in terms of predicted and actual relative velocities for various annular clearances and pressure drops. This extension provides design equations which predict the performance of the hydraulic jar, thereby eliminating trial-and-error solutions and reducing the development time required for satisfactory designs. INTRODUCTION The design of down-hole oilfield tools which use hydraulic delay systems based on flow through annular orifices with relative motion of the boundaries is usually a trial-and-error process. The annular clearances, fluid viscosities and dimensions of the mechanisms were varied until satisfactory delay times were obtained. The development of these tools has been expensive, and a better understanding of the characteristics of annular flow with relative motion of the boundaries could result in superior and less expensive designs. The purpose of this investigation was to provide a method of predicting the performance of down-hole tools which use annular flow and, in particular, the performance of a down-hole tool known as the "hydraulic jar". The hydraulic jar is used to free pipe, packers and other tools that become lodged down-hole. The jar, located in the tubing string between the surface and the object which is stuck, releases the object though the repeated application of upward impact blows. The jar is basically a slip joint that is restrained in a collapsed condition until the desired tubing tension has been developed. The slip joint is then released and accelerates rapidly until it shoulders, delivering an impact blow or jar to the object. The delay obtained by metering the fluid through the annulus formed by the jar valve and housing provides the time delay necessary to stretch and apply tension to the tubing or pipe. Fig. 1A gives a schematic diagram of the hydraulic jar and brief details of its operation. The metering of the hydraulic jar begins when the tension force being applied to the jar by the pipe creates a pressure differential across the valve that is approximately equal to the force divided by the displacement area of the valve. This pressure differential induces flow through the annular restriction formed between the valve and housing. The valve moves with respect to the housing as the

Jan 1, 1969

By H. A. Bourne, E. L. Haden, D. R. Reichmuth

A circumferential-toothed bit with novel tooth form gave improved penetration performance. In this design the exterior flank of all teeth were vertical when in rolling contact with the hole bottom. Rock chips were generated by the interior flank of the tooth displacing the rock inwardly and downslope toward the center of the hole. A unique two-cone laboratory bit assembly enabled evaluation of numerous cone and tooth configurations. Some of the variables investigated, in addition to weight on bit, rotary speed and rock type, were tooth interference, percent tooth, hole bottom angle, attack angle and relief angle. Most tests were conducted dry on a brittle synthetic sandsone or a ductile quarried limestone. Tooth configurations were found to be more significant in the ductile material. This was attributed to the deeper tooth penetration before rock failure. These studies showed that the attack angle (angle beween interior flank of the tooth and rock surface) was the controlling variable; changing the tooth configuration from the assymetric or semi-wedge to the more conventional symmetric or wedge form reduced penetration performance; and penetration performance of circumferential-type cutters was directly proportional to rotary speeds up to 200 rpm. INTRODUCTION Much of the published literature on rock-chisel interactions describe experiments wherein symmetrical wedges are vertically loaded or impacted against a smooth rock surface.1-6 are is usually taken to insure that the indentation is not made near the edge of the rock specimen less erroneous data be obtained. The literature describes relatively few studies in which the investigator deliberately attempted to take advantage of an edge or free surface. In contrast, anyone who chips ice or breaks up a concrete sidewalk almost always works near an edge. Chisel "indexing," which has been considered by some investigator1,2,6,7 makes limited application of an edge or free surface. Probably the best documented investigation into applying this idea to drilling was that of Drilling Research Inc. at Battelle Memorial Institute.' Their "annular wing" percussion bit consisted of paired asymmetric chisels oriented so as to produce and move chips to the center of the hole. They predicted that the lowest energy requirement for chip generation would be achieved with a stepped hole bottom having a median angle of 45" to the horizontal. Results from limited tests showed that approximately 50 percent of the rock fragments were large and semi-circular in shape, as would be expected by a chisel impact near an edge. The remaining 50 percent were fine chips produced by the chisels in re-establishing the steps or ledges. Initial penetration rates with this bit were high, but they rapidly decreased. This was the result of excessive tooth wear caused by the constant friction on the gauge surfaces. The basic idea — circumferentially placed asymmetric chisels — still appears to have merit. If the concept could be applied to a rolling cutter bit, two of the shortcomings of the fixed chisel design could be overcome: (1) reduction in tooth friction, and (2) greatly increased cutter surface. Adapting asymmetric chisels to cutters rolling on an inclined hole bottom is restricted by bit geometry. The basic elements of roller rock-bit construction prevents the practical attainment of a 45" hole bottom angle. Nonetheless, experimentally it was considered desirable to investigate the influence of hole bottom angle to at least 40". This paper describes the laboratory studies conducted in evaluating the circumferential-toothed roller cutter rock bit. EXPERIMENTAL APPARATUS AND PROCEDURE BIT ASSEMBLY The cost of constructing a sufficient number of conventional three-cone rock bits to investigate circumferential cutter performance was prohibitive. Instead, a novel two-cone laboratory assembly which used an external bearing system was designed and constructed. The external bearings made it possible to alter the journal bearing angles and thus allow a wide flexibility in cutter configuration. Fig. 1 shows the laboratory bit assembly, the various bearing mount plates and the appropriate roller cutters for drilling shallow holes having hole bottom angles of 0, 10, 20, 30 or 40". The bit was limited to a drilling depth of 1 1/2 in. at the gauge teeth and a hole diameter of 43/4 in. This more or less intermediate size bit was chosen because it gave a more realistic match between bit teeth and the rock than would a microbit. Also, the rock sample size required was convenient and easy to obtain. CIRCUMFERENTIAL CUTTERS The tooth configuration used in our initial studies is shown in the upper half of Fig. 2. All cutters used in this series had the same tooth form — 43" included tooth angle, 2" positive relief angle and a horizontal tooth flat width of 1/32 in. Each cone cuts alternate rows except for the gauge row. The row-to-row spacing in view was 1/4 in. Static loading tests conducted earlier with asymmetrical chisels had been used to establish this spacing. These tests showed energy requirements for chip production increasing rapidly as the distances to the edge increased beyond

By F. S. Young

Previous laboratory and field experimentation has demonstrated the effect of several variables on drilling rate.1-5 These results have been incorporated into optimization theories6-" for the purpose of reducing drilling cost. Minimum-cost drilling theories rely on a combination of historical data and empirical prediction techniques for selecting optimum bit weight and rotary speed. Past solutions have required extensive use of computing equipment because of both the complexity of the mathematical formulations and the large number of parameters involved. Field attempts to apply these computed results have frequently failed because of the uncertainty of input data requirements. Humble has developed an on-site computer system to control bit weight and rotary speed and thereby implement the concepts of minimum-cost drilling. This system can (1) perform short interval drilling rate tests for formation evaluation, (2) use the results of these tests as input information to solve minimum-cost drilling formulas, and (3) control bit weight and rotary speed in accordance with these computed solutions. The purpose of this paper is to describe the computer control system and present results of initial field testing. Theoretical Considerations Minimum-cost drilling (MCD) requires a quantitative evaluation of the variables involved. Several forms of a basic mathematical model have been sug-gested.'?,' "he relationships reported here form the basis for the solution programmed in this work. Four equations are used, expressing drilling rate, bit bearing wear, bit tooth wear, and cost. A solution for minimum-cost drilling assuming constant bit weight and rotary speed over the entire bit life has been programmed for use in computing MCD schedules. This solution is subject to certain limiting assumptions such as those discussed by Graham et a1.I2: 1. Drilling cost is the summation of bit cost, rotating cost, connection cost and hoisting cost. 2. Diamond bits are excluded. 3. Bit life is limited by either bearing failure or tooth wear, or by a combination of operational factors that make it cheaper to pull an incompletely consumed bit. 4. Circulating hydraulics are adequate and do not limit drilling rate. 5. Bit weight considerations exclude hole deviation. 6. Drilling rate is a function of only bit weight, rotary speed, and degree of tooth dullness; that is, the effects of pressure, lithology, fluid properties hydraulics and drill string dynamics are ignored. In equation form, the four MCD expressions are as follows:

Jan 1, 1970

By A. Lubinski, J. E. Hansford

Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through Such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs. INTRODUCTION Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to unde-sired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated.' However, in wells where the maximum permissible dogleg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll.' The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in doglegs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures. FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffce to read only through the section Abrupt Dog-Legs. 1. Concept of the two extreme kinds of idealized doglegs: gradual and long dog-legs and abrupt dog-legs,' 2. Concept of why the bending moment in drill pipe un- der tension is the largest in the vicinity of the tool joint,' 3. Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension,' and 4. Definition of the rate of change of over-all hole angle (dog-leg severity)." Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.

Jan 1, 1967

By N. E. Garner

Laboratory experiments were conducted to investigate the cutting of a single diamond on limestone and shale under simulated down-hole conditions. A high-pressure chamber was modified by adding a rock-rotating device so that planing tests could be run. Weight on the diamond, diamond geometry and differential pressure across the face of the rock were varied. It was found that (I) high differential pressure reduced the volume of rock cut by the diamond at a given bit weight by strengthening the rock and changing the mode of failure; (2) a finely powdered rock left in the bottom of the grooves reduced the volume cut by as much as 50 percent; and (3) orientation of a single diamond about the axis of a drill point had considerable influence on diamond cutting efficiency. INTRODUCTION Diamond bits consist of many diamonds held in a matrix provided with water courses for fluid passage to clean, cool and lubricate the diamonds as they drill formation. Each diamond contributes its share to the overall effectiveness of a bit, but a lack of understanding of the performance of a single diamond has hampered efforts to engineer improvements in diamond bits. The need for those improvements prompted this study. This paper describes the findings of a laboratory investigation of the outting action of a single diamond where the differential pressure between the wdlbore and formation, diamond geometry and vertical force on the diamond were independently varied. The tests were conducted in a pressure chamber that provided relative horizontal motion (planing) between a rock and diamond under simulated down-hole pressure conditions. EQUIPMENT HIGH-PRESSURE CHAMBER WITH ROTATING DEVICE The high-pressure chamber used in previous rock mechanics studies' was modified for this study by addition of a rock-rotating device. The modified chamber (Fig. 1) differs from the old chamber in that the rock can be rotated to provide relative horizontal movement between the rock and the penetrator which may be a small element of a diamond or a drag bit. In this study the penetrator was a single diamond. The rock sample holder inside the chamber is mounted on a thrust bearing and is connected to the external drive mechanism by a stem that passes through two seal elements. The seal elements are needed to allow formation pressure to enter the bottom of the rock sample through a small hole in the stem. The Kapseal seal elements (Tefion boots backed by O-rings) provide low friction (hand free) even at differentials of 5,000 psi. The drive mechanism is a variable-speed transmission with a speed range from 0 to 30 rpm and an output torque of 2,800 in.-lb. A right-angle-drive gear box couples the drive to the stem. The new design has two independent pressure systems (formation and borehole) to simulate down-hole rock stress environment. Formation pressure enters from the bottom of the rock through a 6-in. diameter area, and borehole pressure acts over the remaining surface. A 14-in. layer of zero fluid loss oil-base mud poured over the top of the rock and an O-ring seal on bottom allow a differential between the borehole and formation pressures. Bayol 50 was used as the hydraulic fluid in the chamber. The differentials reported here were obtained by elevating the borehole pressure while keeping the formation pressure at zero.

By G. J. Wilson

Review of difficulties experienced in drilling directional wells in the offshore Grand Isle Block 43 field showed most failures of drill pipe, drill collars and casing to have been associated with excessive dog-legs. Alleviation of difficulties was approached by synthesizing theoretical and practical concepts in a planned dog-leg control program. Preventive measures necessary to control dog-leg severity and corrective measures used to reduce unacceptable doglegs are discussed. When other measures fail, deliberative measures as outlined can be employed after the probable cumulative fatigue damage to be sustained by the drill pipe has been determined. Results of a program successful in virtually eliminating problems stemming from excessive dog-legs indicate that control of dog-leg severity in directional wells is feasible and will cause no decrease in the over-all drilling rate. INTRODUCTION Prompted by an increasing frequency of drill pipe, drill collar and casing failures, a study of 50 directional wells representing 592,000 ft of hole, including 444,000 ft of deviated hole, drilled in the offshore Grand Isle Block 43 field was conducted in early 1965. A number of drill pipe washouts and six keyseating problems were recorded and a detailed review was made of 16 failures which had required fishing effort in 10 of the 50 directional wells drilled prior to June, 1965. These problem wells are exemplified by Wells G and F for which pertinent data are shown in Figs. 1 and 2. Data pertaining to all of the 16 failures are summarized in Table 1. Inspection of these data shows most of the problems to have been associated with dog-legs in excess of theoretical limits suggested by Lubinski' and excessive dog-legging is indicated to have been concomitant with whipstocking in several of the problem wells. Results of the investigation agreed with those reported by Schenck2 who had concluded that problems could be expected when dog-leg severity exceeded limits proposed by Lubinski. Since Schenck had demonstrated the desirability and feasibility of drilling directional wells without excessive dog-legging, a dog-leg control program was established in June, 1965 for wells drilled in the Grand Isle Block 43 field. This paper reviews the methods by which theoretical and practical concepts were synthesized to develop a program of preventive, corrective and deliberative measures which virtually eliminated problems stemming from excessive dog-legs in directional wells. Dog-legs of a magnitude causing no damage are referred to as permissible +1CONTINENTAL OIL CO. HARVEY, LA.

By F. S. Young, K. E. Gray

Drilling tests with a 11/4-in. diameter roller bit were performed on Berea and Bandera sandstones and Leuders limestone using water and two conventional drilling muds as circulating fluids to evaluate the influence of dynamic filtration on penetration rate. The muds possessed widely differing API fluid-loss properties. Mud filtrate was constrained to flow beneath the bit; no filtrate flowed radially through the borehole wall. Rock pore pressure at three different locations ahead of the bit, cumulative filtrate volume, borehole pressure and bit location were monitored during drilling. The rock samples, cored in three orientations with respect to bedding planes, possessed a wide range of liquid permeabilities. and were drilled at borehole-to-formation pressure differentials of 0, 250, 500 and 1,000 psig. The effect on penetration rate of API fluid loss, borehole pressure and rock permeability was studied. Rock permeability damage and pore pressure gradients beneath the bit were evaluated. The importance of borehole-to-formation pressure differential was illustrated for each drilling fluid and rock permeability combination. Penetration rates decreased with increased borehole pressure and reduced fluid loss. The observed penetration rate reduction due to changing fluid Ioss was attributed to decreased filtrate flow and improved mud cake plastering hy the low fluid-loss mud. The reduction in filtrate flow could not be related to spurt-loss phenomena. Rock permeability influences penetration rate through particle invasion ahead of the hit, which damage leads to high pressure gradients. Penetration rate variance with sample orientation was evident for water-drZled samples but less obvious for mud-drilled rocks. Permeability damage beneath the bit ranged from 1 to 3 cm. Maximum damage occurred in the first 0.1 cm. Pressure gradients varied with API fluid 10.s.s and could be correlated with penetration rate. The pressure gradient was found to influence penetration rare in rocks of all permeabilities tested. INTRODUCTION Early microbit and small-scale drilling experiments proved to be invaluable contributions to understanding the mechanics of drilling at depth. For example, the effect of borehole-to-pore pressure differential on drilling rate was demonstrated conclusively by Murray and Cunningham', Eckel' and others .' However, the effects of various drilling fluid properties on drilling rate, particularly filtration, have not been studied extensively on a laboratory basis. Microbit correlations of penetration rate with different viscosity and API fluid-loss muds led EckelV o conclude that viscosity and density. more than API fluid loss, were the most important fluid properties in controlling drill bit penetration rates. Ferguson and Klotz6 studied filtration beneath the bit and stated that the maximum amount of filtrate which could conceivably flow beneath a drilling bit could be described by a potential function associated with flow from a moving disc source. and be characterized by a depth-of-filtrate invasion. Invasion depth is a function of penetration rate, formation porosity and permeability, flooding efficiency, pressure difference between borehole and formation and borehole radius, assuming that no filtrate flows through the borehole walls. Electric analog and experimental measurements were obtained, assuming no plugging of the formation pores. Theoretically, filtrate invasion was predicted to extend from 1- to 15-hole radii beneath the cutting surface; experimental results indicated that the extent of invasion was only Y2 in. Comparing these data with results of core-plugging experiments by Norwak and Krueger' led Ferguson and Klotz to state that the drilling operation apparently contributes to higher filtration rates than are observed in nondrilling core filtration tests in which the core face is jetted and scraped. Glenn and Slusser: in describing a linear filtering system in which a rotating bit continuously scraped mud cake from the surface but did not penetrate Alundum cores, stated that mud-solids invasion and permeability damage of the cores were most severe in the first 2 to 3 cm. The filtrate flow rate through the core was found to stabilize after sufficient time had elapsed for the formation of an internal mud cake whose effective permeability was estimated to be 50 to 300 times as high as that of bulk filter cake. Krueger and Vogel reported core permeability damage depths up to 12 in. during a 5-day exposure period in which filter cake buildup was prevented. Havenaar pointed out that the discrepancy between reported and calculated values of filtrate volume obtained in the experiments of Ferguson and Klotz was due, among other things, to failure of the reported API fluid loss to truly represent filtration beneath the bit. Williams," Pro-koplz and others"" have shown that dynamic filtration tests (where a flow of fluid parallel to the filter surface continually erodes the deposited filter cake until a dynamic equilibrium between wall-shearing forces and normally directed compaction forces is attained) yield higher filtration rates than do static tests. Cunningham and Goinss reported results of drilling tests in impermeable shales. They found that by reducing

By R. F. Krueger, L. C. Vogel, P. W. Fischer

Previous studies have shown that the permeabilities of sandstone cores are markedly reduced following exposure to drilling fluid and subsequent clean-up with oil at high-pressure gradients. Laboratory experiments reported in this paper indicate that permeability damage from drilling mud or water can be substantially avoided through use of an initial low-pressure gradient followed by gradually increasing gradients during clean-up by reverse oil flow. On the other hand, attempts to improve the permeability of damaged Berea and oil formation cores with high-rate oil backflush (simulated well stimulation) and low-rate clean-up gave erratic results. Essentfully complete permeability repair was achieved in most of the fresh water-damaged cores from Miocene and Pliocene oil-producing formations; only minor improvement was noted generally in tests with both water-and mud-damaged Berea sandstone. Field well stimulation treatments using high-rate back-flush resulted in long-term productivity improvement when production was brought in at gradually increasing production rates and then restricted to a steady value less than the maximum possible rate. Wellbore plugging at high production rates correlated with increasing solids content in the produced oil. Observations and results from these tests agree with current concepts that formation damage in water-sensitive rocks results from movement and bridging of formation fines, rather than from clay swelling alone. INTRODUCTION Many laboratory studies1-g have shown that the permeabilities of sandstone cores are often markedly reduced following exposure to fresh water or water-base drilling mud filtrate. However, work with cores in the restored state has demonstrated that, although permeabilities to water may be very low for sandstones containing hy-dratable clays, flow of oil can often restore a substantial portion of the effective permeabilities to oi1.Neverthe- less, water invasion into water-sensitive sandstone cores results in varying degrees of permanent reduction in permeability to oil.24' Based on field data, Wade's statistical study" of well completion effectiveness also indicated a correlation between productivity damage and water invasion during completion. Similar damage can result from fluid invasion during workover. Nowak and Krueger' and Bertness4 observed in their early work (1951-53) that formation damage in water-sensitive sandstones was associated not only with swelling of expandable clays but also with movement of dispersed particles. Subsequent work by Monaghan et al." (1959), Atwood'' (19641, Mungan" (1965) and Gray and Rex'" (1965) has led to general acceptance of the hypothesis that permeability damage in water-sensitive formations is caused by migration of finely dispersed minerals and bridging in "brush heap" arrangements at pore constructions. In laboratory studies, Monaghan et al.' found the use of chemicals to be of only minor value for repairing formation damage. Atwood? however, was successful in substantially repairing damage in a number of low-permeability cores using an n-hexanol flush. In the field, except for treatments with acids, the use of chemical washes to reduce wellbore damage has had limited and sporadic success and generally is unpredictable. A statistical analysis of stimulation treatments in silt-blocked wells has shown that physical manipulation of wash materials is more important than chemical composition." The recent work reported on formation damage in water-sensitive sands brings to mind the results of some unpublished exploratory work done in 1954 in connection with drilling fluid studies.' This laboratory work and subsequent field stimulation treatments indicated a beneficial effect of controlled pressure drawdown and the associated production rate on formation clean-up. This paper reports the results of this work and more recent supplemental experiments on the clean-up of water-sensitive sandstones damaged by water or filtrate invasion. PERMEABILITY RECOVERY AFTER DAMAGE BY DRILLING MUD APPARATUS AND TEST SAMPLES A drilling mud circulating system was used to expose cores to simulated wellbore conditions. The mud flow system is the same as that described by Krueger and Voge17 except that no provision was made for scraping

By E. A. Hopkin

Laboratory tests conducted by the author. together with actual field experience in Canada. have indicated the magnitudc of some of the factors affecting ability of drilling mud to clean the hole. A correlation was observed between funnel viscosity and particle slip velocity. A relationship was also observed between the Bingham yield value of the mud and the particle .slip velocity. Laburatury tests indicated little change in slip velocity with funnel viscosities up to ahout 80 sec/qt or to yield values of aboul 15 lb/100 .sq ft. The lip velocity of the partic1e.s. studied vuried from 160 ft/min with water to neerly zero for high mud viscositie. lncreasing the mud density, creating laminar annular mud flow or rotating the drill pipe Mlay also improve the carrying capacity of mud. Field tests indicated that during fast upper-hole drilling, the rate of cutting removal must he sufficien to maintain the concentration of cuttings in the annulus at less than 5 percent by volume to prevernt balled-up drill collars and .stuck drill pipe. INTRODUCTION In the Mid-Continent area, hole cleaning during rotary drilling normally involves the use of low-density drilling muds with funnel viscosities varying from 26 to 80 sec/qt. However, frequently it is necessary to raise the mud viscosity in excess of 200 sec/qt to clean the hole. In addition, field experience has indicated that during very fast upper-hole drilling, annular mud velocities considerably in excess of the maximum slip velocity of the cuttings (normally considered to be 120 to 150 ft/min) are necessary to prevent balling the bit and drill collars. In view of these variations in mud properties and circulation rates necessary to clean the wellbore, a study of factors affecting hole cleaning and the relative magnitude of each was undertaken. The study was also prompted by the knowledge that a drilling mud with properties close to those of water would drill at rates several times that of a viscous mud. The carrying capacity of these near-water muds was not clearly understood, however, and many drillers were reluctant to use them. DISCUSSION EFFECT OF MUD PROPERTIES ON DRILLING RATE The effect of mud properties on drilling rate has been studied by a number of investigators. 1t is clear from their work that mud properties close to those of water will significantly improve drilling rate and bit life. If the water-type mud will also effectively clean the hole and cause no logging or formation impairment problems, the choice of an appropriate drilling fluid is clear—use water. Often, however, a water-type drilling fluid is not capable of effectively cleaning the hole. THEORY OF PARTICLE SETTLING The forces acting on a particle that is allowed to settle through a fluid quickly reach equilibrium, and the particle settles at some constant velocity referred to as the slip velocity. The slip velocity of any particle depends upon a number of factors such as density and viscosity of the fluid, the volume, specific gravity, shape and roughness of the particle, and upon the shape and area of the projected face of the particle at right angles to the direction of relative fluid solid movement. Brown' expressed this relationship for spheres in Newtonian fluids in the following equation. where v, = slip velocity D, — diameter of sphere p, = density of spheye p, = density of liquid /a = friction factor g = constant. The friction factor f, varies as the size, shape, surface roughness and slip velocity of the body, and as the density and viscosity of the fluid varies. WaddelV ound experimentally that where dynamic similarity exists. f, was a function of the particle Reynolds number (NRe) of the sphere (Fig. 1). Fig. 1 shows that f, for spheres varies from over 10 for low NKe numbers to 0.44 for N,,. over 600.

By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection' at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969

By C. Bezemer, I. Havenaar

An investigation was carried out on the dynamic liltration behavior of drilling fluids. In a set-up consisting of a porous pipe through which the drilling mud was circulated, dynamic liltration rates and cake thicknesses were determined as a function of flow rate and filtration time. Eventually, a state of equilibrium was reached; i.e., both cake thickness and filtration rate attained constant values. Concurrently, dynamic filtration tests were carried out in a simple dynamic filter apparatus where mud flow was similar to that in a rotational vismmeter. In both arrangements the relation between equilibrium liltration data and rate of shear at the cake surlace was studied. Filter pipe and dynamic filter apparatus were lound to give identical relations. It was therelore concluded that the latter apparatus, which is suitable lor routine measurements on small amounts of mud, could be used to determine the dynamic liltration behavior of mud under borehole flow conditions. Some data are presented on the effect of filtration pressure and temperature on equilibrium filtration rate and cake thickness. INTRODUCTION In oil well drilling, the drilling fluid used generally forms a mud cake on the permeable sections of the borehole wall while filtrate is lost into the formation. As to the conditions under which this filtration process takes place, a distinction should be made between static mud filtration (mud is not circulating) and dynamic mud filtration (mud is circulating). In recent years several investigatorsl-5 have studied the process of dynamic mud filtration about which little had previously been known. This type of filtration is the subject of this paper which confirms several findings of previous investigators. It differs from already published works, however, in the following respects. 1. It contains a description of a simple laboratory apparatus developed for dynamic filtration measurements on small amounts of mud. 2. The effect of rate of shear at the cake surface on dynamic filtration has been studied. As a result of this study, dynamic filtration data pertaining to the borehole conditions of mud flow can be found from laboratory tests. 3. Some data are presented on the effect of filtration pressure and temperature on dynamic filtration. The work was limited to a small number of muds. No attempt was made to compare data on API filtrare loss with dynamic filtration rates. Previous workers have clearly shown that no correlation exists between static and dynamic filtration rates. EXPERIMENTAL ARRANGEMENT To establish whether the effect of mud flow conditions on dynamic filtrations is governed by the rate of shear at the cake surface, two different types of mud flow were used. In this connection the experiments were partially conducted by means of a porous pipe through which mud was circulated, partly in a dynamic filter apparatus which somewhat resembles a rotational viscometer. In both cases the flow conditions of the mud were well defined, thus making it possible to-calculate rates of shear at the cake surface. The filter pipe was 200 cm long with an internal diameter of 3 cm. Its perforated wall was covered on the inside with filter cloth on which the mud cake could form. Mud was pumped through the pipe at linear rates varying from 20 to 186 cm/sec. The required filtration pressure was obtained by means of a lack-pressure valve downstream of the filter pipe. In this arrangement the type of flow existing in the borehole is reasonably well simulated. The dynamic filter apparatus (Figs. I. and 2) consists mainly of two concentric cylinders with a clearance of about 0.5 cm. The outer cylinder (rotor) can be rotated at rates up to 1,000 rpm. The outer surface of the inner cylinder (radius about 2.5 cm) is covered with filter cloth or paper supported by copper gauze. The two cylinders are mounted inside a pressure

Jan 1, 1967

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By B. A. Eaton

The subject of many discussions and technical papers in the last 20 years has been the prediction of the well-bore pressure gradients that are required to induce or extend fractures in subsurface formations. The subject merits this attention because of the frequently recurring problems that arise from an inability to predict fracture pressure gradients. Encountered in several common types of operations in the oil industry are problems associated with the prediction of formation fracture pressure gradients. When wells are being drilled in both new and old fields, lost circulation is often a very troublesome and expensive problem. Complete loss of circulation has been disastrous in some cases. Many times, such disasters could have been avoided if techniques for calculating fracture pressure gradient had been employed in the well plans, and if casing strings had been set, and mud weight plans had been followed accordingly. In areas of abnormally pressured formations, the prediction of fracture gradients during the well-planning stage is extremely important. In fact, it is as important as the prediction of formation pressure gradients, which has received a great deal of attention in recent years. There are several published methods used to determine fracture pressure gradients. However, none of these methods appears to be general enough to be used with much reliability in all areas. In 1957, Hub-bert and Willis published a classical paper that included the development of an equation used to predict the fracture extension pressure gradient in areas of incipient normal fau1ting.l Overburden stress gradient, formation pore pressure gradient and Poisson's ratio of rocks were the independent variables that were shown to control fracture pressure gradient, the dependent variable. In 1967, Matthews and Kelly published another fracture pressure gradient equation that is different from that of Hubbert and Willis in that a variable "matrix stress coefficient" concept was utilized.3 Later the same year, Costley wrote about a similar idea.5 Goldsmith and Wilson used a least-squares curve-fitting technique and field data from the Gulf Coast area to correlate fracture pressure gradient with formation pore pressure gradient and formation depth.' They noted that the fracture pressure gradient increased with increasing depth while the pore pressure gradient remained constant. In each of these cases, the problem for which a solution was sought was to determine the bottom-hole pressure gradient required to initiate or extend a fracture. Results of the previous work show that fracture pressure gradient is a function primarily of overburden stress gradient, pore pressure gradient, and the ratio of horizontal to vertical stress. There is argument for a fourth variable in that in many cases breakdown fracture pressure gradient is greater than the fracture extension pressure gradient. However, if the fracturing fluid is able to penetrate the formation through the pores or existing cracks, there is very little

Jan 1, 1970

By M. R. Annis

Drilling mud rheological and gel property changes due to elevated temperatures frequently cause problems in drilling deep wells. A laboratory investigation of the effects of time, temperatures up to 3001; and mud composition on these properties was made with concentric-cylinder, rotational viscometers of the Farm type. The viscometers were sealed from the atmosphere to prevent dehydration of the sample. Gel strengths were found to be more sensitive than viscosities to changes in temperature and mud cornposition. The high-temperature gel strengths of bentonitic clay drilling fluids were not predictable from low-temper.atl4t-e measurements. At high temperatures, [lie clay flocculates. The floccu-lation temperature depends on the concentration and type of solids in the mud and the degree of chemical defloccula-tion. As the bentonite content of a mud increases, floccrrla-tion temperature decreases. Lignosulfonnte treatment raises the flocculation temperature. To minimize adverse high-temperatrrre effects on mud properties, the mud should be maintainted at minimum solids content, properly treated with. a defloccullant which is stable at the maximum ten?perature encountered and maintained at a pH high enough to insure activation of the deflocculant for the duration required. The Methylene Blue Test for cation exchange cnpacity of a clay was found to be a useful guide in deter.niinirig when a mud contains a dangerously high clay conWnt. INTRODUCTION In drilling a well it is desirable, for several reasons, to know the effects of time and temperature on the rheological and gel properties of the drilling fluid in the hole. Problems associated with drilling fluids normally occur down-hole: so it is reasonable to be interested in the properties of drilling fluids at the conditions which exist down-hole. It has long been observed that high pump pressures are often needed to start circulation after a trip and that the "bottom-up" mud that is circulated back to the surface is usually more viscous than it was before "cooking" at the bottom of the hole for several hours. Burk-hardt' showed that a knowledge of rheological proper-ties of muds under down-hole conditions is necessary to predict pressure surges. He showed that the viscosity of a mud greatly influences the magnitude of pressure surges and the likelihood of lost returns. McLean et aL~ showed that the rheological properties of a mud under down-hole conditions are very important to cementing operations. This paper presents data showing the effects of time and temperature on rheological and gel properties of water-base drilling fluids. Measurements of gel strengths and rheological properties were made with two different concentric-cylinder rotational viscometers of the Fann type. One was the conventional six-speed viscometer modified to operate at temperatures up to 350F and at the vapor pressure of the liquid at test temperature. The other viscometer was newly designed to operate at temperatures up to 500F and pressures up to 1,000 psi. Tests with both instruments were made under essentially the same operating conditions. The new viscometer is shown in Fig. I. In this investigation, great emphasis has been placed on the rheological properties of clay suspensions, since clays are largely responsible for a mud's thixotropic and gel-

By J. B. Cheatham, C. E. Murphey

Presently, computer control of Borobolic direction cannot be obtained during drilling, and most straight-holc drilling methods attempt to resist hole deviation rather than control direction. Many of the theories advanced as possible explanations of the cause of hole deviation are Summarized berein. A new correlation of physical partables is introduced to indicate bow factors such iis drill collar stiffness clearance and hit weight influence borehole deviation, .A methord is proposed for predicting the rate of change of hole angle when drilling conditions are changed. INTRODUCTION Control of borehole direction during drilling can be difficult and costly. Unintentional crooked holes are often lrilleti in dipping formations and many times directional drilling is required when the surface location is not directly above the target area —- for example, at offshore and mountainous locations. Prilllng progress can be greatly hindered in either air or liquid drilling when it be comes necessary to use low bit weight to prevent excessive hole angle build-up. If hole inclination becomes too great, drill pipe drag becomes excessive and fishing risks are increased, logging is more difficult and problems of differential sticking, key seating and fatigue failures may be encountered. Dog-legs and key seats are more serious problems than steep inclination angles: therefore, reducing rate of direction change is preferred to attempting to maintain absolutely vertical holes. Consequently, a straight inclineti hole is preferable to a nearly vertical crooked hole containing numerous dog-legs. In this paper, theories of the cause of hole deviation and analyses of drill string behavior under down-hole conclitions are summarized. Methods for computing hole deviation are presented und systems for resisting deviation as well as neans for provic!ing control of holt- direction are iliscusseI. A new correlation of physical variables is introduced tu indicate how factors such as drill collar stiffness, clearance and bit weight influence borehole deviation. A method is oroposeti for predicting the rate of change of hole anFrle when drilling conditions are clianged. IIEVIEU' OF PREVIOUS WORK ON HOIaE DEVIATION Significant progress in the theoretical analysis of hole deviation problems has been made in the past 1 5 years. The pioneering work has been primarily a result of the efforts of Lubinski and Woods.l-5 In 1950, Lubinski 1 considered the buckling of a drill string in a straig:rt vertical hole, a problem also considered by Willers6 in 1941. It wns concluded that very low bit weights must be used to prevent hole deviation resulting from drill collar buckling. The use of conventional stabilizers was proposed2 in 1951 by Mac Donald and Lubinski as a method for permitting greater Sit weights to he carried without drill collar buckling. These authors pointed out that a 2° nearly vertical spiral hole can cause severe key seatinp, and drill pine near, wilereas n 3 straight inclined hole with deviation all in one direction, while not vertical, will not result in serious drillirig or producing problems. Studies were continued with an investigation of straight inclined holes by Lubinski and Woods3 in 1953. In this paper they concluded that perfectlv vertical holes cannot be drilled even in isotropic forriations unless extremely low bit P-eights are used. .l'l~ey postulated that constant drilling conditions produce holes of constant inclination angle and varying conditions cause the hole to drill at a neiv equilibrium angle. This analysis was not concerned with drill string buckling since it was based on an equilibrium solution in which the ~irill string Was presumed to lie along the lower side of the hole abcrve the point of tangency. Weight of the drill collars below the point of tangency tends to force the hole toyard the vertical, whereas the weight on hit tends to force the hole aurav from the vertica l. The concept of an anisotropic formation Lvas introduced as an empirical method for explaining actual drilling data and as a means for extrapolating known deviation data to otiier conditions of hit

Jan 1, 1967

By C. P. Lawhon, J. P. Simpson, W. M. Evans

Recent efforts to design drilling fluids for increased drifting rates have confirmed some laboratory results of other investigators, but have also produced additional data that should be considered. These data were obtained under controlled test conditions using a microbit drilling machine. Clays and some polymers have previously been reported to cause reduction in drilling rate. Recent data have shown that under laboratory conditions, suspensions of a single day or polymer have sometimes given faster drilling rates than when water was used. Measurements have been made of clay suspensions and polymer suspensions comparing filtration (I) under API conditions, (2) while drilling with temperature of 150F and differential pressure of 1,000 psi and (3) under dynamic conditions after drilling. Some correlation between instanraneous filtration (white drilling) and drilling rate has been observed. INTRODUCTION Several papers have been presented that related drilling fluids to penetration rate. Generally, it was found that a decrease in the solids concentration resulted in significant increases in the drilling rate. Of course, this change also resulted in a decrease in the viscosity of the drilling fluid.' Conclusions from investigations by this laboratory are in agreement. Data have shown that of the simple mud measurements commonly made at the drilling rig (density, plastic viscosity. yield point, API filtrate and total solids), only the density and total solids have a significant relationship to the drilling rate in Berea sandstone when attempting to correlate a single mud property individually.' More recent drilling rate experiments have been designed to study (1) effects of individual clays and polymers on drilling rates in Berea sandstone and Lueders limestone, (2) the relationship between drilling rate and dynamic filtration as measured after drilling and (3) the relationship between drilling rate and dynamic filtration as measured during drilling. Data show that drilling rates are dependent upon type and concentration of particles, type of formation and filtration of the individual fluids while drilling. Mud pressure: pressure of drilling fluid as measured after leaving the drilling chamber (Fig. 1). This is taken to be approximately the mud pressure just past the bit and at the face of the formation. Terrastatic pressure: pressure representing weight of overburden. Formation pressure: pressure of formation fluid as measured at outlet of drilling chamber (Fig. 1). This is taken to be approximately the pressure of fluid in the interstices of the formation. Differential pressure: difference between the mud pressure and formation pressure. LABORATORY EQUIPMENT AND TESTING PROCEDURE The drilling equipment was described in two previous publications."' Main components are a drilling chamber, filter-heater, rotary drive and variable-speed circulating pump. Auxiliary pumps supply pressure boosts for the mud, terrastatic and formation pressures. All equipment is designed for 15,000 psi and 500F. Capacity of the circulating system is approximately 7 gal. The mechanical design was facilitated by moving the rock down onto the bit. Data collected with this design should not differ from that obtained by a normal design where the bit moves into the rock. Drilling fluid is pumped through 50 ft of ID pipe coiled in an oil bath, enters the rotary shaft at a right angle and is pumped through the jets on the bit (Fig. 1). Most of the drilled solids are extracted by a screen mounted in the circulating system on the suction side of the pump. Data reported in this paper were obtained by controlling these parameters: mud pressure, 5,000 psi; formation pressure, 4,000 psi; terrastatic pressure, 5,000 psi; force on bit, 1,000 Ib; formation, Berea sandstone and Lueders limestone; flow rate, 7 gal/rnin; bit, 11/4-in. diameter with two 0.078-in jets; mud temperature. 150F; and rotary speed, 60 rpm. Mud pressure was controlled at 5,000 psi, thus giving a differential pressure of 1,000 psi even though the fluid densities varied. Cores of 3%;-in. diameter and 8 in. long were selected from quarry blocks to provide some control of grain size distribution, permeability and porosity. A 2-in. section was cut off each core and a I -in. diameter plug was taken from this section. Permeability to 5 percent by weight sodium chloride solution was determined and the large cores were

By C. P. Lawhon, J. P. Simpson, W. M. Evans

Data obtained under controlled test conditions using a microbit drilling machine showed that oil emulsified in water muds may either increase or decrease the drilling rate, depending upon drilling conditions. A low-viscosity oil such as diesel fuel can give drilling rates in limestone almost equal to that of water. Data obtained for water emulsified in oil muds showed little decrease in the drilling rate in water-saturated cores as the water percentage of the mud was increased above the 5- to 10-percent range. Changes in drilling rate were found to be dependent upon the oil or water concentration of the mud and upon the type of formation drilled. Changes in static filtration on paper (API filtrate) did not correlate with filtration while the mud was circulated across rock. INTRODUCTION Oil additions to water muds have been reported to increase drilling rates, provide hole stability and improve filtration control. Eckel' showed that water-base emulsion muds used in the West Texas area increased drilling rate with increasing oil concentration up to 15 percent oil by volume, but drilling rate decreased at a concentration of 20 percent by volume. Based on laboratory tests using water muds to drill shale, Cunningham and Goins' reported that drilling rates increased and tendency for the bit to ballup decreased with the addition of oil. Percentage increase in drilling rate varied with the particular formation. They showed oil additions to improve drilling rates ap proximately 75 percent in Vicksburg shale and as much as 150 percent in Miocene shale. Each investigation showed an optimum oil content for the particular formation. Most data that indicated improved filtration control due to oil additions were based on static API Eltrates through paper rather than dynamic filtration through permeable rocks. Some types of dynamic test give a better representation of filtration down-hole while drilling and might be more likely to show some correlation with drilling rate. Static filtration would be important, of course, in relation to hole stability and formation damage. This laboratory's drilling tests, conducted on water-raturated Berea sandstone, indicated that improvements in drilling rate were not evident with increasing oil concentration in water-base muds. Investigation also showed similarity between oil-emulsion (water-in-oil) muds and water-emulsion (oil-in-water) muds while drilling these formations. In Lueders limestone high concentration of water-in-oil muds and high concentration of oil-in-water muds provided the same relative drilling rates. In Berea sandstone there was a large reduction in relative drilling rate with both the oil and water muds that contained low percentages of emulsified fluid. Dynamic filtration rates of water muds on rock did not always decrease with increasing oil percentages even though the static API filtration rates on paper did decrease. Data observed in laboratory drilling of limestone and sandstone indicate that improvements in field drilling operations when water- or oil-emulsion muds are wed may not be the result of increased drilling rates but of improved hole conditions. In some cases, actual drilling rates might be slower but improved hole conditions will result in less total time on the hole. DEFINITIONS Mud pressure—Pressure of drilling fluid as measured after leaving the drilling chamber. This is considered as the approximate mud pressure just past the bit and at the face of the formation. Terrastatic pressure—Pressure representing weight of overburden. Formation pressure—Pressure of formation fluid as measured at outlet of drilling chamber. This is considered as approximate pressure of fluid in the pores of the formation. Differential pressure—Difference between the mud pressure and formation pressure. Relative drilling rate, percent—Drilling rate with experimental fluid divided by drilling rate with water times 100 equals percent. LABORATORY EQUiPMENT AND TESTING PROCEDURES The drilling equipment has been described in previous publications The microbit drill is a closed system (capacity, approximately 7 gal) that can be pressurized to 15.000 psi and heated to 500F. Main components are a drilling chamber, filter-heater, rotary-drive and variable-speed cir-