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The AusIMM/AMIC code for reporting Reserves seeks to improve the calibre of professional reporting on this subject. But have they gone far enough? Should the code appreciate that the degree of reliability of estimates required will vary with the type of mining planned? How does one "confirm continuity" as required by the code? The aim of optimum development drilling is to achieve appropriate ore zone definition for acceptable estimates of reserves and their economic extraction. Can this procedure be in conflict with the code? How does it affect finance decisions?

Jan 1, 1989

By H. C. H. Darley

The principal causes of unstable boreholes* have been known for many years. For example, in a paper published in 1938, Halbouty and Kaldenbachl listed nearly all the classes of troublesome shales that we know today. Much progress has been made since then, but we still have difficulty in identifying the cause of hole problems and consequently in selecting the right technique for combatting them. This subject was discussed at length by Kelly2 in a recent paper and much valuable information was provided. In the Shell Laboratory it was felt that there was a need for a better understanding of the basic mechanisms underlying the various forms of hole instability, and accordingly, a study was undertaken. This entailed reviewing the physics and chemistry of shales, developing tests for characterizing shales, and constructing a model to study borehole stability. Full simulation of underground conditions was not attempted; for example, we used reconstituted shale specimens, and often simple solutions or suspensions rather than practical drilling muds. Such procedures are necessary in order to establish mechanisms, but caution must be exercised in applying the results to the more complex conditions in the field. Part I — Compaction Swelling and Dispersion of Shales Compaction of Sediments Shales are formed by the compaction of sediments. Water is expressed as sediments are buried by subsequent layers, and the degree of compaction is proportional to the depth of burial, provided the water is able to escape easily to permeable formations. The younger sediments, when recovered at the surface, soften and disperse when mixed with water; the older shales have undergone diagenesis (alteration of the clay minerals, secondary cementation, etc.), and remain hard and unaffected by water. In this paper we shall apply the term "shale", as the drilling engineer does, to everything from clays, which are highly reactive to water, to completely lithified materials such as claystones and slates, which are completely inert. However, because these materials behave quite differently when encountered in the drilling well, it is desirable to develop a simple means of characterizing them. The feature that distinguishes the various shales is their dispersibility in water —soft clays disperse readily, harder shales disperse slowly when agitated, the lithified materials will not disperse at all unless milled. In the dispersibility test used in our study, a weighed amount of dry shale particles in the 12-to-100-mesh-size range was placed in a tube filled with distilled water and allowed to soak for 16 hours. The

Jan 1, 1970

By J. L. LeBlanc, R. L. Lewis

This study presents an analysis of annular backpressure variations associated with controlled gas kicks and their pronounced effect on casing .strings and exposed under lying formations. A mathematical model describing the volumetric behavior of an extraneous gas as it is transported from reservoir to .surface conditions under changing temperatures and pressures has been programmed in a Kingston FORTRAN II language for digital computer analysis. The gases under investigation typify Gulf Coast reservoir gases within a 0.6 to 0.7 .specific gravity range. The program output has been substantiated by actual field cases. of gas kicks encountered in Gulf Coart we1l.s. The development of empirical equations for calculating suitable gamy deviation factors for unique temperatures and pressures was incorporated in the program to provide realistic solution.. An output listing of annular backpressures and corresponding equivalent fluid densities resulting at a predetermined critical depth (casing setting depth) and total depth for selected .stages of circulation is provided in a chronological .sequence. Additional information including reservoir pressure and temperature, kill rnrid density, produced gas or surface volume of the expanded gas intro vion, drill pipe and annular volumes can he obtained from the model. This paper illustrates that a precise knowledge of the volumetric behavior of extraneous gases in annular flow and its effect on equivalent fluid densities at a critical depth is significant and should receive .serious consideration in controlling threatened blowouts and in the design of drilling programs. Surface pressures in excess of formation limitations are a threat to zones of lost circula/ion and are potentially injurious to productive intervals. A knowledge of annular backpressure and equivalent fluid density profiles for probable gas kicks aids in a technological accomplishment of drilling programs and provides a .sale tolerance in the event a threatened blowout is encountered. Introduction Drilling operations are frequently interrupted when the drill bit penetrates permeable gas sands with reservoir CtfuJ manuscript was received in Society of Petroleum Engineers ofice Am. 1 1967. Revised manuscript received JuIy 7. 1968. Paper (SPE 1860) kae presented at SPE 42nd Annual Fall Meeting held in Houston. Tex., Oct 1-4, 1967. @ Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineem, Inc. pressures greater than that exerted by the drilling fluid. The differential pressures resulting permit an extraneous influx of gas into the wellbore. A suspension in drilling progress is necessary to restore fluid equilibrium throughout the system. Whether formation gas kicks originate unintentionally or by design, the prospect of a threatened or actual blowout exists and a method assuring a safe and effective well control procedure must be observed. A significant contribution to well control technology was advanced by Records et a1.l in 1962. Using the concept of transmitting a constant equivalent formation pressure at the point of intrusion, Records et al. introduced a calculation technique providing the annular backpressures encountered in a well control environment as a func tion of the volumetric behavior of a 0.6 specific gravity natural gas. In essence, the procedure outlined an annular backpressure schedule in terms of fluid volume circulated at different stages of a well control operation. A number of other publications2-' proposing various techniques for controlling gas intrusions in a wellbore achieve pressure control essentially through maintenance of a constant bottom-hole pressure by surface choke adjustments. The subsequent pressure effects induced in the annulus unfortunately receive little emphasis. Due to the tedious and repetitive nature of annular backpressure computations, a theoretical solution by digital computer is introduced for predicting annular backpressure and equivalent fluid density profiles associated with controlled gas kicks. We point out the effects of volumetric behavior of extraneous gases in annular flow and related field phenomena on equivalent fluid densities at a critical depth. The investigation indicated that equivalent fluid densities at a critical depth are of significance and should receive consideration in the control of threatened blowouts and in the design of drilling programs. Theoretical Considerations The mechanism of vertical gas flow through an annulus is governed by the PVT properties of the fluid, the pressure distribution within the system, the fluid flow rates and the geometry of flow. Due to the numerous variables involved in this type of problem, certain assumptions were imposed in deriving the mathematical model and in establishing the solutions. Two gases, characterized by specific gravities of 0.6 and 0.7, were selected to typify Gulf Coast reservoir fluids. The gas intrustion entered the wellbore as an immiscible 'References given at end of paper. JOURNAL OF PETROLEUM TECHNOLOGY

Jan 1, 1969

By P. F. Gnirk, J. B. Cheatham

The results of combined analytical and experimental studies involving simulated multiple bit-tooth penetration into mck are incorporated into a drilling rate equation for roller-cone bits assuming rather idealized downhole conditions. In particular, it is assumed that the rock behaves statically in a ductile fashion during bit-tooth penetration and that the rock chips are instantaneously removed from the bottom of the drill hole. The general analysis demonstrates an application of plasticity theory for the rock/bit-tooth interaction to the formulation of an upper limit on rotary drilling rate. INTRODUCTION Extensive experimentation involving single and indexed bit-tooth penetration into rock in a confining pressure environment has demonstrated that the chip formation process is of a ductile, or pseudoplastic, nature at sufficiently low differential pressures so as to be of interest in rotary drilling. Coincident with the experimentation, analytical consideration has been given to the theoretical problems of single and indexed bit-tooth penetration into rock. In general, the analyses have assumed that the rock behaves statically in a rigid-plastic fashion and obeys the Mohr-Coulomb yield criterion. The quantitative comparison between experimental and calculated values of bit-tooth load required for chip formation has been remarkably good for a variety of rocks commonly encountered in drilling and at simulated differential pressures as low as 500 to 1,000 psi. Results obtained recently for indexed bit-tooth penetration indicate that the work (or energy) required to produce a unit volume of rock chip can be minimized by a proper combination of bit-tooth spacing and bit-tooth load for a given rock type and differential pressure. By utilizing this information, it is possible to formulate a drilling rate equation, at least in a preliminary fashion, for a roller-cone bit performing under rather idealized downhole conditions. In particular, through the use of characteristic dimensionless quantities pertinent to a roller-cone bit and to indexed bit-tooth penetration, interrelationships among bit weight, rotary speed, rotary power, bit diameter, rock strength and bit-tooth shape and spacing can be explicitly expressed. In the formulation of the equations, however, it is assumed that the rock chips are instantaneously removed from the bottom of the drill hole and- that the rock behaves in a ductile manner during bit-tooth penetration. In addition, the effects of bit-tooth load application and penetration by a yawed tooth at an oblique angle are neglected. Although the analysis is presented in the light of some rather restrictive conditions, it does demonstrate a method of applying fundamental rock/bit-tooth interaction data, obtained by combining the results of analysis and experiment to the formulation of a drilling rate equation for rotary drilling. JNDEXED BIT-TOOTH/ROCK INTERACTION PREVIOUS RESULTS The mechanics of bit-tooth/rock interaction under simulated conditions of borehole environment have been extensively described in a number of papers.l-ll In particular, the effects of differential pressure, mechanical properties of rock, pore fluid, bit-tooth shape and spacing, rate of bit-tooth load application and dynamic filtration below the bit-tooth have been investigated experimentally. From a sequence of experiments.1-4 it was demonstrated that, for dry rock at atmospheric pore pressure, the mode of chip formation exhibits a transition, with increasing confining pressure, from predominantly brittle to predominantly ductile. This transition

Jan 1, 1970

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By C. P. Besse, N. F. LeBlanc

Described in this paper are oceanographic data which should be considered by an offshore design engineer and methods for developing a design wave height from the oceanographic data. The selection of a design wave is predicated on contemplated waves which might affect the site throughout the life of the structure. Selection of a design wave height may be based on (1) arbitrarily established recurrence Frequencies of hurricanes affecting the structure (predicted wave heights are associated with the expected variations of forces resulting from these waves) and (2) a risk-type evaluation wherein all possible storms affecting the area are considered (anticipated wave heights are associated with both investment plus risk costs and expected variations of forces). It is shown how the following oceanographic predictions are integrated into design considerations: (1) a classification of storm intensity which considers all recorded storms which affected the design area, (2) the recurrence interval of storms of a given- intensity (this interval is dependent on the extent of the geographical area considered in the design problem) and (3) a forecast of all wave heights which might affect the area (geometry of a structure often necessitates consideration of waves from a multiplicity of directions). The authors believe that the described techniques can result in selecting an adequate and reasonable design wave. INTRODUCTION Since the inception of offshore operations in the Gulf of Mexico, engineers engaged in designing suuctural facilities have been plagued with the problem of selecting an adequate and reasonable design wave. In the development of any offshore structure it is mandatory that the engineer evaluate the ability of the structure to withstand the ocean waves to which it will be subjected. Selecting such design waves quite naturally necessitates a coalition of the oceanographer and the design engineer. The oceanographer must provide a detailed knowledge of scientific principles which govern the behavior of waters in the Gulf of Mexico. He should also have an adequate knowledge of the manner in which design waves are utilized by the engineer. Although the design engineer's primary responsibility is applying the oceanographer's specialized knowledge in the creation of real structures, it is important that he possess some knowledge of related oceanographic principles to reasonably evaluate and apply the recommendations of the oceanographer. In the Gulf of Mexico it is the hurricane wind waves which generally govern the design of an offshore facility. The oceanographer must therefore develop techniques for predicting the heights, periods and frequency of all hurricane waves which might affect a particular structure. From this mass of oceanographic data, the design engineer must select the design waves which will apply to his particular design. PAST STUDIES ON FREQUENCY AND AMPLITUDE OF HURRICANE WIND WAVES Past oceanographic studies on the frequency of hurricane wave heights in the Gulf of Mexico have been devoted largely to predicting the recurrence interval of hurricanes which will generate maximum significant waves of given heights. The maximum significant wave height is the average height of the highest one third of the waves in that portion of the storm producing maximum wave heights. Since these waves occur over a relatively small portion of the storm (Fig. 1) and since the paths of hurricanes vary considerably (Fig. 2), the recurrence frequency of such heights is largely a function of the extent of the geographical area considered. In establishing the frequency of maximum significant waves for the entire American Gulf coast, the major fully developed hurricanes which affected the coastline from BrOwnsville, Tex., to Key West, Fla., were considered (Fig. 2). These Storms were selected and described by C. L-

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