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By J. B. Cheatham, J. G. Yarbrough

Although adequate removal of cuttings from beneath a drill bit is important for efficient drilling operations, very little basic data are available relative to the fundamentals of chip removal by hydraulic jets. A discussion is presented in this paper of an experimental investigation of the jetting action of hydraulic jets in removing loose particles from the bottom of a cylindrical hole. Conditions for which the jet is no longer capable of removing chips from the bottom of the hole are determined. This situation represents equilibrium between the chip removal force and chip Bolddown forces such as gravity and pressure. In most of the tests loose particles were jetted with water or a water-glycerine mixture to determine the dependence of chip removal on hole size, jet size, height of jet off bottom of hole, flow rate, particle density and fluid viscosity. ,A test with a pressurized mud system indicated that relatively low pressures can completely overcome the removal action of a hydraulic jet. Although the system studied herein is not directly applicable to a rotary drill bit, the work with such simplified systems can provide a better understanding of the chip removal action of jets, and with logical extensions it may provide a reasonable basis for the best use of fluid jets in drilling. INTRODUCTION The primary deterrent to maximum drilling rates is the inability of the drilling system to remove rock cuttings efficiently enough to prevent interference with the drilling action.1-2 The objective of chip removal studies is to permit predicting and controlling removal forces under downhole drilling conditions. Conditions at the bottom of a hole during rotary drilling are exceedingly complex and are not likely to be described in a quantitative way by investigations in terms of the total drilling action until a better understanding is developed of the simplified components of the problem.3 The present study is concerned with the elementary condition of removal of chips by a single central jet. Even this relatively simple model provides mathematical difficulties because of the turbulent nature of the flow from the jet and because of the shape of the bottom of the hole beneath the jet. Theoretical and experimental studies have been made of turbulent jets impinging normally on an infinite body and deductions based on analytical solutions to simplified problems can give some insight into the problem of cutting removal by a jet. However, because of the present lack of understanding of the behavior of the interaction between the fluid jet and the chips being removed, an experimental approach was chosen for the present study. Methods have been developed for maximizing hydraulic horsepower, impact force and jet velocity; but whether maximizing these parameters maximizes chip removal with present drilling bits has not been demonstrated. Simplifying the problem of chip removal may make it possible to develop some understanding of the manner in which the jet velocity is dissipated. Better understanding of a simple case should materially assist in extending analysis to more complicated cases. Thus, we are not concerned in the present study with the rock fracturing process itself but only with the removal of the debris from the bottom of the hole. A problem which is quite similar to the chip removal problem is the suspension of solids in stirred vessels. This problem has been studied by the chemical industry and correlations have been obtained by dimensional analysis which permit the design of mixing vats7 An approach similar to that used in the mixing vat problem is used in the analysis of the jetting data in the present paper. EXPERIMENTAL PROCEDURE The test equipment arrangement shown sche-matically in Fig. 1 allows the jetting action to remove particles until an equilibrium height is attained for each combination of hole size, jet size and flow rate.*** Equilibrium conditions require that the removal force is unable to remove additional particles. This balance between holddown and removal forces implies a relationship between the two forces which is constant for the particular system. When the holddown forces are constant,

Jan 1, 1965

By R. H. McLean

Jet impingement produces two mechanisms to clean the bottom of a borehole during jet-bit drilling operations. One is an impact-pressure wave in the immediate area of jet impingement. The other is crossflow, which spreads across the bottom away from the pressure wave. Measurements of the vertical distribution of the cross-flow at several positions beneath a 4 3/4-in. tricone jet bit in a laboratory model show that the maximum velocity in the crossflow is directly proportional to the square root of the product of the rate of flow and the velocity of the jets through the nozzles (QV). Other measurements in the laboratory model show that gradients in the impact-pressure wave are directly proportional to the jet QV if the diameters of the nozzles are held constant. Consistency of the basic relationships through changes in the Reynolds numbers of the jets from 31,000 to 93,000 suggests that the laboratory results should be representative of typical flow in field operations having higher Reynolds numbers. Estimates of the impact-pressure waves under conditions other than those in the jet-bit model may be made by comparison with a less complex model—impingement of a jet against an unrestricted flat surface normal to the jet. Equations derived from current jet technology describe the wave in this simple system for a wide range of conditions. INTRODUCTION The efficiency of rotary drilling operations is strongly linked to the efficiency with which cuttings are removed. Cuttings remaining on the bottom of the borehole will impede further penetration by the bit until they are removed. Wasteful regrinding is prevented if the fluid circulated past the bit removes cuttings as rapidly as they are made. Most investigations of bottom-hole cleaning under bits have been concerned with the rate-of-penetration effects of bit type, nozzle configuration, fluid properties, pressure gradients and utilization of hydraulic horsepower. These investigations have shown that drilling muds, weighted to keep the pressure in the borehole greater than in adjacent formations and carrying material which forms a filter cake, apparently plaster cuttings against the bottom, making them difficult to remove. In addition to a demonstration of the factors causing poor cleaning, the most significant result of these previous investigations has been the increased use of jet bits accompanied by better hydraulic programs and better selection of drilling fluids. Undoubtedly, these practices have improved bottom-hole cleaning, but rates of penetration when drilling with muds are still often lower than would be expected with perfect cleaning." Although there is general agreement with the concept that increasing hydraulic energy at a jet bit often increases the rate of penetration by improving cleaning, research workers have differed as to the best criterion for evalyating hydraulics. Some lean toward maximizing the product of the rate of flow and the velocity through the nozzles (QV) others prefer to maximize the hydraulic horsepower at the bit;'"-' "till another says that neither criterion is universally suitable."' This controversy shows that conclusive field evidence has not established the superiority of either of these criteria. Analysis of the fluid flow which cleans the bottom should contribute to resolving the controversy. Impinging jets clean the bottom by creating two mechanisms capable of dislodging cuttings. One is the impact from the momentum of the jet and the other is the flaw parallel to the bottom away from the area of impingement. The impact force appears in the form of a pressure wave on the bottom and, in this paper, is called the impact-pressure wave. The flow parallel to the bottom is called crossflow. Fig. 1 illustrates these two mechanisms. This paper describes crossflow and the impact-pressure wave beneath jet bits and relates them to controllable parameters. Through these relations, criteria for use in designing hydraulics to achieve maximum use of the mechanisms of cleaning are derived. PROPERTIES OF CROSSFLOW CONCEPTS DEVELOPED IN PREVIOUS INVESTIGATIONS Concepts of scavenging the bottom by crossflow have been well discussed by Bobo, et al." They examine the means by which crossflow may create forces on cuttings and conclude that the cleaning action of crossflow can be increased by increasing the velocity of the flow stream close to the bottom. Using boundary layer theory, they indicate that a reduction in the viscosity of the drilling

Jan 1, 1965

By A. Lubinski, J. E. Hansford

Jan 1, 1965

By C. D. Hall, F. E. Dollarhide

Conventional static tests of fluid-loss agents do not realistically simulate conditions in a fracturing treatment. The dynamic tests reported here show that fluid-loss volume is better represented as proportional to time, rather than as the square root of time. This leads to a different equation for fracture area. The leak-off rate increases with increasing shear rate at the fracture wall, but appears to approach a limiting value. Pressure effects are minor. Spurt loss ordinarily is not affected by the flow velocity in the fracture and is inversely proportional to concentration of agent. The filter cake, once it is well established, is resistant to damage by the flow of plain fracturing liquid (without fluid-loss agent). The latter two findings indicate that a treatment employing a high-concentration spearhead followed by plain fluid can offer a more economical treatment under suitable conditions. INTRODUCTION The successful design of hydraulic fracturing treatments depends on accurate knowledge of the fluid-loss properties of the fracturing fluid. Howard and Fast,' in giving the basic equation relating fracture area to fluid and treating parameters, described three mechanisms which might control the rate of fluid leak-off from the fracture. One mechanism usually is dominant in a given well treatment. For each mechanism, the leak-off velocity is inversely proportional to the square root of time, and the proportionality constant is designated as the fracturing-fluid coefficient. For the wall-building type of fluid-loss agent, the coefficient is determined by a filtration test in a pressure cell, usually with a rock wafer or core as the filter medium. In these static tests, the cumulative volume generally is proportional to the square root of time, after an initial spurt volume. The static-fluid-loss test is not representative of the con,-&tions under which a fluid-loss agent performs in a fratturing treatment. The marked difference between the dynamic- and static-fluid-loss behavior of drilling fluids reported in the literature2,3 implies that dynamic testing is also needed with fracturing fluids. We have therefore undertaken a study of the dynamic-fluid-loss behavior of fracturing fluids. The testing apparatus has also afforded opportunity to evaluate the resistance of the filter cake to removal or damage by flowing fluid containing no fluid-loss agent, with and without sand. The results of these studies offer a means for more accurate evaluation of fluid-loss agent performance, and point the way to a "spearhead" fracturing technique which may offer more economical treatment for some wells. EXPERIMENTAL METHODS The dynamic-fluid-loss testing method is applicable to any type of wall-building fracturing fluid. The present study aimed first at finding what phenomena are involved, and therefore has been limited in the number of materials tested. All of the results specifically reported herein are for kerosene containing a commercial solid fluid-loss agent, which is commonly used at 50 lb/1,000 gal of oil. Another agent in liquid form, used usually at 20 ga1/1,000 gal oil, has shown all the same phenomena in dynamic tests, and generally the same level of fluid-loss control as the solid agent. The dynamic-fluid-loss core cell used in all tests is shown in Fig. 1. The fracture was simulated by the an-nulus between a 2.03 in. OD sandstone core and the surrounding pipe. Annulus widths of 0.234 and 0.117 in. were used, and the core was 3.5 in. long. The annular geometry provides a uniform fluid velocity and a well-defined shear rate over the entire filtering surface, and permits a large filter area (144 sq cm) in a reasonably compact cell. The leak-off fluid passed into a 0.5 in. diameter axial hole in the core. A hollow steel rod through this hole was threaded into a rounded "streamliner" upstream of the core, and into a mounting stud downstream. The streamliner and the stud had the same outside diameter as the core. In all tests except those where sand was circulated, the mounting stud had protruding rings which constricted the annulus, to minimize any tendency for channeling of the fluid to the side exit port. The ends of the core were sealed by Neoprene, steel and Teflon washers. The leak-off fluid was conducted from the hollow rod to an exit tube, through a metering valve (a fine-pitched needle valve) and a quick-opening toggle valve in series, and into graduated cylinders for volume measurement; Two separate circulating systems were used in the experimental program. The extensive initial testing was done at 50 to 150 Psi. The fluid was circulated by a variable speed Moyno pump, and the flow rate was read by a rota-meter flow meter. The filtration Pressure was supplied by holding a back-pressure with a throttling valve. The discharge streamcould be diverted into any of four sections

Jan 1, 1965

By A. Heim, M. Gondouin

Invasion experiments were run on Berea sandstone cores to get laboratory measurements of resistivity and saturation profiles characteristic of water and oil sands invaded by mud filtrate. Injection rates were as low as 1.13 cm/D, and the cores were 30 to 36 in. long, cut parallel to the bedding planes. In the water-sand case, the resistivity profiles revealed the existence of an extensive transition zone between flushed and uncontaminated zones. In the linear geometry of the experiment, the width of the transition zone increased as the square root of the injected fluid volume. For the oil-sand case the core was prepared by displacing the formation water with kerosene to minimum water saturation. During the subsequent invasion experiment. oil saturation was measured directly by means of an oil-soluble radioactive tracer, and resistivity profiles along the core were taken at the same time. These data were interpreted in terms of an oil-water front, followed by a formation water bank, a zone of mixed waters, and finally, invaded mud filtrate near the borehole. Micro-fingering and capillarity seemed to affect considerably the resistivity profiles observed in the invaded oil-sand experiment. Beyond the regular conductive annulus or "low zone", it was found that a resistive "anti-annulus" could also be formed. As a result of these experiments, some simplified invasion profiles have been accepted and are being used in Grand Slam* interpretations. INTRODUCTION The importance of the mud filtrate-invaded zone in interpreting electrical logs has long been recognized.',* In trying to account for its effect, only very simple models of the resistivity profiles in the radial direction from the borehole have been used. In fact, most log interpretation charts have been based on resistivity models consisiting of two media of uniform resistivity (R, and R,) abruptly separated at the diameter of invasion. Such a clean separation of the media of different resistivities seems unrealistic, since flushing may not be perfect and may vary with radial distance into the formation.3** The nature of the transition zone, when it is within the radius of investigation of the surveying devices, may affect the log readings. Campbell and Martin' verified that a conductive annulus containing a high percentage of formation water may be formed when mud filtrate invades an oil-bearing sand. Interpretations which are to include the effect of such an annulus require the addition to the model of a conductive zone located at the outer rim of the invaded zone.' Using the Buckley-Leverett relations,6 aturation profiles may be derived, from which resistivity profiles can be calculated. Results of such computations by K. S. Kunz and J. H. Moran were given in a paper by Dumanoir. Tixier and Martin,7 and led to the construction of log interpretation charts which were based on a representation with three media of resistivities R, R0 and R1. Fig. 1 shows a schematic representation of a resistivity profile which includes an annulus. Campbell and Martin realized that, during the invasion of an oil sand, both capillarity and mixing would contribute to rounding of the profile shown in Fig. 1. Capillarity tends to draw some of the formation water from the annulus into the uncontaminated (Rt) zone, whereas mixing of the mud filtrate with formation water of the

Jan 1, 1965

By S. J. M. van Leeuwen, R. Feenstra

The effect of jets on bit penetration has been investigated by means of a 50-ton drilling machine and 8½-in. commercial jet bits, drilling under representative bottom-hole conditions. The conclusions apply to the drilling of impermeable rock only. Penetration rate is in all cases primarily hampered by a differential pressure effect, known as dynamic hold-down. Jet action can reduce this slightly. Major gain in penetration rate, up to 25 or 50 per cent, is already ohtained at medium-high jet power. At high bit load, penetration by soft to medium-hard-formation bits is further hampered by bit-balling. Its alleviation requires intensive tooth scavenging, which is best performed by slanted nozzles with trailing, high-velocity, high-volume jets, hitting bottom in front of the teeth. Penetration may then improve by a 100 per cent. At high bit load, bottom-balling limits the penetration of insert-type bits. In this case bottom scavenging is required, which is most effectively performed with high velocity jets from nozzles extended close to bottom. As a result of this measure, penetration may improve 70 per cent in non-friable rock, and less in friable rock. This will make the insert-type bit more versatile. Toothed hard-formation hits suffer at high bit load from both bit- and bottom-balling. Slanted nozzles, possibly much extended, with high-velocity, high-volume jets then have best prospects. INTRODUCTION For years the use of jet bits in oil well drilling has been increasing, in conjunction with ever greater hydraulic horsepower. To the same extent, the need for efficient use of the horsepower has grown.' This paper, it is hoped, will contribute to an understanding of how effective jet action may be obtained. It deals with the effect of jets on phenomena that are known' " to hamper bit penetration. To study this effect, laboratory drilling tests were performed with 8½-in. commercial bits under bottom-hole pressures representative of deep wells. The investigation has been restricted to the drilling of practically impermeable rock. In the following sections, the increase in bit penetration rates due to jetting is discussed for conditions which made the troublesome phenomena stand out one at a time. A brief definition and interpretation of these phenomena is given in Appendix A. Appendix B gives the results of measurements of fluid velocities along the hole bottom, performed in stationary flow tests. Descriptions of equipment, bits, rocks and mud are collected in Appendix C. Unless otherwise mentioned, drilling conditions were kept standard as given in Table 1. CUTTING TRANSPORT TO THE ANNULUS Jet action was for some time believed to merely improve the transport of cuttings from bottom to annulus, resulting in a clean hole bottom. Flow tests performed in 1954 at the Battelle Memorial Institute6 showed, however, that jet velocities of the order of 40 ft/sec sufficed to clear even large (0.4-in.) chips from bottom in the time between two successive tooth actions. In the field, optimum jet velocities are appreciably higher, indicating that other effects must be involved. This much is confirmed by the results of our drilling experiments in soft rocks performed under atmospheric pressure, i.e., in absence of pressure-differential effects. Fig. 1 shows that variation in the nozzle velocity from 40 to 330 ft/sec had no effect on penetration rate, unless the bit penetrated more than 7 mm per revolution, which is about half the tooth height. At such high rates—150 ft/hr at 100 rpm—cuttings would be caught in the tooth cavities, leading to bit-balling, which was noticed on inspection of the bit. The jets thus assisted in keeping the tooth cavities clean. This is just perceptibly reflected in the penetration-rate curves of Fig. 1: Much the same results were obtained in hard rocks with hard-formation three-cone bits. The conclusion is that transport of loose cuttings towards the annulus does not require a powerful jet action. In the following sections we shall see that in deep-well drilling other phenomena are of greater importance. DYNAMIC HOLD-DOWN It is generally accepted that, in deep-well drilling, bit penetration is hampered primarily by the existence of a difference in pressure between the fluid in the hole and that in the rock at the depth of cutting.2-5 In the drilling

Jan 1, 1965

By W. C. Browning

The influence of the hydroxyl factor is more damaging to formations penetrated and causes greater consumption of drilling mud additives than previously realized. This hydroxyl effect on clays is essentially independent of the cations present in the drilling fluid and thus differs from the base exchange reactions that have preoccupied mud chemistry with sodium and calcium bentonite concepts for nearly two decades. The new organic polyelectrolyte-con-ditioned muds haw made it possible to use materials other than sodium hydroxide to maintain the alkalinity of such muds. The properties of silicates, as indicated by their dissociation characteristics and buffering action, are such that they can control he pH and alkalinity of drilling muds at the desired level and, at the same time, minimize undesirable hydroxyl effects associated with sodium hydroxide. This use of silicate compounds is different and distinct from prior applications of silicates as deflocculants or shale preservers. Laboratory and field data presented in this report show that silicate compositions can be utilized to adjust the alkalinity of drilling muds and, at the same time, minimize hydmxyl-promoted clay cleavage. INTRODUCTION Studies for improving the efficiency of rotary drilling techniques must consider the chemistry of drilling fluids and of the formations being penetrated. The chemical aspects of drilling must be studied in conjunction with and in relation to the mechanical factors if, for example, penetration rates are to be optimized. Drilling fluid technology has been largely influenced by chemical reactions of the montmorillonite (bentonite) clay minerals. Most of the literature of mud chemistry concerns the properties of bentonite. Clays of the kaolin or illite type, which are nonswelling, are not generally regarded as sources of drilling mud problems. If these nonswelling shale clays are considered, they are commonly regarded as inert solids. Particularly noteworthy is the fact that the relation of surface and colloid chemistry to massive shale bodies has received only scant attention from drilling technologists. Clay studies reported in the drilling mud literature have dealt, for the most part, with the properties of clays in a finely divided state, and often in very dilute suspensions. Yet frequently during drilling, shale problems not related to the rheology of clay suspensions develop in massive non-bentonitic shale sections of zero or near zero permeability. This paper is concerned with surface chemical reactions that can influence the behavior of these non-bentonite clay masses in such a manner as to adversely affect drilling operations. Browning and Perricone1,2 have pointed out that some of the most troublesome shales to drill, such as the Atoka, contain no montmorillonites. They also pointed out that mud problems can frequently be mitigated by reduction of clay cleavage achieved by using drilling fluids with a minimum of available hydroxyl ions. If pronounced clay cleavage occurs during drilling, the borehole may soften, increasing the possibility of sloughing. In addition, the resulting increased incorporation of high-surface-area clay solids into the mud system can reduce penetration rates and necessitate greater chemical treatment. This increase of shale, of colloidal or near-colloidal dimensions, into the drilling mud is due to clay aggregate cleavage and not to base exchange or swelling reactions, such as occur with bentonites. Searle and Grimshaw3 point out the difference between cleavage or slaking reactions of nonswelling clays (such as illite and kaolinite) and the swelling of bentonite. They further state that the speed of slaking is increased in alkaline water. Eitel1 cites Salmang and Becker, who recognized that clay surface reactions impart plasticity and workability to clay masses. Their results clearly show that all liquids which contain hydroxyl groups in their molecules favor the workability of clays. The ancient technique of aging clays in the moist condition to increase their "workability" is evidence that these clay cleavage phenomena are of considerable importance. The same hydration cleavage that occurs during the aging of nonswelling clays for ceramic use also acts to break up cuttings and soften the borehole during drilling operations. The mechanism of cleavage of the crystalline aggregates of illitic, kaolinitic and other nonswelling clays; and the chemical means of controlling this cleavage are therefore of considerable significance to the drilling mud chemistry. Inasmuch as there is little reference in the drilling mud literature to the cleavage reactions of nonswelling clays, the structure of these clays and certain properties that relate to the mechanism of clay cleavage will be reviewed briefly. STRUCTURE OF NONSWELLING CLAYS Clays such as kaolinite, illite and montmorillonite are compmed of alternate layers of (1) silicon-oxygen tetra-

Jan 1, 1965

By Robert S. Mayo

My subject today is "Drilling-and-Blasting of Small Rock Tunnels". I am sure that there will be some people, primarily college students but perhaps Consulting Engineers, who will say: "Drilling-and-Blasting? I thought that went out with the invention of the Tunnel Boring Machine". A few years ago I talked to Dick Robbins and he told me that they did not try to sell a "Robbin's Mole" unless the tunnel was two miles long. For easy calculations I use 10,000-ft. (3km) A Mole today costs about $2 million which works out to $200 per lineal foot. This is "front money". You cannot place the order unless you are the uncontested low-bidder and then you must wait at least six months for delivery. Of course you can use that time to square up your portals, ready to turn-the-eye, or maybe you have shafts to sink to reach the tunnel grade. But this is "dead-time" and it is a heck of a feeling to have a job and cannot get started on it until you get the Mole. I do not have the American figures on lengths of tunnels but there was an article a few years ago in a British magazine: NEW CIVIL ENGINEER, on this subject. This stated that 75% of the jobs in Britain which were bid were for small tunnels, 10-ft x 10-ft (3m x 3m) or smaller, and that they were less than 5,000-ft (1.5km) in length. This does not mean that 75% of the footage in Britain was less than 10-ft in diameter. It means that 75% of the jobs being bid were less than a mile in length. From my experience in the U.S. I believe that we have substantially the same ratio: so many of the jobs with which I was associated were short, 1,000-ft, 2,000-ft and sometimes 3,000-ft and the bores

Jan 1, 1981

By R. F. Burdyn

The inadequate use of centrifugation to economically recover solids from weighted drilling fluids reflects the need for better equipment and techniques for this putpose. Laboratory studies in the development of an improved separator are described in which an operating equation is derived and tested. Results show that the concentric cylinder geometry employed effectively separates bnrite from a suspension and that the operating equation provides a good approxinmtion for scale-up. INTRODUCTION Our current drilling technology frequently requires a high-density drilling fluid obtained by addition of barite. In the course of drilling, formation solids which are too fine to be removed either by screening or settling become suspended in the drilling fluid and gradually the volume of solids in the mud increases. The volume fraction of solids must be limited (if a satisfactory set of rheological parameters are to be maintained). A centrifugal separatorprovidesan economical way of accomplishing this. The barite recovery process can be considered as a separation of two solids. One, the light solids, composed of formation and added solids, has a specific gravity of 2.6 to 2.7; the other, barite, has a specific gravity of 4.2 to 4.3. This density difference, plus the fact that the average light-solids particle size is much smaller than the average barite particle size, permits separation by a centrifuge. In drilling fluids some of the coarse particles of the light-solids-range will settle faster than fine particles of the barite-particle range. As a result a complete separation of the two species is not possible. since the object of the process is not merely recovering the maximum amount of barite but includes as well removing the maximum amount of light solids, an optimum barite recovery efficiency exists. From a practical standpoint this optimum cannot be determined in the field for each drilling fluid system, and in practice the separation is less than optimum, with some sacrifice of barite. Drilling technology has included centrifugal separators for barite recovery for more than a decade. Results have been reported by a number of investigators indicating that the process is practical and economica1. l-4 The decision to use a centrifuge is based on economics in which direct cost savings and the indirect benefits in rig time derived from improvement of the drilling fluid are important factors. One would expect that centrifugal separation of barite from drilling fluids would significantly affect barite consumption; however, this is not the case. The Minerals Yearbook shows an annual domestic barite consumption in the drilling industry of nearly 1 million tons.5 By rough estimate there are perhaps 80 separators presently in field use. Assuming half of these in use at any one time, operating an average of four hours per day, at recovery rates averaging 3,000 Ib of barite per hour, total annual recovery is about 90,000 tons. This is less than 10 per cent of he total barite used. I conservatively estimate that barite consumption in drilling operations can be reduced by 30 per cent through greater utilization of centrifugal separators. To encourage more widespread acceptance of centrifugal separators in the drilling industry, improved equipment and techniques would be very desirable. The present paper, covering theory and results obtained from a laboratory model, is the first in a series on he development of an improved mud separator for field use. THE CONCENTRIC CYLINDER GEOMETRY AS A SEPARATING DEVICE Consider the geometry shown in Fig. 1, consisting of two concentric cylinders separated by an annular space. These are arranged so that the outer cylinder is fixed and the inner one can be rotated about its axis on shafts sealed against the ends of the outer cylinder. If the outer cylinder is fitted with openings at either end, the inner

Jan 1, 1966

By D. E. Hawk, R. F. Burdyn, F. D. Patchen

Earlier work on a mud separator for barite recovery is extended to the design and construct ion of a rugged field unit. Problems associated with scale-up for field use include the me of dilution water and its effect on capacity, power requirements and pressures developed. Equations for these quantities are derived and applied in maximizing the beneficial effects of dilution and minimizing the power required. Tests on the full-size rotor show that its performance can be predicted by theory. The completed unit is compact and lighter than current decanting types. Its capacity is from 10 to 22 gal/min with corresponding barite recovery efficiencies of 92 to 86 per cent. INTRODUC'TION In an earlier publication a new type of centrifugal device was described for solid-liquid separations.l In that paper an operating equation was derived, and its validity demonstrated in laboratory scale experimentation. Some of the features apparent in this new device seem particularly well suited to the conservation of barite in field drilling-mud systems, hence the development was extended to the design and construction of a field unit. In the present paper the design problems associated with scale-up are considered. A full-scale, rugged self-contained field unit is described, and test results discussed which verify that the performance of the large field unit can be described by a simple operating equation. PRINCIPLE OF OPERATION OF SEPARATOR In principle, the new device is simply a perforated cylinder rotating within a body of fluid which is contained within a stationary case, as in Fig. 1. The frictional drag generated by the rotating cylinder causes part of the fluid to rotate. At the surface of the cylinder, assuming no slip occurs, the angular velocity of fluid and of the cylinder are identical. If there are suspended particles present of greater density than the fluid, the centrifugal force acting on these particles causes them to move radially away from the cylinder at some velocity vp . Where the Stokes settling equation holds, this velocity may be expressed as:2 d2 ?p rw2 If the case is provided with openings at both ends, a suspension can be pumped in at one end at a fixed rate. Part of the suspension can then be removed at a fixed rate at the other end of the case as underflow, and the remainder forced through the perforations and hollow shaft of the rotor to appear as effluent, also at a fixed rate. The radial component of the flow velocity of this stream as it reaches the rotor surface, is simply effluent flow rate divided by cylindrical surface area: Because up is a function of particle size, for some particular particle size, the velocities vp and v, will be equal in magnitude. This is defined as the critical particle size and represents the size above which all particles appear in the underflow and below which all particles appear in the effluent. For this equilibrium condition at the rotor surface, Eqs. 1 and 2 combined give

Jan 1, 1966

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

Single bit-tooth penetration experiments under static load were conducted on six rocks at confining pressures of O to 5,000 psi using sharp wedge-shaped teeth with included angles ranging from 30 to 120° In general, the force-displacement curves for all rocks exhibit an increasingly nonlinear and discontinuous behavior with decreasing confining pressure. The confining pressure at which a rock exhibits a macroscopic transition from predominantly ductile to predominantly brittle behavior during penetration vmies from about 500 to 1,000 psi for the limestones to greater than 5,000 psi for dolomite. The correlation between calculated values of force per unit penetration based on plasticity theory and experimental values is quite encouraging, even at confining pressures as low as 1,000 psi A qualitative correlation between volume of fragmented rock per unit energy input for a single bit-tooth and drilling rate for microbits appears to exist over a confining pressure range of 0 to 5,000 psi. INTRODUCTION Laboratory experiments utilizing a small-scale drilling apparatus have demonstrated that penetration rates are reduced considerably as a result of increasing the confining pressure from atmospheric to a few thousand psi?-3 This undesirable situation can, in general, be attributed to a combination of decreased efficiency of chip removal at the bottom of the borehole, increased rock-failure strength, and a possible change in the mechanism of chip generation and rock fragmentation with increasing confining pressure. To more fully understand the principles underlying the last circumstance, it is the purpose of this investigation to experimentally study the mechanism of single bit-tooth penetration into dry rock at low confining pressures and, in particular, to establish the confining pressure at which the penetration mechanism may undergo a brittle to ductile transition for various rock types commonly encountered in drilling. Confining pressure as used here refers to the differential pressure between the borehole fluid pressure and the formation-pore fluid pressure. EXPERIMENTAL PROCEDURE Using an experimental apparatus previously described: a single, sharp wedge-shaped tool was forced under a "statically" applied load into an effectively semi-in finite dry rock sample subjected to a prescribed confining pressure. To prevent the invasion of the con fining-pressure fluid into the pores of the rock sample during penetration, the exposed surface of the rock was jacketed with a layer of silicon putty.* Electrical instrumentation incorporated into the apparatus yielded a graphical plot of force on the tool as a function of penetration or displacement of the tool into the rock during an experiment. During the course of the experimentation the following conditions were maintained constant: (1) pore pressure — atmospheric (i.e., the rock was dry); (2) temperature — 75F; (3) rate of loading — essentially static (approximately 0.002 in./sec); (4) bit tooth — a sharp wedge-shaped tool loaded normal to the rock surface; (5) rock surface — smooth and flat; (6) drilling fluid — hydraulic oil; and (7) maximum depth of penetration — approximateiy 0.1 in. In addition, each experiment was performed on a different rock sample so the rock surface is free of a layer of cuttings and of any previous indentation craters. The influence of the corners of a borehole was neglected, since each rock sample was cemented inta a section of aLuminum tubing to simulate a semi-infinite body. Indentation experiments were made on a sandstone, two limestones, a marble, a dolomite and a schist with a 60' bit-tooth over a range of confining pressures from atmospheric to 5,000 psi and at a constant confining pressure of 1,000 psi for a variety of bit-teeth with angles ranging from 30 to

Jan 1, 1966

By H. Matlock

Beam-columns with continuous or discontinuous transverse and angular loads and elastic restraints are represented mathematically in a manner corresponding to finite-element mechanical models. Solutions for linearly elastic cases are accomplished by direct recursion-equation elimination of unknowns, and for cases involving nonlinear loads and supports, by repeated trial-and-adjustment of complete elastic-type solutions. Five practical applications are presented by which various capabilities of the general method are illustrated. The examples include simulation of a pipeline launching and the bending and collapse of a conductor pipe in deep-water drilling operations. INTRODUCTION The diversified and complex operations being conducted in support of the production of offshore oil have produced a wide variety of new problems in structural mechanics. Many of these problems cannot be solved by conventional analytical or experimental approaches and have therefore stimulated inquiry into new methods of solution. It is the purpose of this paper to give a brief description of an analytical method for solving nonlinear beam-column problems and to illustrate the generality of the method by applying it to several problems related to offshore operations. Although the data for all of the examples are artificial, the cases discussed will be recognized as being based on actual situations. DESCRIPTION OF METHOD The analytical approach which is to be described stems from research on offshore foundations, in particular, the study of lateral-load behavior of foundation piles. The method represents a generalization of a technique which was suggested by Gleser' and extended by Focht and McClelland2 and Reese and Matlock." To maintain generality and therefore versatility in the method, a considerable variety of input data is considered. Fig. 1 illustrates the various types of loads and restraints which might be applied to a short segment of a beam. Each of the terms illustrated in the figure is shown acting in a positive sense. Capital letters are used to designate concentrated quantities whereas the corresponding lower-case symbols indicate effects which are distributed in some way along the length of the beam. The transverse loads and the elastic restraints may be divided into two classes: (1) loads Q and q and springs S and s, which act normal to the axis of the beam, and (2) couples T and t and rotational springs R and r, which act in an angular sense. In addition, there is an axial force P which may be constant or may vary along the length of the beam. The bending stiffness of the beam (the product EI of the modulus of elasticity and the moment of inertia) is designated by the symbol F. The assumptions of conventional elementary beam theory provide the basis for the present method. Among these are the neglect of shearing and axial deformations and the limiting of consideration to straight beams of symmetrical cross-section. Lateral deflections are considered to be small compared to original dimensions. A deformed element of such a beam is shown in Fig. 2a. The curvature of the beam is approximated by the second derivative of the deflection y with respect to distance x along the beam. It is assumed that the material of the beam is linearly elastic and therefore the relation of Eq. 1 between curvature and bending moment M is the ordinary expression from elementary beam theory. A generalized beam element is shown in Fig. 2b. The element has been deflected in a positive direction by an amount y and tilted through a small positive angle dy/dx. The various loads and elastic restraint reactions are detailed in the figure. Temporarily, only distributed effects are considered; provision for concentrated loads and restraints will be made subsequently. Eq. 2 in Fig. 2b is obtained by summing the forces and moments acting on

By W. C. Maurer

A study of bit-tooth penetration, or crater forniation. under simulated borehole condirions has been made. Pressure conditions existing when drilling with air, water and mud have been sirnulated for depths of 0 to 20.000 ft. These crater tests showed that a threshold bit-tooth force must he exceeded before a crater is .formed. This thresh old force increased with both tooth dullness and diflerenrial pressure between the borehole and formalion fluids. At low differential pressures, the craters formed in a brittle manner and the cuttings were easily removed. At high differenlial pressures, the cunings were firmly held in the craters and the craters were formed by a pseudoplas-tic mechanism. With constant farce of 6,500 16 applied to the bit reeth, an increase in differential pressure (sitnulated mud drilling) from 0 to 5,000 psi reduced the crater volumes by 90 per cent. A comparable increase in hydrostatic fluid pressure (simulated water drilling) produced only a 50 per cent decrease in volutne while changes in overburden pressure (simulated air drilling) had no detectable effect on crater volume. Crater tests in unconsolidated sand subjected to differential pressure showed that high friction was present in the sand at high pressures. Similar friction belween the cuttings in craters produces the transition from brittle to pseudo plastic craters. INTRODUCTION The number of wells drilled below 15,000 ft increased from 5 in 1950 to 308 in 1964. Associated with these deep wells are low drilling rates and high costs. High bottom-hole pressures produce low drilling rates by increasing rock strength and by creating bottom-hole cleaning problems. This paper describes an experimental investigation of crater formation under bottom-hole conditions simulating air, water and mud drilling. Although numerous investigators have studied bit-tooth penetration (cratering) at atmospheric pressure conditions, only limited work has been done on cratering in rocks subjected to pressures existing in oil wells. Payne and Chippendale2 have studied cratering in rocks subjected to hydrostatic pressure using spherical penetrators. Garner et aLJ conducted crater tests in dry limestone by varying overburden pressure and borehole fluid pressure independently and using atmospheric formation-fluid pressure Gnirk and Cheathem4,5 have studied crater formation in several dry rocks subjected to equal overburden and borehole pressure and atmospheric formotion pressure. Podio and Gray studied the effect of pore fluid viscosity on crater formation using atmospheric borehole and formation-fluid pressurc and varying overburden pressure. Although these studies have provided useful information on crater formation under pressure, they were limited in that the three bottom-hole pressures could not be varied independently and, therefore, that many drilling conditions could not be simulated. The prersure chamber used in this study allowed visual observation of the cratering mechanism and independent control of the borehole, formation and confining pressures. By using different fluids in the chamber, pressure conditions existing in air, water and mud drilling to depths of 20,000 ft were simulated. The mechanisms involved in cratering at these different pressure conditions were studied for teeth of varying dullness and at different loadins rates. High-speed movies (8,000 frames/sec) and closed-circuit television were used to visually study the crater mechanism under pressure. EXPERIMENTAT PROCEDURE PRESSURE CHAMBER The Pressure chamber in Fig. I was used to simulate bottom-hole pressure conditions. This chamber has been pressure-tested to 22,500 psi and is normally operated at pressures up to 15,000 psi. The chamber contains four lucite windows' used for illuminating and observing the crater mechanism under pressurc. A closed-circuit television and a Fastax camera (8,000 frames/sec) have been used in these studies. Cylindrical rock specimens (8-in. diameter X 6-in. long) were subjected to three independently controlled pressures simulating overburden, borehole fluid and formation-fluid pressures. Overburden pressure, which corresponds to the stress induced by the overlying earth mass, was applied by exerting fluid pressure against a rubber sleeve surrounding the rock. Borehole pressure, which is the pressure exerted by the column of mud in the wellbore, was simulated by applying pressure to the fluid overlying the rock in the chamber. Formation pressure was simulated by applying pressure to the water saturating the rock. The borehole and formation pressures were equal except when mud was used in the chamber, in which case the differential pressure between these fluids acted across the mud filter cake.

Jan 1, 1966

By H. A. Kendall, W. C. Goins

Several investigations in recent years have shown that drilling rates are increased significantly with increased hydraulic horsepower. But, there has been no over-all method of designing jet-bit programs that efficiently uses the surface power. A study of present practices indicates that frequently as little as 50 per cent of the possible effects at the bit are used. Some observers have indicated that the best utilization of hydraulic horsepower (maximum effect on drilling rate) occurs when the bit hydraulic horsepower is maximum; others have stated that jet impact force is more important, and others have believed that maximum jet velocity is required. Limited efforts to date have shown some optimum conditions for bit hydraulic horsepower and impact, but these conditions cannot exist during drilling of a large part of the hole and do not provide a basis for designing a complete jet-bit program. This paper shows the maximum obtainable bit horsepower, impact force and jet velocity at all depths, taking into account the limitations of the pump, piping, hole and minimum circulating rate for adequate cuttings removal. Ranges of operation are developed; and flow rates, surface pressure and bit pressures are specified for each range to provide a maximum of any one of the desired effects. It also is shown that, by proper selection of nozzle sizes and by following the rules presented, the maximum obtainable quantities can be effectively utilized from surface to total depth. Finally, a simple graphical method of selecting nozzle sizes and flow rates is presented which can be used with familiar bit-company hydraulic tables and calculators to design jet-bit programs for maximum bit hydraulic horsepower, impact or jet velocity, as desired. These programs make most effective use of the pumps. Heretofore, there was no method available for designing field tests which adequately separated the effects of bit horsepower, impact and jet velocity. The programs and procedures developed in the paper are dissimilar and, when used in future field testing, should demonstrate which program is the most important in obtaining the fastest drilling rate. INTRODUCTION During the past decade, rig hydraulics has come into increasing prominence. There has been a definite trend toward providing higher horsepower pumps, jet-type bits have had increased use, numerous investigators"" have reported increased drilling rates as a result of increased hydraulics, and bit manufacturers have provided tablesa-" and calculators that are now commonly used 10 design jet-bit programs. Opinion has varied as to the hydraulic quantity which has the great- est effect on drilling rate. Papers and data have been presented that show pump horsepower,'9 it hydraulic horsepower and jet impact force,' each to be the most significant factor affecting drilling rate. Examinatibn of jet-bit programs of the bit companies indicates emphasis on jet velocity. Only pump horsepower can be eliminated because it can be used to produce any one of the bit effects which, a priori, must be more relevant factors. This contradictory state of opinion and practice regarding the bit effects is unfortunate, but several published references have been concerned with making one or another of the factors maximum; and, because these in each case have given results applicable to only intervals of the hole drilled, there seems to be ample reason to complete the previous efforts. It also is believed that the differences in programs for each effect, where they exist, should be delineated so that future use may determine which hydraulic effect is the more relevant. It is the purpose of this paper to: (1) show the theoretical maximum bit hydraulic horsepower, jet impact force and jet velocity available at all depths, taking into consideration all necessary restrictions on operating conditions; (2) illustrate procedures by which the maximum available horsepower, impact force or veIocity may be obtained; and (3) present a graphical method for rapid selection of jet-nozzle sizes and flow rates to be used with conventional procedures to design jet-bit programs for maximum bit horsepower, impact force or velocity as desired.

By H. C. H. Darley

The influence of particle size and concentration on the development of chip hold-down pressure (CHDP) was studied in an apparatus designed to measure the change of filtration rate during the first second of the filtration process. CHDP is controlled by the "bridging" particles (i.e., particles in the 50 to 0.2 micron range), whereas filter loss is controlled by the colloid fraction. The results indicated that a fast drilling fluid with a low filter loss could be obtained if the concentration of bridging solids and the viscosity were kept very low. A novel group of drilling fluids, which we have named colloid emulsions, was developed to meet the above requirements. These colloid emulsions are made by dispersing art oleophilic colloid in oil and emulsifying about 5 per cent of this dispersion in water or a dense brine. Good results have been obtained in field trials with emulsions which use asphalt as the oleophilic colloid. INTRODUCTION In recent years it has been found that fast rates of penetration can be maintained in hard formations by using "clear" water as a drilling fluid. In some cases, however, water cannot be used because the very high down-hole filter loss creates various difficulties in drilling, in logging, or in producing the well. It then becomes necessary to "mud up", which results in a decrease in drilling rate. The reason that mud decreases drilling rates is a complex subject which has been well covered by such authors as Garnier and van Lingen, Cunningham and Eenink,' and van Lingen.3 One of the principal factors involved is the tendency of the drilling fluid to develop a filter cake on the bottom of the hole. The pressure differential which develops across this filter cake opposes the action of the bit in dislodging chips from the rock. This pressure differential is referred to by Garnier and van Lingen' as the chip hold-down pressure, which is denoted by the initials CHDP in this paper. The work described in this paper was undertaken to develop a drilling fluid which would minimize CHDP but which would still have a low filter loss—in other words, a fluid which would deposit a filter cake on the sides but would lay little or no filter cake on the bottom of the hole. EVALUATION OF CHDP EXPERIMENTAL Conditions governing the growth of filter cake on the sides of the hole are obviously different from those on the bottom of the hole. On the sides of the hole, cake will form continuously but at a decreasing rate, until eventually the rate of growth will equal the rate of cake erosion by the mud stream.' On the bottom of the hole, each time a bit tooth dislodges a chip the cake is removed, a fresh rock surface is exposed, and the filtration process must start over again. Thus the CHDP is determined by the amount of cake which can form in the interval between successive tooth strikes at a particular spot, normally a fraction of a second. Our first step therefore was to study filtration rates over the first second or so of the filtration process. These tests were conducted in the simple type of dynamic filter cell shown in Figs. 1 and 2. In this cell the mud was filtered through a train of rock cores while rotating blades kept the mud flowing over the surface of the core. The procedure was to evacuate the cores to 0.05 mm of mercury, saturate with brine, and assemble in the holder under brine. The permeability of the core train was then determined. A plastic seal was placed on the face of the core train, and a rip cord was attached from the seal to one of the blades. At the start of the test, 500 psi was applied to the mud, and the meniscus in the capillary measuring tube was adjusted to zero. When the blades were started, t,he seal was ripped from the face of the core, and filtration began. The filtration rate was at first measured by photographing the advance of the meniscus in the capillary tube. Using

Jan 1, 1966

By E. I. Radzinovsky, D. W. Dareing

This paper presents theory which is used to predict rock-bit bearing life reduction due to simple harmonic variations in bit forces. The theory is based on the premise that if a constant load acts for a certain fraction of the life which the bearing would have if that constant load were applied for its entire life, then the same fraction of thelife of the bearing is consumed. Total bearing life is related to simple harmonic variations in bearing life associated with instantaneous bearing loads. The results show that rock bit bearing life is not affected appreciably by forces commonly impressed upon a bit, but it is affecied appreciably by relatively large dynamic bit forces occasionally encountered during drilling. In addition, the results show that the life of sealed bearings is more sensitive to bit force variations than is the life of unsealed bearings. INTRODUCTION Roller bearings are important components in roller cone rock bits because they transmit a large portion of the drill collar weight to the formation being drilled. Unfortunately, they have a relatively short life under down-hole drilling conditions. Roller bearings are usually the first bit components to fail, and their failure leads immediately to failure of the entire bit. Short roller bearing life, and thus short bit life, is due mainly to high unit loads transmitted by the bit and to the adverse environment in which the bearings operate. The results of the study discussed in this report show how dynamic bit forces also affect roller bearing life. The purpose of this paper is to discuss theory developed to predict the effect of different magnitudes of periodic bit forces on roller bearing life. Theoretical results are used to compare the life of rock bit roller bearings subjected to steady forces to the life of rock bit roller bearings subjected to unsteady forces similar to the type of unsteady forces measured at the bit with a special downhole recording instrument. BACKGROUND AIanufacturers of bearings have conducted laboratory tests which show how bearing life is affected by steady bearing load. 1 The well-known empirical equation which defines bearing life follows from bearing test data. It is: where L = bearing life, hr P = bearing load, Ib C = constant q = exponent (constant). The effect of environment on bearing performance is manifested through the exponent q and the constant, C. King,2 in similar tests conducted on roller bearings used in rock bits, showed that, in addition to the load, the environment (abrasive materials, chemical components, etc.) greatly affects bearing life. His data, which show how the life of roller bearings in a 7-7/8-in. W7R bit rotating at 60 rpm is affected by bit weight and fluid environment, are displayed on a log-log plot by broken lines made up of straight line segments. Each broken line corresponds to a given environment. One segment (q = 1.4) of the broken line corresponding to a fluid environment of barite mud is shown in Fig. 1 along

Jan 1, 1966

By L. W. Legerwood

During the past three decades, the oil industry has expended increasing eflorts seeking improved drilling tools or systems to reduce drilling costs. The total cost of these efforts is unknown, but it certainly amounts 10 tens of millions of dollars. Most of the "new" system that past and present investigators have sought to develop actually are old public information. In seeking to implement new-systern concepts, investigators have tested the following: impact at frequencies ranging from 6 to 300 cycles per second; electrical, mechanical and hydraulic meam of actuating percussors; bit rotary speeds up to 2,000 rpm; electric and hydraulic bottom-hole means of rotating bits; bottom-hole machines with power outputs up to 400 hp; shock waves; explosives; high-velocity pellets; flame; arc; grinding wheels; abrasive jets; erosion by high-velocity gases; chemical attack; electric current; magnetic waves; retractable rock bits; reelable drill pipe; continuous coring with reverse circulation; and automation of drilling rigs. Table I shows how these investigations are grouped for discussion purposes in this paper. In spite of these efforts to discover new and improved systems, rotary drilling main;aim its economic leadership. Undoubtedly, rotary drilling costs will continue to be reduced by rigid application of the best available technology and by development of new rotary technology. In view of the extensive past development programs, however, significant long-range improvement appears to be a research, not a development problem. Research must postulate and prove theories and principles governing variour subsurface rock-failure processes pertinent to both rotary and new systems. Ah, research must produce physical and engineering data relative to these processes. When such information is available, earth boring will graduate from an art to a science. Major improvements in rotary drilling can then be expected, and the systematic evolution of an improved drilling method can be initiated—with a strong probability for success. Development of drilling methods other than rotary drilling has been one approach investigated by the industry as a means for reducing drilling costs. Major cost-reduction efforts, however, have been centered on engineering development work aimed at incremental improvements in rotary drilling. A relatively minor effort has been expended to establish basic physical principles and engineering data pertaining to the earth-boring process which can serve as a foundation for the development of cost-cutting drilling hardware. Current oil-industry economic trends have added impetus to the need for effective programs to reduce drilling costs. However, areas for expanded future efforts should be selected only after careful study of past investigations. It is the purpose of this paper to review past and Dresent industry efforts to develop new drilling tools or systems and to suggest areas where additional science is needed. Past reviews of drilling methods have been limited to a few processes prominent at the time the reviews were made. This paper seeks to present a concise, well organized review of all methods that have received actual development or test work. The preparation of a paper seeking to review all past developments is fraught with many difficulties, not the least of which are errors in or obsolesence of printed matter used as source material and the lack of data on industry developments which have not been published. Since de-

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By C. E. Hottman, R. K. Johnson

Fluid pressure within the pore space of shales can be determined by using data obtained from both acoustic and resistivity logs. The method involves establishing relationships between the common logarithm of shale transit time or shale resistivity and depth for hydrostatic-pres-sure formations. On a plot of transit time vs depth, a linear relationship is generally observed, whereas on a plot of resistivity vs depth, a nonlinear trend exists. Divergence of observed transit time or resistivity values from those obtained from established normal compaction trends rinder hydrostatic pressure conditions is a measure of the pore fluid pressure in the shale and, thus, in adjacent isolated permeable formations. This relationship has been empirically established with actual pressure measurements in adjacent permeable formations. The use of these data and this method permits the interpretation of fluid pres.rure from acoustic and resistivity measurements with an accuracy of approximately 0.04 psilft, or about 400 psi at 10,000 ft. The standard deviation for the resistivity method is 0.022 psi/ft, and for the acoustic method 0.020 psi/ft. Knowledge of the first occurrence of overpressures, and of the precise pressure-depth relationship in a geologic province, enab1es improvements in drilling techniques, casing progroms, completion methods and reservoir evalzmtions. INTRODUCTION CENKRAL STATEMENT Operators engaged in the search for and production of hydrocarbon reserves in Tertiary basins are more and more frequently confronted with complications associated with over pressured (abnormally high fluid pressure) formations. This is particularly true in the Texas-Louisiana Gulf Coast area. The problems associated with these formations are of direct concern to the combined activities of all phases of operations, i.e., geophysical, drilling, geological and petroleum engineering.' - Knowledge of the pressure distribution of a given area of operations would greatly reduce the magnitude of many of these complexities and in some cases would completely eliminate specific problems. his pape; presents techniques developed for estimating formation pressures from interpretations of acoustic and electric log data. Specifically: the acoustical and electrical properties of shales, reflected by conventional acoustic and electrical surveys, can be used to infer certain reservoir properties, such as formation pressure, at any level in a well. It has been possible to develop these techniques because of a firm understanding of the basic principles that govern and apply to such overpressured provinces. NORMAL PRESSUKES Normal pressures refer to formation pressures which are approximately equal to the hydrostatic head of a column of water of equal depth. If the formations were opened to the atmosphere, a column of water from the ground surface to the subsurface formation depth would balance the formation pressure. On the Gulf Coast, the shallow, predominantly sand formations contain fluids which are under hydrostatic pressure. These formations are said to be normally pressured or to have a normal pressure gradient.* Experience has shown that the normal pressure gradient on the Gulf Coast is approximately 0.465 psi/ft of depth. OVERPRESSURES Formations with pressures higher than hydrostatic are encountered at varying depths in many areas. These formations are referred to as being abnormally pressured, abnormally high pressured, or overpressured. Formation pressures up to twice the hydrostatic pressure have been observed. These formations require extreme care and much expense to drill and to exploit. COMPACTION-FLUID PRESSURE RELATIONS THEORY The generation of overpressured formations in Tertiary sections of the Gulf Coast and several other Tertiary sedimentary basins is, in general terms, considered to be primarily the result of compaction phenomena.' This portion of the paper presents a brief review of the theory which associates compaction and fluid pressure relations, and should thus provide the necessary background for an understanding of the techniques presented. See Hubbert and Rubey' for a more comprehensive treatment of this subject. The theory of the consolidation of a water-saturated clay' has been well established by workers in soil mechanics. The concept is explained by a model with perforated metal plates separated by metal springs and water and enclosed in a cylindrical tube. Fig. 1 is a schematic representation of such a model (see Ref. 5, Fig. 27, page 74). The springs simulate communication between clay particles, and the plates simulate the clay particles. Mano-

Jan 1, 1966

By R. F. Krueger

Results are presented from tests of dynamic fluid-loss rates to cores from clay-gel water-base drilling fluids containing different commercial fluid-loss control agents (CMC, polyacrylate or smt,ch), organic viscosity reducers (quebracho and complex metal lignosulfonate) and oil at several different levels of concentration. In the dynamic system the most effective individual additives to the clay-gel drilling fluid, based on cost-equalized concentrutiom, were found to be starch and the viscosity reducers. These results do not conform with the rankings determined by API fluid-loss rests, which indicate CMC, polyacrylate and starch to be the most effective and comparable. Generally, minimum dynamic fluid-losr rates were attained at cost-equalized concentrations of additive (including thinner) of about $1.00/ bbl, or less. For chernically treated clay-gel drilling fluids, both the standard and the high-pressure API filter-loss tests were found to he inaccurate indicators of trends in dynamic fluid-loss rates under the test conditions used, particulurly for drilling muds containing viscosity reducers. From a practical field viewpoint, restrictions on the applicability of the API fluid-loss test are such that it is open to question whether or not results of this test can be used routinely with confidence as an indicator of control of down-hole fluid loss under field treating conditions. INTRODUCTION The petroleum industry spends large sums of money during drilling operations to control the fluid-loss properties of drilling fluids based on the standard API filter-loss test,' which is a static filtration system. Laboratory studies' ' of dynamic filtration have shown that in a given time period filtrate loss from a circulating mud stream is greater than from a static system and that it is a function of linear mud velocity, pressure and the properties of the drilling fluid. Ferguson and Klotz' and Horner, et al," observed that (I) the dynamic fluid-loss rates for the drilling fluids used were not related to the extrapolated API filter loss and (2) the drilling fluids with the lowest API filter losses did not have the lowest dynamic fluid-loss rates. However, there has been no published information on the relative effects on dynamic fluid-loss rate as a given drilling fluid is treated with increasing amounts of chemical additive to reduce the API filter loss. Such information is economically important because drilling-fluid costs rise rapidly as chemical requirements increase. This paper presents the results of a study of dynamic filtratioi rates to cores from a clay-gel water-base drilling fluid treated with various commercial viscosity reducers and chemical fluid-loss control agents. The dynamic fluid-. loss rates to cores are compared with the standard API filter-loss values at several different levels of additive concentration. Dynamic filtration rates were obtained in each experiment under two different simulated wellbore conditions: (1) filtration just above the bit through a new mud cake laid down dynamically on a freshly drilled formation and (2) filtration up-hole through a mud cake formed by deposition of a static filter cake on top of the initial dynamically formed cake. The latter case corresponds to the bottom-hole conditions existing above the bit when mud circulation is restarted after a stand of pipe has been added or a round trip has been made to change the bit. Except for the short-duration, high-rate filtration beneath the bit where no mud cake can form, these two conditions probably represent the two extremes of dynamic filtration. Because thickness of a dynamic mud cake formed on freshly exposed formation is limited by the shearing action of the mud stream, the filtration rate for this condition is high. On the other hand, once circulation is stopped and a static mud cake forms on top of the dynamic cake, re-starting circulation has only a small effect on the cake properties and filtration rate is much lower thereafter. A discussion of the mechanics of mud-cake deposition and dynamic filtration is outside the scope of this paper but may be found in more detail in publications by prior investigators. APPARATUS AND EXPERIMENTAL CONDITIONS The test equipment used to simulate the dynamic flow conditions existing during drilling was a modification of that described previously by Krueger and Vogel: A schematic flow diagram is shown in Fig. 1. In general, a power-driven, high-pressure mud pump capable of delivering up to 60 gallmin was used to circulate drilling fluid parallel to the faces of 1-in. diameter sandstone cores mounted in a 2 3/4-in. ID high-pressure test cell. Pump rates were controlled by means of a magnetic clutch to maintain an average axial fluid velocity of 110 ft/min in the annular space between the cell wall and a 1 1/2-in. rod positioned on the center line of the cell. The core specimens were Berea sandstone plugs sealed with plastic inside 1 1/8-in. OD tubes and were fluid-saturated prior to use. Burettes were used to accumulate fluid discharged from the cores. The mud sump shown was used for treatment and storage of the drilling-fluid samples during a particular test. The valve arrangement permitted either (1) circulating drilling fluid through the by-pass line while treating with