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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 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 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 B. A. Eaton

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

Jan 1, 1970

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

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

Jan 1, 1967

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

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

By S. Gstalder, J. Raynal

Consideration was given to simple tests which could be performed on rocks to give a measure of rock drillability. Various methods of breaking rocks were considered and the hardness test developed by Schreiner was selected for this study. The test involves application of an increasing load on the rock face through a flat-faced cylindrical punch until rupture occurs. Test results show that hardness is a good measure of the breaking strength of rocks. Useful relationships are shown to exist between hardness and other physical quantities such as specific disintegration, Young's modulus and sonic velocity. Specific disintegration (volume of rock broken per unit of work input) provides a possible means of comparing the effectiveness of other methods of rock breakage. The relationship between hardness and sonic velocity may be very significant for it may be possible to deduce rock drillability from sonic log data. provided that a mineralogical factor is taken into account. TO test further the results of the work, laboratory drilling tests were performed which closely simulated down-hole pressure conditions. Correlations of drilling results with rock hardness measurements were quite good. It was concluded that rock hardness, as measured in the laboratory or as deduced from sonic logs, could be used in relations for predicting rock drilling performance. INTRODUCTION Drillability of rocks cannot be defined in an absolute manner by a single quantity or measured by a single test. Resistance of rock to drilling depends to a large extent upon the means used for rock destruction. This complicates drillability classification of rocks for there may be as many classifications as there are methods of rock breakage without known functional relations between them. The objective of this work was to develop. in terms of rock destruction behavior, means of selecting the best drilling method for a given rock or the conditions for optimum output from a given drilling method. ANALYSIS OF ROCK DESTRUCTION TESTS Gauthier and Baron' have reviewed the many test methods which have been developed for determining the resistance of rocks to breakage. These include drilling tests, punch tests, scratch tests, resistance to shock, wear tests, etc. A standard drilling test might be to determine the time required to drill a standard depth (1/16 in.) in a rock using a bi-cone microbit (1 1/4-in. diameter) when a standard load (417 Ib) is applied at a standard speed of bit rotation (110 rpm). From the standpoint of similarity, the results of microbit drilling tests would seem to be most representative of the several methods suggested above. However, evaluation of drilling performance by this method is only qualitative and cannot be applied directly to actual drilling conditions. Punch tests basically measure rock hardness. Punches of various shapes and sizes, including small cones for Vickers' and Knoop's tests, the wedge for Epstein's test and the right circular cylinder for Schreiner's test, have been used. Results of these tests lead to a quantitative hardness classification which would seem to be related to the resistance of rock to bit-tooth penetration. Scratch tests are related to the resistance of rocks to abrasion such as would be encountered in drilling with diamonds. Either the width of the scratch obtained at a fixed load or the load required to give a scratch of a fixed width may be used to evaluate surface hardness of the rock. This should be related to the resistance of the rock to wear. The above tests, and probably many others. give relative measurements of the breakage or destruction characteristics of rocks. There is no direct relation between results of these tests and the drillability of rocks. Also, the tests each measure different quantities which have different dimensions and they do not permit direct comparison of numerical values. As one step in rectifying the above difficulties. it is proposed that the results of all test methods be expressed in terms of volume of rock destroyed per unit of work required; this is referred to as "specific disintegration". Test results may then be reported in a form which shows both a classification of rocks in regard to each method and a comparison of methods with regard to each rock. The disadvantage in using specific disintegration is the difficulty of measuring this quantity with accuracy. The volume of rock damage is difficult to measure. as is the true value of work input. Rock heterogeneity adds to the

Jan 1, 1967

By J. R. Eckel

It has long been known that mud properties affect drilling rate and that drilling with water is as much as six to .seven times faster than with mud. However, it is not known why drilling rates with mud are lower. Recent studies show what fluid properties govern microbit drilling rate and also provide a quantitative correlation of these fluid properties and hydraulics with microbit drilling rate. All the microbit tests reported in this paper were made with a low permeability (about 10 md) limestone. They were conducted at constant bit weight and rotary speed with varying fluid properties, flow rate Q and nozzle dinnteter d. The tests showed that (1) drilling rate in a given system with constant circulating rate and nozzle velocity is a function of the kinematic viscosity [viscosity /density, (cp)/ p (density)] of the drilling fluid measured at near bit nozzle shear rates; (2) the combined effect of fluid properties and hydraulics on microbit drilling rate is defined by a Reynolds number function (kQp/dp); (3) for the same kinematic viscosity, drilling rate is independent of solids content; and (4) for the same kinematic viscosity, drilling rate is independent of fluid loss. INTRODUCTION The fact that mudding up reduces rate of penetration is well known, but the reduction varies from well to well. The rate with mud may be 80 percent of the water rate or it may be as low as 15 percent. Since this reduction of up to seven-fold takes place under conditions of constant bit weight, rotary speed and mud circulating rate in a uniform formation, it can only be a result of the change in fluid properties. Previous work1-" both in field tests and in laboratory microbit tests) showed that drilling rate with mud is lower than with water (Figs. 1 and 2). Microbit tests also confirm, at least qualitatively, the field observation that drilling rate slows with increased pressure differential from borehole to formation (Fig. 3). The qualitative effect of drilling rate of bit weight, rotary speed and rate of mud circulation are also the same for the field and microbit rig. For these reasons, the industry generally accepts microbit results as being qualitatively meaningful in terms of field application.

By J. G. Bouwkamp

This paper presents three general approaches towards the solution of the stress distribution and the behavior of tubular connections as used in offshore well drilling structures. First, the possibilities of using plastic models and photoelasticity techniques in evaluating the stress distribution in gusset plate connections are analyzed. The results of photoelastic studies on the stress distribution in the in-plane gusset plate of two-dimensional joints are presented. The influence of the configuration of the gusset plate (with and without cut-outs) is discussed. Second, the paper deals with recent developments and applications of computer programs to analyze connections with directly inter-welded tubes and with gusset plates. The possibilities and limitations of these programs are discussed. Stress patterns analyzed with these programs are presented for different joint configurations. Finally, the basic test procedures and results of a test on a tubular joint under static and alternating loads are discussed. INTRODUCTION The effective design of tubular connections as encountered in offshore well drilling towers or floating platforms has been complicated basically by the radial flexibility of the tube walls. This flexibility is a source of severe stress concentrations which can initiate an early failure of these joints. In an attempt to reduce the influence of the wall flexibility of the column tube, certain joints are presently designed by inter-welding the incoming branch members. In those designs, the force acting normal to the chord tube can be reduced considerably. A second group of joints incorporate gusset plates or stiffening rings to stiffen the column wall and to distribute the incoming branch member forces over a larger part of this wall. A third approach to improve the stress distribution in a tubular joint is to increase the wall thickness of the column member. This can be achieved by simply applying a thicker wall section in the vicinity of the joint. A fourth possibility to restrain the radial flexibility of the tube wall is to fill the column member with concrete. Also, a single, cast steel seat welded to the column tube can be used to improve the stress distribution in this wall. Although all these designs improve, in general, the state of stress in the column wall, the altered stiffness often causes the development of critically stressed areas in the web members. At the same time the actual design in most instances is decisively influenced by the site which governs the depth and controls the forces produced by waves, earthquakes and ice flow. Also, the towing, erection and foundation requirements of offshore structures can affect the actual design selection. Because of the complexity of the structural configuration of tubular joints, the stress analysis of these connections has necessarily been based on simplified and often crude assumptions. For the earlier and smaller type of connections with about 4-ft diameter column sections, the primary problem was to evaluate the relative stiffness of the column wall section and the load transfer between joint members. Due to the recent developments of offshore drilling structures with increasingly larger connections (e.g., column diameter. 32 ft; web members, 8.5 ft) this problem has become even more critical. One design philosophy for such large joints follows a member-to-member connection with radially heavy reinforced column sections. This radial stiffness can be attained by closely spaced and intensively stiffened horizontal diaphrams together with vertical stiffeners. A second solution incorporates a concrete-filled section between the outer and inner walls of the column tube. Another philosophy considers large gusset-plated joints. The problem in these joints is to develop an effective load transfer between the branch tubes and the gusset plate and to minimize the stress concentrations in the member walls as effectively as possible. Several concepts are followed to achieve this gradual transfer between web-member walls and gusset plates. Because the number of joints in these huge platforms is limited compared to the over-all size, a proper design of these joints is even more important than was the case for the many joints in the smaller, but multi-legged towers. A failure of one of those ultra-large joints could well cause the complete collapse of such a structure. Under these circumstances an accurate analysis of the large joints is of the greatest importance, together with information regarding the expected behavior of such joints under critical alternating load conditions. Recent applications of photoelastic model techniques have proved to be quite effective in evaluating the elastic behavior of such joints. Although a complete study of such connections is quite well possible with present-day photoelastic techniques, it might often be feasible and necessary to limit the objectives and to restrict these investigations to the study of a specific aspect of the joint. Another very promising avenue of approach to solve the complex stress pattern in these connections seems to be the recent development of digital computer programs. In this category, cylindrical shell programs and finite element methods for more complex configurations have

Jan 1, 1967

By J. H. Yang, K. E. Gray

Results of single-blow bit-tooth impact tests on saturated rocks under elevated confining pressures and zero pore pressure were reported in a previous publication.1 This paper presents an extension of the earlier work to include a study of crater formation during tooth impact on both gas- and liquid-saturated Berea and Bandera sandstones at elevated confining and pore pressures. The basic data obtained were force-time, displacement-time, velocity-time and force-displacement curves during crater formation. Crater volume was also measured and the mode of crater formation determined. Bit tooth geometry, depth of penetration and velocity of impact were held constant. Results indicate that, with pore fluid present in the rock, failure trends from brittle to ductile as pore pressure is increased at constant confining pressure (pore pressure and borehole pressure were equal) For a given rock type, the mode of crater formation was dependent not only upon the nominal effective stress, but also upon the fluid which saturated the rock pore space. When confining pressure and pore pressure were equal (zero nominal effective stress), bit-tooth impact resulted in brittle failure for nitrogen-saturated Berea, and brittle to transitional failure for nitrogen-saturated Bandera; when saturated with liquid both rocks failed in a ductile manner at zero nominal effective stress. INTRODUCTION Dynamic wedge penetration tests have been conducted by investigators in several fields, but the failure mechanism of rock under dynamic stresses is not understood completely. The complex action of drilling bits, even considering the action of a single tooth, may be considered as a combination of drag bit and rolling cutter action. Thus, as a first step in understanding rock breakage in oil well drilling, single chisel impact and rock planing are of fundamental importance. For example, Gray 2 and Crisp3 studied drag bit cutting action at brittle stress states. Simon4 and Hartman5 studied the reaction of rocks to vertical impact by means of drop tests. The depth of penetration, crater volume and force-vs-time curves during crater formation were observed. The significance of indexing single-bit impacts has been noted.4,6-8 Gamer et al,9 reported impact tests on impermeable Leuders limestone at atmospheric and elevated confining pressures. In all cases the tests were accomplished on dry rock and pore pressure was considered to be zero. The importance of both confining pressure and pore pressure on the failure characteristics of rock was described. 10-12 It was found that the yield strength and ductility of porous rock depend on the state of stress under which the sample is tested. The importance of pore pressure on drilling rate in microbit experiments was noted by Cumingham and Eenink. l3 Robinson 12 also pointed out that in drilling the most important parameter in rock failure is the effective stress, where effective suess is defined as confining pressure pc minus pore pressure pp. The effect of pore pressure and confining pressure on rock strength was also noted by Serdengecti and Boozer 14 in strain rate tests, and by Gardner, Wyllie and Droschackl5 in elastic wave studies. Until recently all reported wedge impact studies under simulated wellbore stress states have been conducted on dry rock. Maurer 16 reported impact tests on samples saturated with deaerated water. Borehole and formation fluid pressures were equal in these tests except when mud was used in the borehole. With mud in the borehole and a high borehole-to-formation fluid pressure differential. Maurer observed "pseudoplastic" crater formation. Podio and Grayl reported impact tests on Berea and Bandera sandstone saturated with pore fluids having wide ranges in viscosities. In Podio and Gray's tests, confining pressure was elevated, but pore pressure and borehole pressure were held fixed at atmospheric pressure. The presence of

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By A. A. Toprac

The recurring problem of joint failures in ofjshore structures, coupled with the catastrophic collapse of many of these structures during Hurricane Hilda (1964), hay forced reconsideration of techniques presently used to design sfuctural joints. This paper presents results of studies conducted for this reconsiderat?on. Only right-angled T-joint,s and cross-joints where a brace was welded directly to the undisturbed surface of another tube (the chord) were considered. Tests were performed on seven T-joint and 12 oross-joint specimens of two types which were designed to give a broad but practicd range to the geometrical parameters believed to be of significance to the problem. These paramefers were expressed in dimensionless form. Each specimen of the T-joints was instrumented wirh both electrical resistance strain gauges and deflection dials. After the elastic tests were concluded, each specimen was loaded to failure by applying an axial tensile load to the brace. The cross-joints were tested to failure without measuring elastic strains. Theoretical solutions for the stresses in a cylindrical shell due to a distributed radial load over portions of its surface were numerically evaluated. The experimental results are compared with calculated values obtained using Bijlaard's and Dundrova's theoretical analyses. INTRODUCTION During the last IS years a large number of structures were built for the offshore exploration of oil both in the Gulf of Mexico and dong the Pacific Coast.' In all these offshore platforms, the tubular shape was extensively used since this shape provides outstanding strength in proportion to its weight, compared to other shapes, when all directions (x, y, z) are considered. Past use of tubes was hampered because of connection details. But with the advent of welding, it became no more difficult to connect tubular shapes than to connect rolled shapes. However, some problems have been encountered in actual construction in making welded joints that are adequate and yet economical. In trying to connect tubular members, designers have used a varied number of methods; consequently, some of the joints seem to be very expensive in detail while others appear weak and underdesigned. An inspection of offshore platforms owned by different companies indicates the use of a large number of joint arrangements and configurations. Such a variety of joint types in current service indicates the wide divergence of opinion that exists on how such joints should be designed, stiffened and strengthened. Fig. 1 shows the various types of connections that have been used in practice. This paper reviews the present state of art on tubular joints of the T and cross type, and presents results of experimental and analytical work being conducted at The U. of Texas and elsewhere. It is believed that such information will be of great help to designers for the formulation of proper design procedures for joints. CONNECTION PROBLEM Recently, cracks have been observed in several welded connections in offshore structures. Fortunately, until about 1 1/2 years ago, these failures have been localized and have not resulted in the collapse of structures or loss of life. For example, one platform installed in Louisiana during 1955 in about 60 ft of water had been subjected to four tropical hurricanes. This platform successfully withstood these forces and was later removed because operations at this location had been completed. Many joint failures were observed during the removal.

By L. R. Raymond

With the trend toward deeper and consequently hotter holes, measurements of drilling mud properties at atmospheric temperatures are becoming increasingly inadequate.' Both the prediction and control of down-hole mud properties depend in part upon our knowledge of temperatures in the wellbore. Consequently, a better understanding of factors that affect temperatures during circulation and trips could improve drilling operations. It was toward the goal of obtaining this understanding that this study was directed. Other investigators2 have studied the response of fluid temperature in the borehole during trips. However, all of these studies have used an assumed formation temperature profile at the conclusion of circulation and have provided no means to calculate this profile directly. In this study, the formation profile during circulation was calculated. Other investiga-tors3-5 have also studied bottom-hole temperature during circulation. However, they have developed neither general techniques for calculating the entire temperature profile in the system nor generalized methods for predicting bottom-hole fluid temperatures during circulation. Such techniques and methods have been developed and are discussed briefly in the following pages. Temperature Behavior During Circulation Circulation of fluid during the drilling operation is represented schematically in Fig. 1. The process of circulation has three distinct phases: (1) fluid enters the drill pipe at the surface and passes down the drill pipe; (2) fluid exits the drill pipe through the bit and enters the annulus at the bottom; and (3) fluid passes up the annulus and exits the annulus at the surface. To simulate the thermal behavior of the fluid in the system, each of the phases of circulation must be described mathematically. In Phase 1, the fluid enters the drill pipe at a specified temperature, TDo. As the fluid passes down the pipe, its temperature is determined by the rate of heat convection down the drill pipe, the rate of heat exchange between the drill pipe and the annulus, and time. Phase 2 of the circulating process merely requires that the fluid temperature at the exit of the drill pipe be the same as the fluid temperature at the entrance of the annulus; i.e., TD(L,t) = TA(L,l). Thus in Phase 3, the fluid enters the annulus at TD(L, t). As the fluid flows up the annulus, its temperature is determined by the rate of heat convection up the annulus, the rate of heat exchange between the annulus and the drill pipe, the rate of heat exchange between the formation adjacent to the annulus and the fluid in the annulus, and time. These rates of heat exchange and the time dependency of mud temperature are described by well known heat-flow equation.6 Consequently, as shown in the Appendix, the temperature profiles in the drill pipe, annulus, and formation can be obtained by solving Eqs. 1 through

Jan 1, 1970

By K. C. Strebig, C. W. Schultz, A. A. Selim

The effect of some organic additives in diamond drilling of quartzite was investigated in the laboratory. The drill was designed to measure the rate of penetration, the thrust, and the torque and to record each as a function of the distance drilled. A statistical plan was followed throughout the investigation and an equation representing the bit performance was derived from the mathematical theory of reliability. The drilling torque was found to increase with the use of additives while the sliding coefficient of friction and the wear coefficient decreased. The energy per unit volume consumed was found to increase with the use of additives. A hypothesis explaining the effects achieved with the additives is given. INTRODUCTION For some time researchers have attempted to increase drilling efficiency by adding certain agents to the flushing medium. Much of this interest is the result of the observations of Rehbinder, Shreiner and Zhigach1 They postulated that "...in processes for the mechanical destruction of solids, a region of increased crack formation is created in the deformed layers adjoining that surface of destruction, forming the predestmction zone. The surrounding medium (for example, a liquid) which wets a given solid will penetrate the embryo microcracks of the predestruc-tion zone. Increasing the molecular affinity of this liquid for the surface of the solid considerably facilitates the deformation and destruction by softening the solid in the zone of increased crack formation. In this manner, the hardness or strength of the deformed body is decreased by the influence of the penetration of the liquid into the predestraction zone." This is known as the "Rehbinder effect". Rehbinder's work has prompted many investigators to examine the effect of additives on the mechanical destruction of rocks. Engelmann, Terichow and Selim reported that the maximum penetration of the rock by a diamond point in a solution environment was at the isoelectric point of the solution.* Robinson reported that his results did not appear to support the theory of Rehbinder.3 Joris and .McLaren suggested that additives with surface tension lower than water will be more efficient in cooling the diamonds.4 Their effectiveness in removing the fine cuttings from the face of the bit will also improve the efficiency of the system. They reported an improvement in impregnated bit life and penetration rates with the use of soluble oil additives. In contrast, Long and Agnew, drilling with surface set bits, reported that lubricating agents increase bit temperature and wear.5 A significant change was reported6 in the mechanical properties of rock with polar additives. It was concluded that this change in the mechanical properties of the rock in the presence of the additive is due to the rock hydrophilic properties. Ethylene glycol, glycerine and anionic detergent were selected for this investigation because their surface tension is lower than that of water. The surface tension of these additives for the concentrations studied was 42 to 75 percent of the surface tension of water. A low surface tension additive would wet the surface of the diamonds more easily and hence would be more effective in cooling the diamonds. Another characteristic of these low surface tension additives is their effectiveness in removing the cuttings and preventing the flocculation of the formed particles in the drilling process. This article summarizes the results of an investigation performed at the laboratories of USBM, Twin Cities Mining Research Center. The objective of the investigation was to study the over-all effects of some organic additives on the performance of diamond impregnated bits in atmospheric drilling conditions only and not in downhole pressured conditions.

Jan 1, 1970

By J. B. Cheatham, M. D. Biggs

This paper presents a systematic method for determining the forces on a simplified roller bit. The kinematics of an actual roller bit drilling in rock is complex; nevertheless, it is desirable to obtain an accurate analytical model.. As a preliminary study, the roller bit is represented here by a simple two-dimensional bit and the rock by a Coulomb plastic material. Results from previous work, plus additional assumptions, are incorporated into a computer program to determine the forces required to move the bit in a specified manner. Example problems are worked by use of this program. By studying similar drilling problems and by supporting laboratory work, one could eventually obtain an accurate analytical model for drilling by an actual roller bit. This could lead to the compilation of a catalog of results that, in turn, would allow selection of the optimum drill bit for any given situation. INTRODUCTION

Jan 1, 1970

By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By Olaf Hondrum

CHURN drilling equipment at Bagdad consists of two Bucyrus Erie 27-T model drills and one 22-T drill with gasoline engines. The drilling tools weigh approximately 1600 lb. The holes are drilled with 7-in. bits which are heated in an oil burning furnace and sharpened in an electrically powered bit sharpener. A service truck brings the bits to the drills and takes the dull bits back to the shop. The bits weigh around 250 lb. when new and are handled by drill crews without any mechanical handling device. When the management decided to start open- pit operations in 1945 the ruggedness of the terrain was one factor that led to the purchase of the small 22-T model drill. The orebody lies on both sides of Copper Creek Canyon. The sides of the canyon are steep and are cut by numerous narrow branch gullies. The drill had to travel over roads that were narrow and steep. It proved adequate for drilling the capping formation and is still in use.

Jan 1, 1950

By McIntosh A. H, Torlach J. A

Since the last paper on mining methods was presented to the Annual Conference of the Australasian Institute of Mining and Metallurgy in 1:960, numerous advances have been made in drilling and blasting techniques at Mount Morgan. This paper describes the drilling and blasting methods being employed in the open cut. The change over to track mounted percussion drills for all types of primary drilling is almost complete and new techniques such as detergent drilling and pressure loading of ANFO are being applied successfully.

Jan 1, 1965

By T L. Horsley

This paper deals with the drilling and blasting methods employed at the Cassiar mine, which is located just south of the B.C.-Yukon border. It covers both the "pit" and "peak" mining operations. Specific problems, such as working in frozen ground, are discussed, and the breaking characteristics of the various rock formations are outlined. The paper concludes with a brief mention of the equipment used in the operation, as "~ell as an outline of the breaking costs. Introduction T HE Cassiar asbestos mine is located just south of the British Columbia -Yukon border high on a spur of McDame mountain. Chrysotile asbestos fibre occurs in a faulted enlargement of a serpentine sill lying conformably be-tween a series of sedimentary beds and volcanic flows which dip at 45 degrees into the mountain. One end of the orebody is eroded by a cirque in which a layer of permanently frozen ore and waste talus lies at the end of the mining benches. The topography at the mine is steep, with no flat areas. Roads, dumps, and areas for crushing,

Jan 1, 1965