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The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

By Bijan Taheri, Behrouz Maghsodi, Monireh Heshami, Reza Kohan

A common problem recently encountered with the increase in the rate of input feed at Enrichment Plant 2 of the Sarcheshmeh Copper Complex is the loss of value to the tails, translating to lower recoveries. The feasibility of the direct transfer of part of the high-grade concentrate from rougher stages to an appropriate position along the circuit was studied, and two positions were proposed for direct transfer of the concentrate. One position was the feed flow into cleaner cells, and the other was the feed flow into the recleaner cell. The results indicated that transferring the concentrate from the first unit of the rougher stage to the feed flow into the cleaner cells was feasible, with no limitations, while the second position required the installation of a set of hydrocyclones. It was found that the transfer of concentrate to the proposed positions not only addressed the problem of limited cell capacity, resulting in debottlenecking of the circuit, but also improved metallurgical separation efficiency up to 1.4%.

By Robert McClure, Carlton Lehman

Rendering safe explosives in an urban environment presents a unique challenge due to the safety concerns and disruption to the general public. Potential damage to the surrounding homes, businesses, utilities and transportation infrastructure are some of the major concerns when planning the render-safe operation. Engineering controls to mitigate blast effects, such as damaging air over pressure levels, material ejection and ground borne vibration, need to be implemented as part of the operation. Monitoring of seismic and air overpressure during these operations are needed to protect against potential claims when controlled or unplanned detonations occur. Two recent render-safe operations conducted in and around urban environments dealt with deteriorated, sensitive dynamite and damaged blasting caps. Utilizing innovative neutralization chemicals and processes to render-safe the deteriorated dynamite, while protecting the general public, proved to be the safest, most environmentally responsible and cost-effective way to approach the problem. In both cases, the explosives, old dynamite and detonators were found in abandoned, unlocked magazines. The dynamite was in a significantly deteriorated state, which was evident due to the nitroglycerine found leaking in,around and under the dynamite cartridges. Iron wire permissible electric blasting caps were also found in a corroded condition with exposed explosives and un-shunted lead wires. With occupied buildings within 180 feet (54.86 meters) of the magazines, any procedure (e.g. transporting, countercharging, burning) that could potentially cause a detonation was not an option. In the event of an unplanned detonation during neutralization operations, several blast mitigation methods were employed to safeguard the site. This operation and a similar one with over 1,000 pounds of crushed and buried leaky dynamite were unique since all the explosives were rendered-safe and neutralized on site. The use of advanced neutralization products and filtering processes allowed for a safer, more environmentally responsible way to resolve the problem. The magazines and all residual solids and fluids were tested and confirmed by independent labs to have no explosives residues. The effluents were treated on site, tested and met safe levels, so they were disposed of at a local municipal wastewater facility.

Colloquium on shaft sinking A successful colloquium which was attended by approximately 175 people was held on Shaft Sinking on the 15th November, 1972 at Kelvin House. Four papers were presented. The chairman for the first session was Mr W. W. Malan, Consulting Engineer, Goldfields of South Africa.

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 Keith A. Heasley, John L. Ellenberger

The National Institute for Occupational Safety and Health (NIOSH) has continued the research role of the former U. S. Bureau of Mines to develop techniques that will reduce the hazards in the mining work place associated with coal bumps. Current research focuses on both analyzing historical seismic data from bump-prone operations and utilizing a mine-wide seismic network to investigate the exact strata failure mechanics associated with bump-prone geology. The anticipated outcome of this research will be reduced bump incidences through advanced engineering concepts and designs which implement the new understanding of strata behavior. The analysis of the historic seismic data consists of correlating observed mining seismicity with the geologic and geometric parameters at the sites. The primary seismic parameters are the timing, location and magnitude of are corded seismic event. These parameters are correlated with such mining parameters as: the overburden, the size of the immediate gob, the size of the district gob area, etc. This detailed analysis of historical seismic data has provided an informative quantifiable relationship between many of the specific mining parameters and the induced seismicity. The second aspect of the coal bump research is the instrumentation of an appropriate field site to determine the main roof, floor, and gob behavior associated with bump behavior. The chosen field site is a deep-cover longwall mine with competent geology in a historically bump-prone area. The primary field instrumentation is a three-dimensional, full-waveform, seismic array with both surface and underground sensors surrounding an active multi-panel district. The purpose of this seismic array is to determine the timing, the exact location, and the mechanism (tensile fracture, bedding plane slip, etc.) of the failure of the strata surrounding the active and multi-panel gobs. The preliminary results presented in this paper help to define the strata failure areas around the longwall panel.

By Alexander L. Holley

A CHARACTERISTIC, and, to Americans, an amusing discussion of the three-high rail-mill, arose out of the reading of Mr. Lauth's paper on three-high plate-mills, at the Glasgow meeting of the Iron and Steel Institute. From the report of the meeting in the English papers, it appears that Mr. Menelaus, the celebrated rail-maker of Dowlais, could not wait for the discussion of Lauth's plate-mill, but launched at once into the British objections to the three-high rail-mill, which is quite another matter. The American mill, which is very different in principle and ar288

By Hon. Abrams S. Hewitt

Gentlemen : If my first words were other than those of thanks for the high honor of being called to preside over the American Institute of Mining Engineers, I should do injustice alike to you and to my own sense of the obligation, under which I have been placed by your voluntary choice. When the position was first suggested to me, I resolutely declined to allow the use of my name, on the ground that, by training and occopation, I was not entitled to this honor, which, it then seemed to me, should be conferred only on a professional engineer. In fact, the history of the Institute, which had honored itself, as well as my distinguished predecessors, David Thomas, Rossiter W. Raymond, and Alexander L. Holley, by elevating then] to its highest office, seemed to indicate the line and the limit of safe precedent, in which I did not then see how I could be included. But my scruples were finally removed by the consideration that, as in the course of human industry, the pioneer, of whom Mr. Thomas was so marked a type, must precede the mining engineer, so fitly personified in Dr. Raymond, and be followed by the mechanical engineer, whose incarnation we behold in Mr. Holley; so all these must be supplemented by the man of affairs and finance, in order that "enterprises of great pith and moment" may be prosecuted to a successful issue. I felt, therefore, that I had no longer any right to resist your preference, or to deprive myself of what I must regard as the crowning honor of an active career. On an occasion like the present it seems appropriate to review the history in this country, during the last hundred years, of those industries which the Institute of Mining Engineers specially represents. There is much in the story with which other members of this body are more familiarly acquainted than myself; yet I fancy that to all of them, and not less to our distinguished and most heartily welcome gnests from abroad, a comprehensive outline of the progress of mining and metallurgy in the United States mill prove interesting. I ask your attention, therefore, to a condensed account of that subject, embracing a statement of the beginnings of the industry on our shores, of the notable events attending its increase, and of its present

By J. A. Drummond

The duties and efficiencies of a number of main and auxiliary fans were determined by standard and thermal methods. Some observations on the effect of water and dirt accumulation on fan performance were made.

By A. E. Anderson, H. J. Hilll

Laboratory data for 155 field muds and 77 .shales have been used to develop correlations to estimate the net streaming potential component of the SP. Analysis of these data and comparison with field tests show that streaming potential corrections must be made to obtain an accurate estimate of the electrochemical potential for use in the determinntion of formation water resi-iiviy. The self-potential curve is related to formation water resistivity, and considerable effort within the oil industry has been directed toward clarifying this relationship. The Schlumbergers and Leonardon1,2 recognized that two types of potentials, electrochemical and electro-kinetic, resulted in the net potential variation in the borehole. Most of the later papers have dealt with the electrochemical component and its controlling parameters. The investigations of Wyllie,2" Salisch' and Moore5 provide the most extensive sources of data on streaming potentials across mud cakes. These authors observed streaming potentials of sufficient magnitude to be of critical importance in SP interpretation, if it is assumed that streaming potentials develop only opposite permeable beds. Streaming potentials across shales have been reported by Schenck and by Gondouin, et al.7 Since SP magnitude is the difference in potential opposite shale and sand beds, these authors suggested that the net streaming potential component may be negligible. The present investigation was initiated to evaluate empirically some of the parameters controlling the magnitude of the net borehole streaming potential and to determine whether useful relations between mud properties and net streaming potential could be established. Field muds were used in this investigation. These muds were characterized by the amount and type of chemical treatment utilized for five days before Sampling. Filter loss, mud resistivity, mud density and filtrate resistivity were determined for each mud with conventional methods and apparatus. Mud filtrate pH was estimated with Hydrion pH paper for the appropriate range. Streaming PotentIals Across MuD Cakes Commercial calomel-saturated KC1 electrodes are subject to potential changes attributed to contamination of the very small fiber-tip bridge by particles of clay from the drilling mud.3 To minimize this difficulty, a large diameter bridge (Fig. 1) was constructed with saturated KC1-agar gel and a filter disc of microporous porcelain. Experiments showed that streaming potentials across this bridge are less than 0.2 mv at pressure dif-

By J. P. Hugo

Nuclear energy - its interactions with mining and metallurgy - PRESIDENTIAL ADDRESS given by J. P. Hugo Pr. Eng., B.Sc (Eng.) (Rand), Ph.D. (Sheffield) Energy is the life blood of the modern technological era in which we live and it was, I think, Benjamin Franklin who said that the manipulation of energy was the basis of all science and technology. This is perhaps an oversimplification, but there can be little doubt that our life today, and the improved standard of living we aspire to, are governed almost entirely by our ability to generate and manipulate energy. This ability has made it possible for Man - each specimen a feeble twentieth of a horsepower - to travel to the moon, to recover valuable minerals from the depths of the earth, to do arithmetic at unbelievable speed, to lessen the drudgery of manual labour. For these and virtually every aspect of our life we are dependent on energy from external sources. It is, therefore, not surprising that the per capita consumption of energy, and more particularly electricity, has become one of the most reliable criteria by which to measure the standard of living and technological advancement of a country.

By Pavol Loderer

Mineral froth pumping utilising centrifugal slurry pumps is a major engineering challenge for the end users and pump manufacturers due to the undesirable outcome of unstable pump performance. Most of these challenges occur due to incorrect pump selection and suction tank design. The traditional approach is to oversize the pump for pumping mineral froth. New horizontal slurry froth pump designs offer opportunities to improve the mineral froth with challenging (high) Froth Volume Factor while maintaining high efficiency, long wear life and stable pumping performance. This paper examines the flotation process in detail and how froth pumps are designed to handle this arduous process.

By Archiblad MacMartin

The Kunigin-Marien-Hiitte is the only works in Germany where the Bessemer process is carried on by the direct method. The Besserner plant there, is arranged after the true English type, and the only resemblance to the Swedish mode of 'procedure is the dispensing with the use of spiegeleisen at the end of the "blow." In a new department of the establishment, started within three years, each of the converters is turned by means of a very neat and compact reversible engine, the steel shaft of which is an endless screw, which turns against the oblique cogs of a large wheel attached to the shaft of the vessel. An advantage which this arrangement possesses over the ordinary English hydraulic arrangement, is the fact that the endless screw suffices to turn the vessel, in either direction, any number of complete revolutions; while even the latest American improvements, so clearly explained to us by Mr. Holley at the opening session of this meeting, do not secure even one complete revolution without changing the angle of inclination of the hydraulic piston. In the endless screw arrangement, there being no limit to the working of the motor in either direction (no return-stroke necessary), the vessel can always, unless outside reasons demand the contrary, be turned around to any desired position by the shortest cut, whether backwards or forwards. Also, the diameter of the cogwheel attached to the vessel can be made sufficiently great to avoid all unevenness of motion. In the old department the motive-power still continues to be hydraulic. If reports be true, the new department produces spiegelized steel, for the manufacture of all-steel rails. But the old department is still, as from the beginning, devoted to the production by the direct method of steel for steel-headed rails. The most remarkable fact connected with this direct steel is the ease with which it welds to the iron 'of the rail-packets, although no borax or other fluxing agent is used to facilitate the welding. It is very rarely that an exception occurs, and an ingot or a charge is discarded by the rail-mill. The mixture of pig-iron used for the production of this steel is melted in cupolas of very interesting construction (not to be de-

By R. H. Grau, S. B. Robertson, R. B. Krog

The National Institute for Occupational Safety and Health (NIOSH) has conducted research to improve the ventilation of large-opening mines. Large-opening mine ventilation is unique for the following reasons: (1) it is challenging to keep airflow velocities high enough to effectively remove or dilute airborne contaminants, (2) large air volumes can be moved through the mines with little static pressure drop, and (3) stoppings to direct ventilation airflows are costly to construct and maintain. The research results suggest that by incorporating ventilation planning into the mine planning process, using propeller fans, developing new stopping materials and construction methods, and using long pillars to eliminate crosscuts where possible, the ventilation of large-opening mines can be significantly improved. The ventilation improvements created by incorporating these various techniques into the ventilation plan will help reduce the exposure of mine workers to airborne contaminants in underground large-opening mines.

By R. L. Zick, J. D. Byars, T. P. Mucho

Recently, a large Pittsburgh seam longwall mine was nearing depletion of a major portion of its current reserves and had begun to develop in a different direction from its original portal area to access additional reserves. This meant that a large area of the mine would be abandoned and sealed. However, continued use of the original mine portal area required that the water accumulating in the abandoned mine would eventually need to be pumped to the surface. This would be in addition to the discharge water associated with the new portion of the mine. Several pumping and sump options were investigated to handle the quantity and quality of the anticipated discharge water. This paper describes some of these options, their advantages and disadvantages, and the final engineering decisions. Some problems and unanticipated outcomes, as well as the eventual solutions are discussed, including: (1) estimates of pump requirements, (2) water pool size, (3) eventual water quality, (4) anticipated inflows, and (5) integration into the overall mine water system.

By Joseph M. McCann

The Brightwater regional wastewater treatment facility, under construction in King County, WA, includes an extensive conveyance system that will feature deep, soft-ground tunnels and shafts. Excavation of the Ballinger Way Receiving Portal to 65.8 m (216 ft) below grade through challenging geology was accomplished by means of artificial ground freezing. This paper discusses freeze design development, system installation and monitoring, and the contractual and construction challenges that were overcome, including work sequencing and excavation means and methods, together with lessons learned.

By Christopher Mark

The first International Conference on Ground Control in Mining opened with the topic of pillar design. Two classic papers were presented, one by Bieniwski and the other by Wilson. Unfortunately, the two methods were so radically different from each other that it was nearly impossible to reconcile them. Adding to the confusion were the many other pillar strength formulas (such as the Salamon-Munro, the Holland-Gaddy, and the Obert-Duvall, just to name a few) that were also available. Little wonder that discussions of pillar design in those days often ended with anguished cries of “but which formula is the right one?” The past 25 years have seen substantial progress in the science of coal pillar design. Indeed, one testament to the improvement is the relative scarcity of papers on the topic at recent Conferences. Two factors have been largely responsible for the progress that has been made. The first has been the collection of large data bases of actual case histories of pillar performance in a variety of settings, from shallow room-and-pillar mines through deep cover longwalls. These have made possible the development of empirical design procedures that are closely linked to real world experience. The second important factor is the development of sophisticated computer models that can accurately simulate pillar behavior and roof/pillar/floor interactions. Together, these two lines of research have led to a new understanding of pillar mechanics that identifies three modes of pillar failure: • Sudden, massive collapse, accompanied by airblast, for slender pillars (width/height<4) • Squeezing, or slow, non-violent failure, for most room and pillar applications (4<w/h<10) • Entry failure or bumps for deep cover and longwall applications (w/h>10) It is particularly satisfying that the insights gained from numerical models broadly support those obtained from the empirical studies. While far less controversial than in the past, pillar design problems continue to arise. One recent example is pillar design for highwall mining. NIOSH has just released a software package, called ARMPS-HWM, which employs a number of modern pillar design concepts. Since highwall mining web pillars are long and slender, the greatest danger is that of a sudden collapse. ARMPS-HWM suggests two possible prevention strategies, one which

By C. S. Matthews, H. C. Lefkovits

Drilling progress is often delayed by sticking of the drill string. The development of preventive and remedial methods has been hampered by incomplete understanding of the sticking mechanism. A recent lahorntory investigation hns indicated that one type of sticking may be attributed to the difference in pressure between the borehole and formation. This paper shows, by means of soil mechanics, that the primary cause for differential pressure sticking is cessation of pipe movement, whereas diflerential pressre and stanrtding time determine the severity of the sticking. The analysis stresses the importance of using low-weight muds with low solids content and low water loss to alleviate diflerential pressure sticking and describes why packed hole drilling, long strings of drill collars, and a large deviation from the vertical are conducive to sticking. Finally, preventrve and remedial methods ore evaluated, and a theory is presented on the release of stuck pipe by spotting oil. INTRODUCTION Since drilling with long strings of oversize drill collars has become standard practice in many areas, the incidence and severity of the stuck pipe problem has increased. It has been noticed that in the majority of these cases the sticking could not possibly be attributed to key seating or caving of shales. It appeared that, due to the differential pressure between the mud column and the formation fluid, the collars were pressed into the wall and so became "wall stuck". Points to note about differential pressure sticking are: (1) sticking is restricted to the drill collars, (2) the collars become stuck opposite a permeable formation, (3) the sticking occurs after an interruption of pipe movement, (4) circulation, if interrupted, can be restarted after the sticking is noticed, and (5) no large amounts of cuttings are circulated out after restarting circulation. Helmick and Longleyl investigated pipe sticking by differential pressure in the laboratory and found an empirical relationship between the differential pressure, the sticking time and the required pull-out force. In this paper an explanation of the mechanism is given based on Terzaghi&apos;s theory of clay consolidation. A qualitative description is given in the following paragraphs while the derivation of fonnulas is given in Appendices. This paper is a first attempt to explain pressure differential sticking and many points will require additional theoretical and practical investigation before the problem can be fully understood. PRESSURE DIFFERENTIAL STICKING AS A CONSOLIDATION PROBLEM In any borehole, where the mud pressure is higher than that exerted by the formation fluids, a mud cake is formed opposite the permeable sections of the hole and a continuous flow of filtrate takes place from the mud, through the cake and into the formation. This radial flow pattern requires a certain distribution of the hydraulic and the effective (grain-to-grain) stresses inside the mud cake. Any quantitative or qualitative change in the external pressure conditions will produce a change in the flow pattern and, consequently, also in the internal stress distribution inside the cake. In view of the low permeability and the high compressibility of a clay mud cake, the adjustment of the internal stress distribution is slow and is accompanied by a change in volume. Time dependent stresses are thus created which gradually diminish as the new state of equilibrium between internal and external pressures is approached. Some 30 years ago, Terzaghi developed his "Theory of Consolidation" to account for the time-dependent stresses and settling of clay formations under the influence of external loads. He derived a differential equation by which the time-dependent hydraulic stress and the consolidation can be computed for any point inside the layer during the consolidation process. His theory is based on the assumption that the change in stress is solely due to a change in water content and it may only be applied to one-dimensional consolidation phenomena. Other investiga-tors5,10 have expanded his theory to include processes of more than one dimension. The difference between the external pressures on the mud cake before and after sticking is a qualitative one (isolation of part of the cake by the static contact with the drill collars after pipe movement has been stopped)&apos;, and the time-dependent stresses thus created may be investigated by means of Terzaghi&apos;s theory. By this analysis the changes in the nature of the contact surface between the drill collars and the mud cake during the sticking can be explained; and the friction force between the two may be computed as a function of the sticking time, the borehole dimensions and the mud cake characteristics.