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By Charles Williams

BOYLE'S law states that the volume of a gas at B constant temperature varies inversely as its pressure, PV = C, or V = C/P Therefore, the volume of a gas at any pressure is to its corresponding pressure as the volume of the same gas at atmospheric pressure is to atmospheric pressure, V, = V° Also, P1 P0 the volume of the gas at any other pressure is to its corresponding pressure as the volume of the gas at atmospheric pressure is to atmospheric. pressure, V2/P1 V0/P0 V°P VA Solving for V1 and V2, V2 = and V2 =V0P2/P0

Jan 2, 1927

By D. J. Pyra, J. Kudelko, Korzekwam W.

Polkowice region (Lower Silesia, Poland) is an area, where the copper mining activity started about 40 years ago and new technologies were applied. There are 3 underground mines, 3 processing plants, tailings pond (the biggest one in Europe), pipelines for flotation waste transport, railways. Although new technologies were applied during the copper ore exploitation, the environment in this area were polluted mostly by dust containing copper, lead, zinc and arsenic. Estimated values of heavy metals in polluted soils were compared to the natural contents of this metals. The geochemical background for Polkowice area was defined. The pollution zones occur around mining facilities. Copper ore exploitation and processing is planned for the next 20-40 years depending on market situation. After mines and other facilities closing the most important problem will be sustainable development of this area. To evaluate the scope of revitalization activities the analysis of recent soil environment condition will be necessary as well as forecasts for pollution migration. Geostatistic methods used also in mining will be very helpful for this task.

Jan 1, 2005

By J. D. Miller

Physical separation of bitumen from low-grade Utah tar sand deposits containing a relatively high viscosity bitumen phase (Sunnyside and Tar Sand Triangle deposits) has been accomplished by traditional size reduction and froth flotation techniques. At appropriate experimental conditions more than 90 percent of the bitumen can be recovered in a concentrate, containing more than 20 weight percent bitumen, which should be a suitable feed material for subsequent hot water or thermal processing. The efficiency of bitumen recovery depends on the extent of size reduction, promoter and dispersant addition. Rejection of greater than 60 percent of the sand at ambient temperature and ease of water removal from the concentrate make such a process strategy both energy and cost effective. The energy required to achieve effective separation by the ambient temperature process is significantly less than the energy required for the recently developed hot water process. The flotation behavior of the tar sand has been analysed with respect to flotation pH, contact angle measurements and the apparent iso- electric point of the bitumen. The best flotation response at pH 7.8 to 9.0 can be correlated with the maximum in contact angle developed between the air bubble and bitumen surface and with the apparent iso-electric point of the bitumen (-pH 8.0).

Jan 1, 1981

By L. V. Wade

The use of longwall/shortwall mining systems is under increasing scrutiny by the U. S, coal industry as a means to reverse the decline in productivity. The success of these mining systems depends to a great extent upon designing the system hardware to best suit local conditions. Of particular importance in this regard is designing the various elements of the total ground support system, including face, face end, and gate road supports, to accommodate local geologic conditions. This presentation centers on the problem of selecting the face support system. The existing geologic situation can influence the selection of the face support hardware in a variety' of ways. In general terms, these influences can be grouped into the following four areas: 1. The capacities required of the support unit; 2. The roof, coverage supplied by the support units; 3. The flexibility required of the support unit to meet changing geologic conditions; and 4. The required stiffness characteristics of the individual support units both vertically and horizontally. The following will center on the first area, i.e., the required d capacities of the support unit, in particular, the maximum required load density for a particular geologic situation.

Jan 1, 1976

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

The formation density logging tool provides a radioactivity measurement that yields formation densities in situ. The relationship between bulk density and porosity is well understood. With knowledge of grain and fluid densities, porosity may be computed from the indicated formation bulk densities in shale-free formations. The porosities thus determined may be used with a resistivity log for water-saturation determinations. One technique utilizes a density vs resistivity plut. A plot of density vs Sonic-log transit time is used for porosity determinations in shaly sands. This method is particularly suited to wells drilled with oil-base or salt muds. In shale-free formations, comparisons of density values nnd neutron-log readings are used to identify lithologr and, thus, to select appropriate values of grain density for porosity computations. Through the use of Formation Density, Sonic and neutron logs, the interpretation problems caused by complex matrix lithologies are simplified. Other applications of the Formation Density log are found in the identification of minerals in evaporite deposits and in yield determinations of "oil shales". INTRODUCTION Widespread field application has demonstrated that the measurement of formation density is a useful and revealing technique for well logging. Responding to the bulk density variations of the formation, the Formation Density log affords valuable data on the porosity, lithology and fluid content of the formations. Although not without its own limitations, the Formation Density tool may provide effective interpretation under conditions that hamper or preclude the use of other porosity devices. When used in conjunction with other devices, such as the Sonic or neutron, complex matrix conditions may be better understood, defined and evaluated. A previous paper' described the valuable contribution of the Formation Density tool in the logging of empty, or gas-filled, holes. The purpose of the present paper is to describe applications of the device in liquid-filled holes. THE FORMATION DENSITY TOOL The Formation Density tool was devised to measure the bulk densities of formations in situ. Actually, the device responds to electron density, but in the overwhelming majority of cases of interest, the electron density is very closely proportional to the bulk density. In other cases appropriate corrections can be made if necessary. Comparisons of log-derived densities with true densities for the more common matrix minerals are shown in Table 1. The tool consists of a gamma-ray source and detector mounted in a skid which, during the logging operation, is in contact with the borehole wall (see Ref. 1 for schematic). Gamma rays are emitted by the source and diffused through the formation. The number of diffused gamma rays reaching the detector at a fixed spacing from the source are counted. An increase in counting rate by the detector indicates a decrease in bulk density in front of the skid. Conversely, a decreased counting rate signifies an increase in bulk density. A measurement of hole diameter, between the face of the skid and that of the eccentering arm, is recorded simultaneously with the measurement of diffused gamma rays. Since the tool is a wall-contact device, the size of the borehole has little influence, provided good contact is maintained with the wall of the hole. Only in extremely large or small boreholes does the actual diameter become significant. However, for most accurate measurements the borehole size should be taken into account. Fig. 1 presents the departure curves for the conversion of counting rate to bulk density for liquid-filled holes of various sizes. It is of utmost importance that the skid maintain good contact with the wall of the hole. If, due to roughness or caving, there is mud between the skid and the formation, the tool will include in its response the relatively low-density mud, and the apparent density reading will be too low. Normally, permeable beds do not cave appreciably, so that reliable readings are usually available for zones of interest. Nevertheless, the caliper reading over the zone of interest should be examined for any wall roughness. When mud cake exists between the skid and the formation, the Formation Density log sees it as part of the formation. When thick mud cakes exist, a correction is required. For best results in wells having thick mud cakes,

By David Norval

Water solidification of mattes, metals, alloys and certain slags with high metal entrainment has customarily not been practiced due to the belief that such processes are too dangerous and unproven in the Pyrometallurgical Industry. Slag granulation on the other hand is extensively applied, although in some cases crudely, with disastrous effects, as a result of not recognising the high heat capacities prevalent in slags. This paper will examine the most common air solidification processes and compare such processes with water solidification, mainly slag and matte granulation processes and design criteria for safe and reliable operation. Finally, purpose designed granulation and solidification processes will be discussed taking into account specific applications and the individual signatures of alloys and slags, emphasising that no slag, matte or alloy responds in similar fashion to a granulation practice.

Jan 1, 2006

A failure of the Pit IA highwall in July 1989 led Newcrest Mining Ltd's Telfer Gold Mine to commence underground operations approximately 12 months ahead of schedule. The failure presented four major challenges to management: 1. how to maximise the recovery of the Middle Vale Reef (MVR) in the open pit: 2. how to minimise the risk to personnel involved in the extraction of the remaining open pit ore; 3. how to avoid disruption to ore supply: and 4. how to maintain a permanent and safe means of accessing the underground operations from the base of the pit. The risks associated with meeting these challenges were minimised through the installation of a complex network of real time slope monitoring equipment. These monitors were connected to an alarm system which was combined with detailed operational procedures to be carried out in the event of a highwall alarm being triggered. The accuracy with which the risk of failure has been managed was demonstrated recently when the onset of a second failure was initially identified some 13 months prior to its ultimate collapse in October 1992. The location, timing and size of the failure was able to be predicted allowing appropriate precautionary measures to be taken to ensure safety of access to the underground portal and pumping equipment in the base of the pit. This paper reviews the sequence of events leading to both the July 1989 and October 1992 failures of the Pit 1A highwall and the monitoring equipment and procedures used to identify, quantify and manage the risk to personnel operating in the base of the pit.

Jan 1, 1994

By Royle A. G

The paper describes a geostatistical structural analysis of an 80 square mile lease of the Athabasca tar sands. Each step of the analysis is presented with the ultimate objective of condensing the principal structural characteristics of the chosen regionalised variables into the opera- tional form of the variogram model. The variogram model is then used to form kriged local and global estimates, with the corresponding estimation errors.

Jan 1, 1977

By J. A. McLennan

Geological uncertainty is an unavoidable characteristic of all mining projects since only limited information is available from sampling. Mine planning and development decisions with significant economic consequences are made when the geological heterogeneity is inherently uncertain. Geostatistical simulation is preferred over kriging because the methodology provides alternative property realizations that can be combined into a model of geological uncertainty. Geological uncertainty can be transferred into production uncertainty, which can help characterize the economic risk of the project. This paper presents a case study for the Pogo property, being prepared for development near Fairbanks, Alaska. The exact dimensions, grades and production predictions have been modified; however, the methodology is illustrative. The geostatistical methodology consists of (1) assembling the relevant drillhole data and establishing a suitable coordinate system, (2) calculating the target distribution, (3) creating a model of spatial correlation, (4) generating multiple realizations at a small scale and (5) linearly averaging all the realizations to the chosen selective mining unit (SMU) support size. The geostatistical model is then used to calculate production uncertainty.

May 1, 2004

Factors leading to the necessity for some individual testwork in solving most specific hydraulic transportation problems are listed and a description is given of a method used in determining critical flow conditions. An outline is given of the basic theory of the purpose of the testwork, and a means of applying test results for varied pipeline diamet.er and material conditions follows. Engineering and economic factors are applied to the solution of a specific hydraulic transportation problem and the use of the test results in plant practice is illustrated. The advantages of connecting pumps in series in centralised pumping stations rather than individually along the pipeline are stressed. Some notes are added on the future possibilities and economies of post pump injection of solids into high pressure pipelines.THE HYDRAULIC TRANSPORTATION OF SANDSAs well as all the classical variables involved in a pipeline installation, one must consider, when solids are to be transported, the effects of such variables as:(i) Proportion of solids in the pulp.(ii) The average specific gravity of the pulp.(iii) Specific gravity of the solid material.(iv) Solid particle average sizing and possibly shape.(v) Solids particle grading.(vi) Pipeline diameter for effects other than classically hydraulic.(vii) Pipeline material.(viii) Fluid viscosity.(ix) Pump characteristics.(x) Abrasive or corrosive properties of the pulp.Not surprisingly, the application of published data to the hydraulic transportation of a specific material is difficult if not well nigh impossible. Most hydraulic transportation investigations also involve economic and site factors vary...

Jan 1, 1959

By R. M. Stewart

INTRODUCTION Requirements for achieving economic slope stability in open pit mining must not only be met during the operating stages but in all preceding stages of mine development. In many operating mines little or no emphasis was ever placed on evaluating the stability of possible slopes during the exploration and planning stages. The purpose of this discussion is to emphasize the necessary considerations that should be made in all stages of development in order to achieve the safest and most economic pit slopes. The most economic slopes may not always be the safest slopes and it is incumbent upon the mine operators and engineers to achieve an optimal combination of economics and safety. The stability requirements outlined are based on the profit motive and are, therefore, practically oriented. Long-term basic research or theoretical studies are considered important only to the extent that they can be shown to have a definite payoff. Consideration will first be given to the information required for stability analysis, which can be determined during the exploration and evaluation stage, followed by further stability work necessary during the mine planning and layout stage. Particular emphasis is then placed on the operating stage in which blasting, dewatering, artificial stabilization, and slope failure are discussed. Lastly, the importance of a logical and orderly research procedure is stressed. EXPLORATION AND EVALUATION STAGE The purpose of the exploration and evaluation stage in the mining scheme is to find and delineate a potential orebody. Discovery and delineation commonly involve drilling tens and in many cases hundreds of boreholes. These boreholes, which may cost as much as $20.00 per foot of depth for a cored hole, are usually abandoned once drilling is completed. Stability evaluation for a potential open pit should begin at this stage by taking advantage of the existing boreholes. Rock and soil properties, as well as hydrologic parameters, may be obtained from both the borehole and the core. Seismic velocity and neutron probes may be used to log the borehole to obtain elastic moduli data. A borehole dilation jack may also be used to give backup information on the rock and soil elastic parameters. Use of a core orientation system can result in the determination of fault and joint frequency and distribution. Before splitting or otherwise disturbing the fresh core, qualitative evaluation

Jan 1, 1972

Although I have, for most of my working life, been associated with research into problems of water pollution, this has been exclusively in a country where problems arise from having too many people rather than too little water, a country furthermore, where for the past few decades, mining, except for coal, could hardly be called a major Industry.

Jan 1, 1971

By Rose L. Ballard

This chapter summarizes data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Included also are the tables that show the principal nonfuel mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage bf measurement used in this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines.

Jan 1, 1983

By Aidan Giblett, Karen McCaffery, Robert Dunne

"A worldwide decline in competency levels of practicing metallurgists over recent decades has become clearly evident and is a common topic of discussion among senior practitioners and professional associations. The associated impacts on the industry are material and include operational inefficiencies, missed optimisation opportunities and suboptimal new plant designs. There are many contributing factors to this condition. Decrease in competency is particularly evident both in regions where imbalance between supply and demand has led to a general reduction in experience levels for comparable roles over time and in emerging regions where a rapid rise in demand for practitioners has occurred in conjunction with rapid economic development and industrialization. The context, depth and breadth of education curricula and levels vary with location such that solutions to the technical competency dilemma may need to be developed specifically for each region with these influences in mind. Delivering, demonstrating and maintaining competencies are a critical requirement of undergraduate training and ongoing professional development. Other factors such as generational and cultural characteristics and expectations, political influences, role requirements and employment reward and recognition systems all play a critical role in determining if core competencies can be effectively developed, applied and subsequently maintained. This paper reviews factors impacting and some common approaches to competency development. The authors’ experiences in the management of professional development efforts within the global industry are reviewed and a blueprint proposed to address industry requirements in this area."

Jan 1, 2014

By E. N. Smith, J. C. Redmond

The increasing need for materials capable of withstanding higher operating temperatures for various applications such as gas turbine blading and other parts, rocket nozzles, and many industrial applications, has brought consideration of cemented carbide compositions. The well known usefulness of cemented carbides as tool materials is attributable to their ability to retain their strength and hardness at much higher temperatures than even complex alloys. However, it has been found that the temperatures encountered in cutting operations do not approach by several hundred degrees1 those involved in the applications mentioned above where the interest is in materials possessing strength and resistance to oxidation at temperatures of 1800°F and above. At these latter temperatures, the tool type compositions which are made up essentially of tungsten carbide are found to oxidize very rapidly and to produce oxidation products of a character which offer no protection to the remaining body. As a further consideration, the density of the tungsten carbide type compositions is high, from about 8.0 to 15.0. The refractory metal carbides as a class are the highest melting materials known as shown by Table 1 which summarizes the available data from the literature for the carbides of the elements which are sufficiently available for consideration for these uses. The density is also included in the table, since as mentioned above it is an important consideration in many of the applications for which the materials would be considered. It has been established that in the tool compositions the mechanism of sintering with cobalt is such as to result in a continuous carbide skeleton and that the properties of the sintered composition are thus essen- tially those of the carbide.2 On the hypothesis that this mechanism holds to a greater or less degree in cementing most of the refractory metal carbides with an auxiliary metal, it appears from Table 1 that titanium carbide compositions would offer possibilities for a high temperature material. Titanium carbide has extensive use for supplementing the properties of tungsten carbide in tool compositions. Although the literature contains several references to compositions containing only titanium carbide with an auxiliary metal,3,4,5,6 it may be inferred from the meager data that such compositions were deficient in strength and were considered to have poor oxidation resistance.7 Kieffer, for instance, reports the transverse rupture strength of a hot pressed TiC composition at 100,000 psi as compared to up to 350,000 psi for WC compositions. The work described herein was undertaken to determine the properties of compositions consisting of titanium carbide and an auxiliary metal and to improve the oxidation resistance of such compositions. It appeared possible that the inclusion of one or more other carbides with titanium carbide might improve the oxidation resistance and also that this might be more desirable than other means from the point of view of maintaining the highest possible softening point. Consideration of the available carbides in Table 1 suggests tantalum and columbium carbides because of their high melting points and general refractoriness. The work on improving oxidation resistance was concentrated on the addition of tantalum carbide or mixtures of tantalum and columbium carbide. The auxiliary metals used included cobalt, nickel and iron. It was also desired to learn the general physical properties of these compositions. Experimental Procedure The compositions used in this study were made by the usual powder metallurgy procedure applicable to cemented tungsten carbide compositions. The powdered carbide or carbides and auxiliary metal were milled together out of contact with air. In some cases cemented tungsten carbide balls and in other instances steel balls were used to eliminate any effect of tungsten carbide contamination. A temporary binder, paraffin, was then included in the mix and slugs or ingots were pressed with care to obtain as uniform pressing as possible. The ingots were presintered and the various shapes of test specimens were formed by machining, making the proper allowance for shrinkage during sintering. Thereafter the shapes were sintered in vacuum at temperatures of from 2800 to 3500°F. Final grinding to size was carried out by diamond wheels under coolant. The titanium carbide used contained a minimum of 19.50 pet total carbon and a total of 0.50 pet metallic impurities as indicated by chemical and spectrographic analysis. It was found by X ray diffraction examination with

Jan 1, 1950

By Ho-Sang Sohn

The kinetic study on desulfurization of copper matte by gas bubbling was designed under the presumptions of lower FeO activity and of no slag formation, Copper matte with 59% Cu and 22.6% S in weight was oxidized at 1523K by bubbling of Ar + O2 gas through a submerged nozzle. The effects of oxygen partial pressure and flow rate of gas on the oxidation rate of matte were discussed. The desulfurization rate and the evolution rate of SO2 gas of copper matte were significantly influenced by the oxygen partial pressure, but the dependence on gas flow rate was rather complicated. The desulfurization rate and evolution rate of SO2 gas of copper matte were described by the mass transfer rate through the gas film around the rising gas bubbles. Thermodynamic correlation equations between the partial pressure of gaseous species and matte composition were incorporated to the kinetic calculation, The present model shows that the reaction path starts to transiently cross over an isobar line of PSO2 to asymptotically approach to the particular isobar line drawn in a matte composition plane of %S and %O.

Jan 1, 2003

By D Craw

TheSouthern Alps in the South Island of New Zealand are currently rising rapidly as a consequence of continental collision along the Pacific-Australian plate boundary. Rapid uplift has resulted in a major thermal anomaly in the shallow crust beneath the alps. Alpine topography and associated intense precipitation, coupled with the thermal anomaly are responsible for vigorous combined topographic/convective circulation of water through the shallow crust.   Uplift is greatest in a wedge-shaped region between the Alpine Fault and an associated second-order backthrust system, the Main Divide Fault Zone, approximately 20 km to the east. The Main Divide Fault Zone is segmented into NNE and NE striking faults, which are regionally sub-parallel to the Alpine Fault, but dip northwest in the opposite direction. Reverse oblique-slip on the Main Divide Fault is in an easterly direction, with a greater component of strike-slip movement on the NE trending faults. Elevated topography in the Mt Cook region is related to thrusting of a relatively homoclinal sequence of semi-schistose rocks on top of lower-grade greywacke, which controls the position of the Main Divide. Tectonically induced fluid flow resulted in only minor alteration and hydrothermal mineralisation of fault-rocks in Alpine and Main Divide Faults, and localised deposition of quartz and/or carbonate in the immediate hangingwall.   The wedge between the Alpine and Main Divide Faults is segmented by third-order structures north of the Mount Cook region. A series of right-lateral (-085/700S) and left-lateral (-150/600SW) faults, which are synthetic and antithetic to the Alpine Fault, respectively, developed as a conjugate set during uplift. Fluid-flow in the Southern Alps is controlled by these third-order fault/fracture systems. Cu-Au mineralisation, hydrothermal veins, and surface hot spring activity are localised by third-order fault/fractures and appears to be enhanced where conjugates intersect.

Jan 1, 1995

G. F. COMSTOCK (author's reply to discussion *).-The discussion of this paper has been of such volume and interest as to constitute in itself a sufficient excuse for the paper, even though the paper itself may have been as much in error as some of its critics have maintained. Mr. Howard does not appear to realize some very practical facts that the opponents of his theory have advanced. Among these are: the coarsely crystalline fracture of the nucleus of a transverse fissure, so different from the smooth fatigue break around it; the occurrence of fissures in large numbers in certain heats or rollings of rails, while other heats or rollings do not develop them; and the much smaller proportion of transverse fissures found in rails rolled .from reheated blooms as compared with direct-rolled rails. These facts are not explained by Mr.

Jan 6, 1919

By David deVries, James Rajith, Paul Mascrenhas, Nurzhan Dyussekenov, Lawrence Hanschar

Kansanshi Copper Smelter commenced operation in March 2015. The smelter features four Peirce- Smith Converters (PSCs) operated in a three hot, two blowing configuration. This paper describes some of the process automation and design features implemented to maximize operational and environmental performance. To ensure that the converters were easy to operate, efficient, and were protected in emergency situations such as power failures or loss of tuyere air supply a significant focus was placed on automated sequences initiated by “one button” operator commands or otherwise automatically by the Distributed Control System (DCS). Examples include: main converter roll-in and roll-out sequences; emergency roll-out in the event of power failure; and the charging sequences for reagents (silica and reverts). Other automated features configured for the PSCs were specifically aimed at maximizing converter capacity and reducing the environmental impact from fugitive emissions. These features include: “one button” in-stack charging; automated restriction of blowing rate based on the available acid plant capacity; and fully-automated control logic for the Secondary Ventilation System. In-stack charging allows anode furnace oxide slag to be poured into the PSCs while the converters are still blowing and still sending off-gas to the acid plant. PSC Secondary Ventilation control logic was configured to require minimum input from the operators while ensuring maximum utilization of the available draft from the ventilation system. Highly automated PSC controls contribute to high utilization, averaging 41.2 in-stack hours per day. INTRODUCTION Kansanshi Copper Smelter (KCS) is located near Solwezi at Kansanshi copper mine in Zambia's Northwestern province. The smelter treats concentrate produced at Kansanshi mine as well as Sentinel mine located 150 km west of Solwezi. Four Peirce-Smith Converters (PSCs) are installed at KCS. The nominal capacity of each converter is to treat 350 t of copper matte and produce up to 250 t of blister copper per batch. Normally three PSCs are hot, with two able to operate (produce off-gas), and the third converter on hot standby. The fourth converter is normally under cold repairs. The blister charge size is relatively low for the matte charged due to the unavailability of tank house or other high copper scrap.

Jan 1, 2019

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,' who first dealt with the coning problem; (2) Chaney, et al,' who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.' Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,' and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy's law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966