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I find that during the short time I have been in this district, the majority of boilers are, and have been, receiving very bad usage owing to the difficulties which they have to contend against, viz., oil and bad water. Oil on the heating surface of a boiler is of a highly dangerous nature inasmuch as it allows the surface to become overheated, owing to the water not coming into direct contact with the plates, and it naturally follows that when the crown sheets of a flue or firebox become overheated, you lose a considerable amount of the strength of the plate, and the flue or crown comes down. Referring to the oil question, I find that too much care cannot or exercised on the part of engine drivers in order to minimise as much as possible the internal lubrication of the various engines under their control. For I consider that it is here that the most of the trouble is caused. My reasons for stating such to be the case, are:-That the majority of enginedrivers before coming to this field have been used to driving engines that have been exhausting into the atmosphere, and probably they have been taught that it is far better to use a little extra lubrication than to have a hot bearing. So far so good. But one thing that must not be overlooked is that on these fields the conditions are altered in this respect, as the majority of engines in this district are not exhausting into the atmosphere, but are condensing their exhaust steam and using the water so condensed for feed purposes.

Jan 1, 1901

By L. W. Brandt

The Bureau of Mines, as part of its mission to effect pollution abatement, conducted research to study various means of dewatering Florida phosphatic clay wastes and reclaiming mined lands. The work was done in cooperation with 10 Florida phosphate companies. During this work, a novel technique to effectively dewater phosphatic clay wastes was developed. The solids contained in the clay waste slurry are slowly compressed by moving wire mesh screens through the system. In a typical application, the screens were moved downward, compressing solids ahead of the screens. The rate of movement of the screens is an important variable in the process. It is believed that the moving screens distort the gel structure of the phosphatic clay system and cause the release of water. Samples of 18 clay wastes, including a high-grade attapulgite from beneficiation plants of the Florida phosphate field, were studied using the method. Typical samples were concentrated from initial solids of 4.7 and 11.9 percent to 16.8 and 25.2 percent, respectively, in 3-1/2 days. The high-grade attapulgite sample was dewatered from 2.7 percent solids to 13 percent solids in the same period.

Jan 1, 1980

By Adriaan de Villiers

Many conventional structural analysis and design methods in current use are not appropriate for the mining industry. Two major reasons for this are that: • The economic life of a particular mine is limited, and • Much of the equipment and machinery used by the mining industry operates at relatively low speeds. Both of these factors can have significant cost implications if they are not properly accounted for during plant design. In particular, the often used practice of mitigating excessive vibration by adding mass to machinery supports is not only expensive but may worsen the vibration effects. Some of these problems, such as increased wear and tear, are not always easy to trace back to inappropriate design. This article focuses on vibration related issues and demonstrates that the mining sector has unique problems requiring unique solutions. Vibration: the basics Historic developments leading to current vibration design practices provide the key to why such practices are often inappropriate for the mining industry. To understand this, it is necessary to introduce some basic vibration theory. Consider a simply supported beam or foundation on which a vibrating machine is mounted. For analysis of the system's dynamic response, it may be viewed as a mass attached to a spring and a damper, such as the shock absorber of a car.

Jan 1, 1992

By V. Rajaram

R.K. Leininger, N.R. Hasenmueller, and D.D. Carr The content of the paper by V. Rajaram does not fulfill the expectations of the title. But Rajaram submitted the article in October 1983, and he could not have foreseen the numerous developments that would occur before his paper was published more than two years later. Nevertheless, Rajaram failed to mention the interest in oil shale development in southern Indiana beginning in late 1979 and continuing through the present as a result of special financial encouragement of three oil shale projects in May and August 1984 by the Indiana Energy Development Board and the Indiana Corp. for Science and Technology. A session at the 1985 Eastern Oil Shale Symposium in Lexington, KY, Nov. 18-20, 1985, gave the current status of oil shale developments in the eastern United States. Speakers at this session reported on the three Indiana projects. First, Gary D. Aho, Cliffs Engineering Inc., spoke on a feasibility study by Cliffs Engineering and Allis Chalmers for a site-specific pilot plant using the Allis Chalmers process. The plant site is in Clark County, IN, on property of the Midwest Energy Resources Co. The project is funded by $240,908 each from the Indiana Energy Development Board/Corp. for Science and Technology (EDB/CST) and the US Department of Energy (DOE) and $120,454 from the corporate sponsors (total $602,270). Completion is scheduled for mid-1986. Next, Edwin M. Piper, Stone and Webster Engineering Corp., discussed the American Syn-Crude/Indiana Oil Shale Project. This effort followed the completion of two smaller projects funded by the Indiana EDB/ CST: "Testing of Indiana Oil Shale in a Petrosix Pilot Plant" (total funding by EDB/CST at $50,000) and "Assessment of the Petrosix Process for an Indiana Shale Oil Plant" (total funding by EDB/CST at $100,000). The status at the time of the report at the Oil Shale Symposium was that a request for an extension of time for securing nonfederal support had been submitted to the US Synfuels Corp. The proposal included building an 11-m (36-ft) diam retort in southeastern Indiana to process the New Albany Shale and to produce 366 m3 (2300 bbl) of shale oil per day by the PETROSIX process. The Indiana EDB/CST had contracted with Stone and Webster at $401,100 from EDB/CST and $245,835 from Stone and Webster for activities to advance the project in the negotiations with Synfuels Corp. At the time of the report, this project was the only eastern oil shale proposal that was still on the agenda of the Synfuels Corp. As a result of Congressional action in late December 1985, federal support from the Synfuels Corp. is no longer possible. Finally, Victor H. Carr, Eastern Shale Research Corp., described his firm's project, which is jointly supported by DOE ($227,749) and the Indiana EDB/ CST ($73,850) and is entitled "Feasibility Study to Determine Suitability of an In-Situ Process to Recover Hydrocarbons from Eastern Shale." An area in Scott County, IN, had been chosen, but not a specific 9 x 15-m (30 x 50-ft) site. One burn of a small in situ retort is contemplated as part of the project. Besides these three projects, several reports on shale research were presented. Joseph Damukaitis, American Syn-Crude Corp., reported that a pilot plant using the hydrogenation-extraction (H-E) process (described at the 1984 Eastern Oil Shale Symposium) was 94% built and would go through shakedown with oil shale but would then shift mechanical devices to process coal mine waste. Current status of research on the HYTORT process was then presented by Raymond C. Rex, Jr. Oil shale beneficiation research at the University of Alabama/Minerals Research Institute was reported by R. Bruce Tippin. Scott D. Carter discussed continued research on fluidized-bed retort¬ing of shale at the Kentucky Center for Energy Research Laboratory. Carl E. Roosmagi of DOE, Morgantown, reported on the oil shale research at the Morgantown Energy Technology Center (METC) laboratory. Henry J. Gomberg, Ann Arbor Nuclear Inc., discussed "Radiation Combined with Donor Solvents for Extraction and Up-Grading of Kerogen." Aurora M. Rubel and coauthor Eileen Davis presented results of research at the Kentucky Center for Energy Research Laboratory under the title "The Effect of Shale Particle Size on the Products from the Bench Scale Fixed Bed Steam Pyrolysis of Kentucky Sunbury Shale." Lastly, Maria Rockwell, Technical University of Nova Scotia, presented "Processing and Up-Grading of Low Grade Nova Scotia Oil Shale for Potential Use." A review of shale oil prospects by Gerald Parkinson in Chemical Engineering for Feb. 3, 1986, covers both western and eastern projects and includes a report that the US DOE is funding a few relatively small projects; most of the fiscal 1986 budget of $12 million for shale oil is for fundamental research. Projects include a $3.2 million three-year contract with Hycrude Corp. (Chicago) for development of the HYTORT process and a $1.2 million three-year contract with the University of Alabama's Mineral Resources Institute on beneficiation of eastern oil shale by froth flotation. The report incorrectly states that current projects include a total investment of $466 million in a pair of 18-month technical and economic feasibility studies for proposed projects in southern Indiana. The correct figure is $468,657 [$240,908 for the Cliffs Engineering/

Jan 10, 1986

By D. K. Denton, J. M. Girard, D. F. Scott, T. J. Williams

Personnel from the Spokane Research Laboratory, National Institute for Occupational Safety and Health, examined an underground pillar at the Homestake Mine, Lead, SD. Investigations involved strain relief and seismic tomography studies in the mine, and ultrasonic velocity measurements on pillar core in the laboratory. Measured octahedral normal stress was 37 MPa (5,366 psi); seismic P-wave velocities averaged 5.2 km/s (17,060 ft/s); and ultrasonic velocities at a pressure of 39.6 MPa (5,750 psi) averaged 6.3 km/s (20,669 ft/s). The difference between in-mine and laboratory velocities is attributed to the attenuation of seismic energy by mine fractures larger and more numerous than those in the samples of core measured in the laboratory. Using these results, researchers hypothesize that pillar rocks have the ability to withstand stress an order of magnitude greater than they currently sustain.

By Mark Van Dyke, Ted Klemetti, Joe Wickline

"The identification and mitigation of adverse geologic conditions are critical to the safety and productivity of underground coal mining operations. To anticipate and mitigate adverse geologic conditions, a formal method to evaluate geotechnical factors must be established. Each mine is unique and has its own separate approach for defining what an adverse geological condition consists of. The collection of geologic data is a first critical step to creating a geological database to map these hazards efficiently and effectively. Many considerations must be taken into account, such as lithology of immediate roof and floor strata, seam height, gas and oil wells, faults, depressions in the mine floor (water) and increases in floor elevation (gas), overburden, streams and horizontal stress directions, amongst many other factors.Once geologic data is collected, it can be refined and integrated into a database that can be used to develop maps showing the trend, orientation, and extent of the adverse geological conditions. This information, delivered in a timely manner, allows mining personnel to be proactive in mine planning and support implementations, ultimately reducing the impacts of these features. This paper covers geologic exploratory methods, data organization, and the value of collecting and interpreting geologic information in coal mines to enhance safety and production.The implementation of the methods described above have been proven effective in predicting and mitigating adverse geologic conditions in underground coal mining. Consistent re-evaluation of data collection methods, geologic interpretations, mapping procedures, and communication techniques ensures continuous improvement in the accuracy of predictions and mitigation of adverse geologic conditions. Providing a concise record of the work previously done to track geologic conditions at a mine will allow for the smoothest transition during employee turnover and transitions. With refinements and standardization of data collection methods, such as those described in this paper, along with improvement in technology, the evaluation of adverse geologic conditions will evolve and continue to improve the safety and productivity of underground coal mining."

Jan 1, 2019

By Cesar Sáenz Acosta

El presente texto señala las mediciones de impactos que se han realizado a los programas de responsabilidad social de una empresa minera. Esta medición se realizó a través del cálculo del indicador “Retorno social de la inversión”, aplicando el modelo SROIM o Gestión del Retorno Social de la Inversión. Los proyectos de RS medidos permiten actuar a las empresas de manera responsable con su comunidad y comprenden: salud y nutrición, educación y desarrollo económico. Asimismo, esta medición contribuye a mejorar la comunicación de los impactos generados y desarrolla una gestión adecuada de estos.

Sep 12, 2011

By Joseph M. Kurtak

The U.S Bureau of Mines conducted a five-year mineral resource assessment of the 16.6 million acre Colville Mining District in northern Alaska, which includes part of the National Petroleum Reserve in Alaska. The study was initiated at the request of the Bureau of Land Management, which administers the majority of the region. The study was done in cooperation with the Alaskan Division of Geological and Geophysical Surveys, the U. S. Geological Survey, and the University of Alaska. During fieldwork, 1593 rock, soil, and stream sediment samples were collected and four bulk samples taken for beneficiation studies. A total of 40 mineral occurrences were documented, including 27 which were previously undescribed. No mining has occurred within the district. Mississippian carbonaceous shale and siliceous mudstone contain stratiform exhalative lead-zinc-silver occurrences. Grades average 8.0% combined lead/zinc and 51 gm/mt silver. Upper Devonian to Lower Mississippian sandstones host breccia veins, containing up to 29% combined lead/zinc and 274 gm/mt silver. Mineralized quartzites of similar age have potential for disseminated-type lead-zinc deposits. Samples from Lower Cretaceous mudstone and shale beds up to 6.5 meters thick, contain as much up to 12% manganese. Upper Mississippian carbonaceous shale and limestone beds contain up to 23% phosphate. Stratiform barite deposits hosted by cherts, are up to 27 meters thick with an average specific gravity of 4.16. Vein-type fluorite occurrences are associated with Mississippian limestone. Moderate potential exists for development of zinc -lead-silver, barite, and phosphate deposits.

Jan 1, 2011

By R. T. Jones

Technical publications in the field of mining and metallurgy have existed for a long time. Recent developments in electronic publishing on websites make it possible to disseminate information more widely and cost-effectively than before. Professional societies have an opportunity to serve their members and their industry by publishing high-quality peer-reviewed papers on their websites as well as in printed form. Older publications can be scanned, and optical character recognition used to provide searchable text. Various business models exist around this process. This paper outlines the approach used by the Southern African Institute of Mining and Metallurgy (SAIMM) to provide free open access to their journal papers and conference proceedings, as well as the work being done by OneMine.org to collect technical papers from a number of international societies and make them available to subscribers via a large database. An approach is outlined that should be of benefit to authors, readers, and society at large.

Jan 1, 2012

By Hamid Butt

Information Technology ??Advanced Information Technology is dramatically changing information flow within organizations. This enables employees to have information at their fingertips to make informed and prompt decisions. ??Real-time information allows timely analysis, which dramatically reduces cycle times, making organizations faster and more flexible. Business Challenges ??Continual growth of mining and Mine mobile fleet.??Increasing maintenance costs. ??Difficult to identify and troubleshoot equipment problems while equipment is operating. ??New equipment is increasing in complexity and cost. Therefore, each failure results in a greater impact to production and cost. ??Troubleshooting practice is reactive. ??Protect and optimize the use of mining assets to realize maximum business value. ??Maintenance and Operating information is not easily accessible ?no near real-time system that provides complete information.

May 1, 2006

Copper Recovery from Printed Circuit Board by Carbonisation

Sep 13, 2010

By E. G. Baglin

As part of an effort to decrease U.S. dependence on imports of critical and strategic metals, the Bureau of Mines investigated three leaching methods for extracting the base metals and recovering platinum-group metals (PGM) from matte prepared from Stillwater Complex flotation concentrates. Because of a limited supply of natural material, synthetic matte of composition similar to matte prepared from natural concentrates was used to devise the extraction sequences. The validity of the sequences was verified with matte prepared from Stillwater concentrates. In two-stage matte leaching, first-stage H2S04 leaching extracted 99 pct of the nickel and iron from the matte but negligible amounts of copper and PGM. Second-stage oxidative leaching with Fe2(S04)3 or FeC13 solubilized more than 98 pct of the copper and no precious metals. Sequential leaching, in which acid and oxidizing lixiviants were added sequentially to the matte without an intervening filtration step, extracted 99 pct of the Fe, Ni, and Cu. A roasting-leaching technique, in which the residue from first-stage leaching was roasted between 360° and 500° C before a second leaching with H2S04, solubilized 98 pct of the copper. The three leaching methods yielded high-grade PGM residues containing more than 98 pct of the PGM in the matte.

Jan 1, 1982

By B Belle

Dust sampling is pivotal in estimating the ‘dose’ of dust exposure and in deriving dose-response curves in epidemiological studies. Over the last half century, gravimetric sampling has been the fundamental means for dust exposure monitoring using recognised respirable size-selective standards. In Australia, a gravimetric sampling technique has been followed since 1983 using the Higgins-Dewell (HD) type cyclones (AS2985). The re-emergence of ‘Black Lung’ or Coal Workers Pneumoconiosis (CWP) in Queensland, Australia has re-kindled the need for better understanding of personal dust monitoring, compliance determination, accuracy, timeliness of sampling results and dust control systems. Reporting dust levels in real time empowers miners and operators to take immediate action to avoid being exposed to excessive airborne dust. Two decades of intensive research in the USA has led to the introduction of gravimetric based continuous personal dust monitors (CPDMs) called PDM3700 as compliance tools. The new real-time mass based sensor is a continuous mass based dust monitor using the Tapered Element Oscillating Microbalance (TEOM) principle and is regarded as significantly superior to the current gravimetric sampling methodology.Recently the overall respirable dust standard in USA coalmines has been reduced from the historic 2.0 to 1.5 mg/m3. This paper provides the results of a comparative pairwise study of an existing gravimetric sampler and the PDM3700 carried out in 3 different Australian underground mines. The field results consistently suggest that there is a significant ‘measurement bias’ between the current gravimetric HD sampler and the PDM3700 monitor operated using a similar HD type cyclone. The results show that the currently used cyclone measurements are approximately 59 per cent higher than the ‘auditable’ PDM3700 monitor data at the current compliance limit of 3 mg/m3. Based on a review of the extensive data collected, the differences can in part be attributed to the aerosol size selectivity of the samplers with the current gravimetric sampler used in mines, collecting more larger sized particles (D90 of 15 µm). This finding has significant consequences for historic exposure results and their use in medical surveillance programs, as well as the current approach to non-compliance determination.CITATION:Belle, B, 2017. Pairwise evaluation of PDM3700 and traditional gravimetric sampler for personal dust exposure assessment, in Proceedings Australian Mine Vent Conference 2017, pp 87–92 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 28, 2017

By F. M. L. Mulaudzi

Behaviour studies of metal dusting processes and associated filamentous carbon formation were undertaken on Alloys 600, 601, and 800 using a simulated metal dusting environment of 25C0-70H2-5H20 (vol.%) at 650°C. These samples were studied visually and by optical microscopy, scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX), transmission electron microscopy with energy-dispersive X-ray spectroscopy (TEM-EDX) and x-ray diffraction (XRD). Visual examination and SEM surface observation showed that Alloy 800 suffered metal dusting attack at an early exposure reaction period. The coke deposit amounts increased significantly with reaction time from 168 hours to 336 hours in Alloys 600, 601, and 800. Alloy 800 showed pitting after 168 hours' exposure, and the degree of pitting increased after 336 hours. XRD showed all these alloys had a common austenitic phase, with Alloy 800 also having ferritic metal particles. Alloy 800 after 168 hours' exposure had a complex phase mixture on the surface, consisting of ferritic Fe and austenitic FeNi phases. For coke deposit, there were also Fe304, Fe3C and graphitic carbon. The existence of Fe, Ni, and Cr metal particles, and also graphitic carbon in coke deposits, was confirmed by EDX analyses.

Jan 1, 2013

The AMIRA Code of Practice and Guidelines for Metal Accounting was developed in response to demand from a number of sponsor companies, including one major platinum producer. Since its publication in 2007, the Code has become widely accepted in the mining industry world-wide as a guide for best practice in metal accounting. With the changes in the structure of the platinum mining industry in South Africa over the last 10?15 years, in particular, the starting up of a number of small platinum producers who must have their concentrate smelted and the contained valuable metals refined by third parties, the need for metal accounting systems that are accurate and have an acceptable level of precision has become even more critical to the success of a platinum-producing operation. The current state of metal accounting in the industry is discussed, and possible areas for improved accounting and associated metallurgical efficiencies are identified.

Jan 1, 2013

By W. R. Hardwick

This paper describes mining methods and practices of the Chino Mines Division, Kennecott Copper Corp., Grant County, N. Mex. It is one of a series being prepared by the Bureau of Mines on mining methods, practices, and costs in various mining districts of the United States. A similar program was conducted from 1928 to 1939, which helped to improve the efficiency of mining operations. The primary purpose of the program is to promote development and conservation of our mineral resources by disseminating technologic information on methods, practices, and related features in mining mineral deposits. It is expected that the program will: (1) Promote efficiency in operating mines; (2) assist operators and engineers in evaluating and developing new mineral deposits; (3) provide data for engineering curriculums in mining schools; and (4) furnish performance and cost data for revising engineering handbooks and for inclusion in engineering textbooks.

Jan 1, 1958

By E. Mongilardi

The construction of large underground openings through cohesionless or weak cohesive soils and under the water table in particular, often requires a ground improvement to be done from the surface or ahead of the excavation face in tunnelling problems. To this purpose various injection procedures have been used in the past and new outstanding techniques have been developed recently, such as "jet-grouting", extending the feasibility range. The paper presents a review of basic principles and practical design criteria with particular reference to the newest trends of development. Case histories have been selected within the experience of specialist contractor Rodio Co. showing the variety of problems solved by manifold grouting procedures and layouts, in widely different soils ranging from the sandy-gravelly alluvia of Milan to the soft marine clays of Singapore.

Jan 1, 2010

By Trevor Hamm, Nick Holl

"Cameco Corporation is operator of the world's richest uranium project, the Key Lake mine/mill complex, located within the Athabasca region of Northern Saskatchewan. Mineable resources from the Key Lake ore bodies with an average U,08 content of 2.5% will be exhausted by the year 2000 and open pit mining at Key Lake will be phased out at that time. The mill will continue to operate at increased capacity, using high grade ore from the McArthur River project, a new underground mine at a distance of about 80 km from the Key Lake site. The McArthur River ore with an average U308 content of about 15 % will be blended with separately stockpiled low grade materials from Key Lake with a U,08 content of about 0.1 %. The average (blended) mill feed grade will be about 4%, similar to peak concentrations found in Key Lake ore.The Key Lake ore tailings are presently being placed in the mined out Deilmann pit under sub-aerial conditions, using spigots and a highly efficient pit/tailings drainage system. The tailings resulting from the processing of the blended McArthur River ore will be deposited on top of the Key Lake ore tailings under sub-aqueous conditions. This staged approach shows distinct technical and environmental advantages over an alternative, fully sub-aerial in-pit deposition scheme.The first part of this paper presents an overview of site specific geotechnical and hydrogeological features found at Key Lake and details some of the extensive test and modelling work that was required for environmental impact predictions during the development phase of the facility. The second part of this paper deals with tailings modifications, innovative placement technologies and drainage methods that have been (and will be) employed at the Deilmann Tailings Management Facility {TMF) to produce a highly consolidated tailings body under non-buoyancy conditions. The application of this technology at Key Lake is expected to produce a tailings ""plug"" in the Deilmann TMF which will have a permeability similar to or lower than the original in-situ Deilmann ore, resulting in a minimization of contaminant mass loadings to the environment both during operation and after decommissioning."

Jan 1, 1998

By John J. Mulligan

The Bureau of Mines investigated the tin deposits of the Cape Mountain area during July and August 1962 to test the effectiveness of detrital-cover sampling in permafrost areas as a relatively cheap and simple means of guiding mine development and exploration. Results indicate that systematic detrita1-cover sampling can be used effectively to delineate obscure deposits with sufficient accuracy to permit sampling with a minimum of trenching or drilling. Extensions of known outcroppings were traced in sufficient detail to guide lode sampling and several previously unknown tin-bearing lodes were found and sampled. Lode sampling was limited to the minimum needed to establish the reliability of detrital-cover sampling results. The results of previous lode and placer investigations are summarized and detrital-cover sampling methods and results are described in detail.

Jan 1, 1966

By R. A. Wattenbarger, H. J. Ramey

The trend in gas well testing has been to rely more on the early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modern gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks. It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore. Russell and Truittl published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark2 applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis. The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz3 presented the drawdown equations for *Now with Scientific Software Corp., Denver. ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice. Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore. The Mathematical Model The geometry of our mathematical model is similar to that used by Prats.4 The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through the wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model. The equation for the flow of real gas in a porous medium with uniform porosity, permeability and thickness is5-7

Jan 1, 1970