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By R. E. Hummel, J. W. Koger

IT is generally accepted that the martensitic start temperature (Ms) can be determined by resistivity measurements and is that temperature where the resistivity vs temperature curve on cooling first deviates from a straight line.1-4 Both Titchener and ever' and pops5 have used resistivity measurements to follow the martensitic transformation in b1 Cu-Zn and ternary Cu-Zn-based b-phase alloys, respectively. Actually because of the nature of their measurements the temperature of minimum resistivity (M) was used by these authors to determine "Ms" . Also, due to experimental difficulties in detecting M, with resistivity measurements, Pops and Massalski 8 determined M, by optical microscopy. The present communication is concerned with high-precision, low-temperature resistivity measurements which reveal a definite M, temperature which differs from the temperature of minimum resistivity (M). It is also shown that M is merely the result of the geometry of the percent-transformation curve and the temperature coefficient of resistivity of the alloy. In other words, it will be demonstrated that M has no apparent significance (except that it denotes a temperature at which some percent of martensite can be detected in a given alloy). Alloy specimens were made by melting 99.999 pct Cu and 99.9999 pct Zn in sealed and evacuated quartz tubes and homogenizing them at 601PC for 300 hr. After the alloy was cold-rolled into foils suitable for resistivity measurements, it was quenched in ice water from 871PC. The chemical analysis showed a zinc content of 38.8 wt pct. The cooling rate during the martensite transformation was 1°C per min and was controlled with a thermistor. Electrical resistivity measurements were made using a K-3 type potentiometer; the reproducibility of the resistivity values was better than 0.03 pct. Temperatures were measured with a thermocouple to an accuracy of better than 0.2° C. Fig. 1 shows the resistivity vs temperature curves of the martensitic transformation in B1 Cu-Zn for both cooling and heating. The starting point of the martensitic transformation (M,) was taken as that

Jan 1, 1968

By H Arvidson, C Morley

Reconciliation has become very topical over the last ten years but how do we distinguish what is good practice, and even more importantly, show how it adds value? Reconciliation at Anglo American has received support from the very top of the company and this has enabled success in the design and implementation of a range of processes, reporting activities and actions. Focus has been on full Mine Value Chain Reconciliation (MVCR) from Resource to Product and on proactive cross-functional engagement. A standardised set of reconciliation definitions and relationships are used at all mines across the company to diagnose planning and performance issues. Results are formally presented in an efficient dashboard format, accompanied by a concise narrative to communicate what has been learned and what is being done to correct, improve or change practices. Importantly, effort has also been made to sustain MVCR by embedding good practice and quantifying the benefit of reconciliation explicitly via linking results to value.This paper sets out the lessons learned from the past two-years’ journey, highlighting areas where good practice has been defined and achieved. A ranking for quantifying reconciliation confidence over time is presented as a means of putting results into context and continuously improving the reconciliation process. Finally, a solution to define the value that can be derived from reconciliation is described, detailing how cross-functional personnel meet monthly to review results and implement actions that are tracked in terms of value creation.CITATION:Morley, C and Arvidson, H, 2017. Mine value chain reconciliation – demonstrating value through best practice, in Proceedings Tenth International Mining Geology Conference 2017, pp 103–116 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 20, 2017

By G. Krogman, C. Walla, B. Wood

The Gebo Mining District (District) is located in the Bighorn Basin of Wyoming. Commercial underground coal mining began in 1906 with the arrival of the railroad in Thermopolis, which is located approximately 11 miles to the south. Mining in the District ceased by the early 1970’s. In Fall of 1999, Lidstone and Associates, Inc. (LA) and their subcontractors were retained by the Wyoming Abandoned Mine Land Division (WyAML) to perform an inventory of over 500 abandoned mine sites across Wyoming. During the summer of 2000 field inventory, a 30-foot deep headcut (Figure 1) and sink-hole were noted in the West Fork of Sand Draw (WFSD), immediately west of the Town of Gebo. The headcut and sink-hole were located at the culvert outfall associated with a stream crossing of a relatively well traveled county road. Upon further investigation, it appeared that underground mine workings had been exposed at this location. This resulted in a condition whereby water would be conveyed directly into the mine workings during a runoff event. The exposed mine workings as well as stream capture created a very hazardous condition. The WyAML implemented mitigation measures in the summer of 2000 by constructing a temporary stream crossing upstream of the existing failed crossing. To address this hazardous situation as well as a number of other hazards identified in the District during the field inventory, the WyAML retained PHC Reclamation, Inc. (PHC). PHC was directed to perform a field investigation and develop a Reclamation Plan to address all existing abandoned mine hazards in the District. Federal, state, and private parties own lands within the District. Hazards identified during the investigation included an underground mine fire, open adits, open shafts, subsidence, drainage problems, and coal slack. A Report of Investigation (ROI) was submitted to various regulatory agencies that documented the existing conditions and conceptual reclamation plans to remediate the hazardous conditions. After review of the ROI by the US Department of Interior - Bureau of Land Management (BLM) an on-site meeting was conducted. BLM Cultural Resource personnel declined to approve a District reclamation project until a historical overview of the entire District was prepared. Due to the hazardous situation associated with the WFSD stream crossing, Hot Springs County Road and Bridge Department convinced various state and federal regulatory agencies to allow reclamation of the stream crossing to occur. A decision was made to allow reclamation on privately owned lands within the WFSD drainage. This decision limited the amount of channel that could be subjected to reclamation upstream of the crossing to privately owned lands. PHC contracted LA to perform a geologic, geomorphic, hydrologic, and hydraulic investigation of the drainage to assist in the development of a WFSD reclamation plan. LA’s investigation consisted of four parts: Delineate the extent of mine workings in the area; Identify all drainage structures that required mitigation; Survey a series of channel cross-sections and a longitudinal profile of the impacted channel; and, Develop basin hydrology to assist in the design of a stable reclaimed stream channel.

Jan 1, 2006

By H. Naghavi, M. Karimi

"In self-aerated flotation machines, the gas rate depends on operational variables (e.g. froth depth and impeller speed), pulp properties (e.g. solid content and viscosity), and reagent addition (e.g. type and concentration of frother). The gas rate has a strong correlation with the flotation performance by influencing the gas dispersion properties and froth retention time. A factorial experimental design was used to study how the gas dispersion properties, the froth retention time, and the flotation performance respond to changes in froth depth and impeller speed (as the most common operational variables). An in-depth understanding of the effects of impeller speed and froth depth on the gas dispersion properties, especially the bubble surface area flux and froth retention time, is necessary to improve operating strategies for self-aerated flotation machines. All experiments were carried out in a 50 m3 selfaerated flotation cell in an iron ore processing plant. The results showed that the froth depth affected the metallurgical performance mostly via changing the froth retention time. The impeller speed had two important impacts on the metallurgical performance via varying both the froth retention time and the bubble surface area flux in the froth and pulp zones, respectively. The interaction effects of the froth depth and impeller speed were also established. This allowed us to develop a strategy for operating selfaerated flotation machines based on varying the froth depth and impeller speed with regard to the cell duty. IntroductionA mechanical flotation machine may be divided into two distinct zones. namely the pulp zone and the froth zone (Goodall and O’Connor, 1989; Yianatos, Bergh, and Cortes, 1998; Rahman, Ata, and Jameson, 2015a, 2015b). The overall flotation recovery, Ro, including the true flotation (particles attached to the bubble lamellae) and entrainment (particles recovered in water held in the bubble plateau boundaries), is a function of the recoveries in the two zones. It is calculated as follows (Dobby, 1984):"

Jul 1, 2019

By R. P. Maloney

Since mining operations began in 1900, Government geologists and mining men have periodically recorded the presence of the minerals of mercury and antimony in the extensive gold placer deposits near Flat in the Iditarod district of the Yukon River region, Alaska. No serious effort was made to recover the cinnabar contained in the gold placer gravels, and there is no evidence that veins of cinnabar and stibnite exposed in the placer operations (as reported by the Geological Survey) were ever explored or developed. A large monzonitic intrusive, which is the dominant geologic feature of the immediate area, is believed to be the lode source of the valuable minerals in the placer deposits. In contact with the monzonite are argillite and quartzite, metamorphic products from the Cretaceous shales and sandstones.

Jan 1, 1962

The Autogenous Fine Grinding Kelsey Axial Displacement (KAD) Mill The marginal improvements which continue to be made to fine grinding practices have exposed the limits of conventional technologies and highlighted the need for a radically new approach. The patented autogenous Kelsey Axial Displacement (KAD) Mill design consists of a rotating spherical grinding chamber, which shares the same spherical centre as the shaft-mounted counter-rotating disc assembly. The axis of the disc assembly can be inclined to the axis of the spherical grinding chamber by pivoting the disc shaft about the common spherical centre. The inter-particle energy transfer required for breakage results from particle velocity differentials created by the discs intercepting the rotating mass. Particle size reduction is concentrated in high shear zones, which envelop the outer surface and periphery of the discs. This paper traces the development of the KAD Mill from pilot to commercial scale. Pilot work covers a range of minerals including magnetite, calcite, dolomite, barite, limestone and talc. Test results include open and closed circuit operation in wet and dry modes. Conventional milling constraints and energy consumption issues are addressed while new dimensions are added to the feed size range acceptable for wet and dry grinding to fine and ultra-fine sizes.

Sep 13, 2010

By Monika Patrycja Polak - Micewicz

This paper presents an approach for estimating the fatigue life for the base of powered roof supports (shield) manufactured by the FAZOS roof support company. FAZOS?s powered roof supports are designed to operate on an inclined coal seam in full caving with a medium, strong roof strength. This shield support is utilized in conjunction with a shearer and face conveyor for a complete longwall mining system. To design shield support, it is essential for contractor to know the physical (hardness, toughness, etc.) and mechanical properties of material (tensile strength, Young?s modulus, etc.) used for the shield support as well as the geotechnical properties of the mine site. The fatigue strength of the shield support material depends on the mean stress, alternating stress, cycle frequency, transport dimensions, mine environment and other factors. In order to estimate the fatigue life for a powered roof support system, it is assumed in this paper that the support must keep the roof stable in the mine under variable load cycles. The approach selected in this study contains Goodman?s model (Goodman, 1899) for all blocks in the design housing which is subjected to sinusoidal load. On this basis, the degree of fatigue damage was calculated and compared to the results of experimental tests. It will be shown that there is a significant detrimental effect on the fatigue life of the base of the powered roof supports due to geometrical notches. The Ramberg-Osgood model and damage accumulation rule (Palmgren-Miner) (Miner M., 1945) were used and numerical analyses were conducted, utilizing ANSYS finite element software. These analyses play a very important role in longwall casing design. The proposed method allows assessment of the yield state and forecast of the structure cracking, taking plastic strains occurrence into account. The presented method is universal and can be applied for fatigue life estimation of other subassemblies of powered roof supports. The final portion of the paper presents results of variable amplitude loading simulations on the S355N and S690Q steel used to make powered roof supports. The results of the physical tests were compared with the results from finite element methods. The proposed approach to calculate fatigue life gives the best correlation between the experimental results and calculated values of fatigue life for the powered roof support base. Finally, the design process uses a simple approach to predict fatigue life in a short time, reducing design costs and providing longer service life for roof supports.

Jan 1, 2012

By Wolfgang Roth

In 1990, a residential area above the North Outfall Sewer (NOS) tunnel constructed in 1924, experienced subsidence. After sewage was diverted into the North Outfall Replacement Sewer (NORS), soil probing from within the tunnel was conducted, soil-improvement options were developed, and a preferred grouting scheme was analyzed by numerical modeling to evaluate the stability of the 80-year+ old tunnel liner under grouting-induced loading conditions. This paper discusses the initial field investigation and the development and analysis of a grouting scheme originally intended to be implemented before relining of the tunnel. The scheme was later modified, and the new liner was installed before the final probing and grouting work was done.

Jan 1, 2008

By A. Taylor, M. Blanchette, J. Doucet

"A Z1600 Jameson Cell Test Rig was rented for test work at Vale’s Clarabelle Mill operation. This paper discusses the evolution of renting the unit for test purposes to owning the unit and operating it as a revenue generating process component. The paper focuses on three aspects of the Z1600 project; the initial rental and installation, the test work performed in the cleaning circuit, and the business factors which led to the unit being permanently incorporated into the copper circuit.INTRODUCTION Clarabelle Mill is located in Sudbury Ontario (approximately 350 km north of Toronto) on the southwest rim of the Sudbury basin a meteoric impact crater that is 62 km long and 30 km wide. The result of the meteoric impact was concentrated nickel (Ni), copper (Cu) and platinum group metal (PGM) ore bodies in the outer perimeter of the basin; described in more detail by Hanley (1957). Vale currently has seven operating mines in the Sudbury basin, from which nine distinct ore types are mined. Ores are also received from two QuadraFNX mines. Clarabelle Mill processes all of these ores for the Ontario Operations of Vale. The mill, commissioned in 1971, was originally built as one of four mills operated by then Inco Limited. Between the late 70’s and the early 90’s process changes were made to consolidate the Sudbury Operations milling processes into a single operating mill, Clarabelle Mill. In 1990, the SAG mill was installed resulting in peak mill throughput of 11.9 million short tons per annum (Mstpa), with typical throughputs of ~10 Mstpa. Mill average feed grades were 1.4% Cu and 1.2% Ni. During the resources boom, plans were developed to increase the mill capacity at Clarabelle Mill in stages to a final capacity of 13.5 Mstpa. The project known as the Clarabelle Mill Expansion and Recovery Project (CMERP) included expansion and reconfiguration of the grinding and flotation circuits. The first stage was a planned increase in grinding capacity with the reallocation of existing mills, the existing flotation capacity would be required to treat higher throughput until the new flotation circuit was constructed."

Jan 1, 2012

By M Hourn, D Turner, P Voigt, D Mallah

The GPM Gold Project is located in Armenia, and consists of an open cut mine at Zod, near the Azerbaijan border, and a CIL processing plant at Ararat near the Turkish border. Mining at Zod commenced in 1976, and focused on near surface oxide ores, which overlay deeper refractory sulphides. Historical mining has now almost depleted the oxide ores, and the sulphide content of ore delivered to the processing plant at Ararat is increasing. Gold and silver recoveries through the Ararat plant were declining steadily.GeoProMining, the owners of the project, have expanded the Ararat facility to deal with the increasing sulphide content in the ore. In 2014, GeoProMining refurbished an existing concentrator on site to recover a sulphide concentrate from the ore, and have constructed an Albion ProcessTM plant to oxidize the refractory concentrate. Glencore Technology (GT) provided the Albion ProcessTM plant as a technology package.In July 2014, the progress of the GPM Gold Project Albion ProcessTM Plant was reported (Hourn, Voigt and Turner, 2014). At the time of writing, the construction of the plant was nearly complete. This paper presents an update of project progress, covering commissioning and ramp up of the GPM Gold Project.The commissioning phase occurred over June to August 2014, which included an M3,000 IsaMillTM fine grinding plant, a 6 tph limestone milling plant, a 60 tpd vacuum pressure swing adsorption oxygen plant, a 10 m residue thickener and a 12 tph Albion ProcessTM oxidative leach plant. Since commissioning was completed, ramp up occurred over the following three months with downstream gold recoveries from cyanide leaching reaching over 98%.CITATION:Voigt, P, Hourn, M, Mallah, D and Turner, D, 2015. Commissioning and ramp-up of the Albion Process at the GPM Gold Project, in Proceedings MetPlant 2015, pp 207–219 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 7, 2015

By M. Drozd, M. Somppi, Z. Yamak

"Granular activated carbon is widely used in the gold mining industry for gold extraction from aurocyanide-containing slurry. The extraction process can employ carbon as part of the gold recovery operation for various circuit designs including carbon-in-pulp (CIP), carbon-in-column (CIC), and carbon-in-leach (CIL) circuits. However, various qualities of activated carbon exist and the durability of the material can change significantly from source to source. Handling this expensive reagent can pose challenges when fine carbon losses occur in the CIP, CIC, and CIL circuits. Additionally, any gold that is adsorbed to these carbon fines can also be lost by various mechanisms including carbon attrition and fracturing, inefficient coarse-fine separation, and poor carbon fines capture. With the above in mind, a series of tests were conducted to investigate standardizing simple laboratory methods for testing carbon quality. A standard procedure beyond or enhancing ASTM methods can serve as additional starting points for evaluating carbon specific to the gold industry. The investigation focused on size distribution, flatness, wet attrition resistance, surface area, gold kinetics, and gold loading. The final results provided information to generate an equation for ranking carbon samples to plant performance.IntroductionActivated carbon for use in gold extraction is amongst the most commonly found processes in modern gold-milling plants. Although gold losses are inevitable in the milling process, operators often focus on the importance of maximizing gold recovery. One focus area that is important in gold recovery is optimizing the use of activated carbon and examining potential changes to realize improved economics for carbon-in-pulp (CIP), carbon-in-column (CIC), and carbon-in-leach (CIL) processes."

Jan 1, 2017

By D Craw, P Upton

"An EXTENDED ABSTRACT is available for download. A full-length paper was not prepared for this presentation. The Otago Schist belt of southern New Zealand hosts widespread orogenic gold deposits. Erosion of these orogenic gold deposits has led to the formation of numerous placer deposits distributed across and beyond the host schist belt. Numerical modelling of crustal scale deformation and geomorphic evolution has defined the key tectonic features that have controlled the severance of detrital gold deposits from their sources. Tectonic activity over the past 20 million years, during development of the modern Pacific-Australian plate boundary, has severed links between some placers and their sources. Detrital gold was transported south from the Otago Schist source region in two different river systems in the Miocene. Mesozoic orogenic gold deposits shed gold into rivers that flowed to the south. These rivers were terminated by the rise of north-west-trending basement ridges at the boundary between weak schist crust and strong greywacke crust, and the ridges were controlled by pre-existing faults at that rheological boundary. In contrast, rising mountains close to the developing plate boundary in the Miocene were the locus of new orogenic gold deposits hosted in extensional faults. These gold deposits were rapidly exhumed and contributed detrital gold to orogen-parallel Miocene rivers that flowed to the south-west. Pleistocene deformation on mainly north-west and north-east orientations, and associated river capture, has severed the links between these Miocene orogenic deposits and downstream detrital gold.CITATION:Craw, D and Upton, P, 2015. Tectonic severance of links between placer gold and its sources, southern New Zealand , in Proceedings PACRIM 2015 Congress, pp 541–544 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 18, 2015

The design/optimization of the pump and cyclones to maximize grinding circuit efficiency first requires a concise understanding of, and clearly defined specifications for, desired grinding circuit performance. Subsequently, the pump and cyclone performances that provide the desired grinding circuit performance can be defined. Once the performance requirements of each process unit are determined, selection of physical equipment parameters that will deliver those performances can be carried out. The Functional Performance Equation shows that there are two distinct efficiencies in closed circuit ball milling. One of these, ?Circuit Classification System Efficiency? (CSE), is the fraction of ?coarse? material inside the ball mill upon which grinding energy is deliberately expended, versus the remaining fraction of ?fines? or finished size material inside the mill, upon which grinding energy is wasted (on over-grinding). The role of the pump and cyclones is to maximize CSE, which is the desired grinding circuit performance. The obtainable, target CSE for any given circuit can be estimated, for example by referring to a plant data base of CSE?s. Design/optimization guidelines then allow us to specify the pump and cyclone performances that will achieve the target CSE. This paper outlines the step-by-step, systematic method of pump and cyclone selection which maximizes CSE. Numerous examples of its successful application are provided.

Jan 1, 2011

The Mount Lyell Mining Field is Australia's chief productive source of copper. It is situated near Queenstown, on the western flanks of the West Coast Ranges, about 20 miles from the west coast of Tasmania (Fig. 1).The following observations on the mineral composition of the copper ores of the Mount Lyell Field are based on a...

Jan 1, 1939

By D. H. Zellers

Since its inception the United States Bureau of Mines has fostered the development of portable mine lamps. Although there is still much to be desired with respect to illumination in coal and metal mines and the replacement of open lights has been slow the Bureau has been given credit for assisting materially in the development and introduction of the safe and efficient portable mine-lighting equipment available today. Much of the work conducted by the electrical section of the Bureau entails approval tests of various types of electrical equipment, including lamps; to be used in atmospheres that may contain methane or coal dust in explosive proportion. If a can lamp meets the requirements-for safety, efficiency, and adequacy, as published in Schedule 6B,4 it is approved and is generally known as a "permissible" lamp. The terms "approved" and '"permissible' often are used interchangeably. The manufacturer must put an approval plate on each approved lamp, showing it has mot the schedule requirements. The approval plate is not a guarantee that the lamp is safe. However, if the lamp, once in service, has not had any parts changed or improperly assembled or if carts that wear out or depreciate have been properly replaced it should still, be safe, efficient, and adequate for the service intended. Virtually all electric cap lamps in service today in the United States and a great many that have been sent to foreign countries bear the approval plate of the United States Bureau of Mines. Although many explosions have been attributed to open lights none has been charged against the permissible cap lamp. Nystagmus, a disease of the eye attributed to working under insufficient illumination, is practically unknown among; American miners, although it is quite prevalent among European miners.

Jan 1, 1935

By Thomas W. Camm

This study was done to evaluate the costs of various dumping operations at waste and spoil piles. It has been theorized that accidents associated with dumping operations might be reduced by short-dumping rather than edge-dumping, but many operators have been reluctant to use short-dumping because they believe it is not as cost effective as edge-dumping. To evaluate this perception, researchers at the Spokane Research Laboratory of the National Institute for Occupational Safety and Health reviewed the costs of various dumping methods at waste and spoil piles. The study found that overall cost differences between the two methods were not significant in most cases. However, while overall cost differences between the two methods appear small, capital costs could be more significant when short-dumping if numerous dump sites are used concurrently. The choice of which method to use should be based on considerations of the safety of dozer and truck operators.

Jan 1, 2000

The purpose of this report is to describe the work accomplished by Mine Safety Appliances Company under Contract No. H0110845. This contract required the design, installation and testing of a permissible mine surveillance and communication system for the USBM Bruceton experimental mine facility. While much of the design and operational detail of this system can be drawn from the instruction manuals delivered with the equipment, some of it will be repeated here in Volume I for the sake of clarity, but the principal objective will be to report on overall system and subsystem performance and to suggest design alternatives for future consideration. Details of the overall system design will be found in Volume II of this report.

Jan 1, 1973

By Julian Prada

Tunneling requirements are presenting designers with greater challenges. The design and construction of the 2000-ft long unidirectional twin highway tunnels for the approach to one of two bridges of the Louisville-Southern Indiana Ohio River Bridges (LSIORB) Project is no exception. Excavation under low cover, beneath an historic site, with each tunnel of 70-feet wide and 50-feet high dimensions will set precedents for US highway tunnel excavation size. To investigate ground conditions to supplement final design of the highway tunnels, an exploratory tunnel excavated through karstic limestone and shale will be located within the confines of the proposed final alignment. With the LSIORB Project, Jefferson County, Kentucky and Clark County, Indiana will have improved cross-river mobility between them. The Indiana Department of Transportation (INDOT) and the Kentucky Transportation Cabinet (KYTC) are developing the LSIORB Project jointly, in coordination with the Federal Highway Administration (FHWA). Section 4, one of six sections, as shown in Figure 1 is the East End Kentucky Approach and Connections to I-265. Key elements of Section 4 are the twin three-lane highway tunnels under the historic Drumanard Estate. The property is located on the north side of US Highway 42 (US 42) at the intersection with the Gene Snyder Freeway (also KY841) as shown in Figure 2. One aspect of the project consists of the excavation of an Exploratory Tunnel along the southbound alignment tunnel. At the time of preparation of this paper, KYTC has not awarded the Exploratory Tunnel Contract. This paper will focus on the planned geotechnical investigation program that will occur during excavation of the exploratory tunnel and how the design of the twin highway tunnels will incorporate the findings to achieve an innovative and efficient configuration.

Jan 1, 2008

By A. Moergeli

The Swiss are currently building the world’s longest tunnel, the 35-mile long Gotthard Base Tunnel. At Sedrun, for the first time in tunneling, four Roadway Support Machines will drive through most difficult ground, supporting variable diameters of up to 13 m. The machines are prepared for their first deployment. At Amsteg, two Hard Rock TBMs have successfully crossed a known fault zone by applying full circle steel arches and shotcrete immediately behind the cutter head. Comparisons between Drill& Blast and Hard Rock TBM are shown.

Jan 1, 2005

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970