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By Naum S. Malts, Victor M. Sizyakov, Nikolai S. Shmorgunenko

A method has been developed in the USSR for processing the low-grade high-silica raw material by sintering the aluminacontaining mixes, which is widely used both as a principal process and in combination with the Bayer process. The process parameters were obtained on the basis of a study of interaction and equilibrium states of the individual profiles of a multi-component system Na20-A1203-Fe203-CaO-Si02 at the sintering temperatures. The compositions and melting temperatures of eutectics of the individual profiles are given. It is shown that the most easily meltable mix is one having a red mud as the main component. The variations are given of the sinter physical characteristics and recovery of the useful components with the sintering temperature. Considerations are given on selection of a sinter leaching flowsheet and directions are shown for improving a series method of processing the low-grade raw material.

Jan 1, 1984

By P. E. Snoek, R. L. Gandhi, C. S. Miller

Slurry operations are an integral part of mineral processing. There is therefore reason to consider using slurry pipelines for long distance mineral transportation. This paper reviews the current state-of-the art of such systems and, in particular, the design factors which must be addressed. It also discusses the selection of major components such as pipe, pumps, valves and storage facilities. Finally, the major steps required to determine the economic feasibility of a slurry system are listed and the major advantages and disadvantages of slurry pipelines compared with other forms of land transport are summarized. SLURRY PIPELINES: GENERAL OVERVIEW Minerals Transported Long distance slurry pipelines have been successfully used for transporting coal, iron concentrate, copper concentrate, limestone and phosphate. Additionally, several tailings disposal pipelines of considerable size and length have been built, but these generally are not categorized as long distance commercial mineral transportation systems. Table 1 lists selected examples of commercial slurry pipelines.

Jan 1, 1986

By Stefano Colombelli, Nicola Bona, Gabriele Eccher, Luca Schiavinato, Paolo Cucino, Domenico Nave

"BIM technologies provide tools and processes to effectively support the entire life of an infrastructure, from strategic planning to maintenance. As a consequence, infrastructure design processes currently make frequent use of BIM tools. This paper describes the BIM oriented design of the underground railway extension in the metropolitan area of Catania. The paper highlights the design process and the chosen BIM tools considering the boundary conditions characterizing the project, i.e. basic information missing in the final design project, need of coordination between different design disciplines and designer companies, and, finally, need for a flexible design approach able to adapt to changes occurring during design development. INTRODUCTION The underground railway extension in the metropolitan area of Catania is composed of two lots of approximately two km each, namely “Stesicoro-Aeroporto” and “Nesima –Misterbianco”. Works to be realized are: •,Main tunnel: mechanized tunneling using a TBM-EPB machine, for the entire length of the lot; •,Underground stations: San Domenico, Vittorio Emanuele and Palestro, conventionally excavated as enlargement of the TBM tunnel after the partial demolition of precast segments; •,Ventilation and emergency shafts: connecting seven tunnel levels to road level on Stesicoro-Areaposto lot, six on Nesima-Misterbianco lot; •,Additional structures such as technical rooms and parking lot; •,Electric Substation at Monte Po' stop; •,Temporary works: TBM launching and arrival pit to be dismantled at the end of the works."

Jan 1, 2016

By Jake Beale, Joe Wickline, M. Van Dyke, Ted M. Klemetti

A longwall coal mine in southwestern Virginia mining the Pocahontas #3 Coal Seam experienced a history of mining-related seismic events. The events were never large enough to cause concern until three major events occurred recording 3.4, 4.3, and 3.4 ML in 2005, 2006, and 2007 respectively. Two of the seismic events generated an air blast which damaged stoppings which fueled a mine fire in 2005 and 2007. The mine responded to the events by narrowing the longwall widths, changing ventilation controls, installing a 7-sensor seismic system around the active panel, and creating a mining hazard map to avoid similar geology in the future. All of the actions taken have prevented seismic activity from impacting mining operations, but it did not prevent other large seismic events from occurring (Van Dyke et al., 2018). In 2016, another large seismic event, measured at 3.7 ML, occurred in the gob that was reported by the local media and recorded by the United States Geological Survey (USGS). While the event did not directly impact mining operations, mine management wanted to know where and under what conditions could large seismic events occur in the future. The National Institute for Occupational Safety and Health (NIOSH) became involved to help understand what conditions precipitated these events so that future mine design could more accurately assess seismic hazards and reduce the risk to mine worker safety. Researchers at NIOSH and mine management created a seismic forecasting map that combined three factors: (1) overburden thickness, (2) sandstone thickness, and (3) the expected caving height of the gob. The criteria were developed based on the geologic data the mine collected from core drilling, e-log analysis, and fiberscope observations. The forecast map was able to provide an accuracy of 72%–85% of events 1.5 ML or greater and 100% accuracy of events that were 3.0 ML or greater based on historical data. The seismic forecasting map was applied to the entire future mining area to show areas where seismic potential could be the greatest based on current mine design planning, ultimately improving the ability of the mine operator to assess the seismic hazards surrounding active and future mining areas (Van Dyke et al. 2018). Following this research, the seismic forecasting map was implemented into the mine’s hazard recognition program and is continuously updated and evaluated prior to mining each longwall panel. This paper will cover in more detail how the seismic and lithologic data was processed and how the mine implemented a new seismic mitigation program based on the forecasting results.

Apr 26, 2022

By S. M. Hossaini, M. Ataei, H. Moosavi

The abstract highlights the importance of pillar stability in underground coal mines and the influence of rock mass strength and joint orientation on pillar behavior. The study employs numerical modeling using the distinct element code (UDEC) to investigate the impact of these factors on pillar stability. The research considers different joint orientations and varying rock mass strengths, analyzing parameters like stress distribution, displacement, and failure patterns. The findings reveal that both joint orientation and rock mass strength significantly affect pillar stability, with specific combinations leading to reduced safety factors and increased deformation. The study concludes by emphasizing the importance of considering these factors in pillar design for safe and efficient mining operations.

Apr 4, 2022

By R. Y. Wan

Newmont Gold has advantageously used the capabilities of mineral oxidizing bacteria to develop a process for the pretreatment of low-grade sulfidic and carbonaceous-sulfidic refractory gold ores. The biooxidation process results in the oxidation of the sulfidic minerals with increased exposure of gold for subsequent gold recovery. The biooxidized carbonaceous-sulfidic ores cannot be heap leached with cyanide because of the preg-robbing characteristics of the carbonaceous matter in the ores. Therefore, an alternative heapleach process using ammonium thiosulfate was developed to extract gold from these preg-robbing bioaxidized ores. The ammonium thiosulfate leach process was successfully applied in both laboratory and pilot plant tests. Satisfactory test results were achieved, encouraging the continuation of process development.

Jan 1, 1997

By Norbert Patzelt

Today the standard method for grinding ore is the wet process. This is mainly due to the fact that the downstream process is wet and considering the total circuit dry grinding is not the most eco­nomical method for the comminution of the ore. Presently in gold ore processing dry grinding is only applied in cases where whole ore roasting is required downstream from the milling plant or if organic carbonaceous matters and sulfides are the primary reasons for the refractoriness. Since dry ore can be fed to the roaster, a dry grinding mill can advantageously be applied. In cases where d1y grinding could be applied advantageously for instance if the ore contains water soluble material and wet grinding is not possible there are serious concerns prevailing within the industty against this technology due to several reasons. Besides of the aspects as discussed later in this paper, there are several plants in operation with little success and considerable operational prob­lems. The reasons for this often lie in the fact that the several com­ponents of such a plant are bought from independent sources with­out considering the system requirements. It is essential that the dry grinding plants require accurate design between drying, pneumatic transport and grinding of the ore in the circuit. This paper will address some of these concerns raised in the industiy from a mill vendor's view along with discussing the development for the selection and configuration of the various dty grinding circuits.

Jan 1, 1998

By W. S. Fyfe, R. J. Puddephatt, S. Zhou

Gold is easily mobilized at temperatures within range 600-11OO°C by gases such as Cl2, CO, H2S, in gas mixtures, at low pressures. Such gases are relevant to conditions of granulite facies metaomorphism in environments of magma underplating. These observations suggest an efficient mechanism for moving gold to the upper crust during major thermal events. The efficiency of precipitation of gold at lower temperatures is related to available mineral surfaces and pyrite appears to be an excellent substrate for gold precipitation.

Jan 1, 1989

By Harold B. Goldman

On the basis of tonnage, the sand and gravel industry is the second largest nonfuel mineral industry in the United States. In 1990, the production of sand and gravel was 927 Mt valued at $3.4 billion. California, which leads the nation with more than 126 Mt, together with Texas, Washington, Michigan, and Ohio, account for 36% of the total production in the nation (Table 1). In commercial usage, sand applies to rock or mineral fragments ranging in size from particles retained on a No. 200 Sieve (0.074 mm openings) to those passing a No. 4 Sieve (4.76 mm openings). Gravel consists of rock or mineral fragments larger than 4.76 mm, ranging up to 88.9 mm maximum size. The construction industry consumes 97% of the sand and gravel produced; the remainder is sand used for specialized products such as glass (see chapter on Industrial Sand and Sandstone and Glass Raw Materials). Utilization The building industry uses sand and gravel chiefly as aggregate in portland cement concrete, mortar, and plaster; the paving industry uses sand and gravel in both asphaltic mixtures and portland cement concrete. Aggregate is commonly designated as the inert fragmental material that is bound into a conglomerate mass by a cementing material such as portland cement, asphalt, or gypsum plaster. Sand and gravel is also used as construction fill, road base and subbase, and decorative material. Portland Cement Concrete Aggregates: Portland cement concrete consists of sand and gravel surrounded and held together by hardened portland cement paste. Concrete mixes commonly contain 15 to 20% water, 7 to 14% cement, and66 to 78% aggregate. Sand and gravel used as concrete aggregate have to meet many requirements (Goldman and Reining, 1983). Premature deterioration of concrete has been traced in many instances to the use of unsuitable aggregates. Asphaltic Aggregate: Asphaltic mixtures used predominantly for paving consist of combinations of sand, gravel, and mineral filler (material finer than 0.076 mm), uniformly coated and mixed with asphalt produced in the refining of petroleum. Sand and gravel used as asphaltic aggregate must meet the same general physical requirements as materials used for portland cement aggregate. GEOLOGY General Requirements of Aggregates Construction aggregate has many requirements that are difficult to meet if only unprocessed material from natural deposits is used. Suitable material is composed of clean, uncoated, properly shaped particles that are sound and durable. Soundness and durability are terms used to denote the ability of aggregates to retain a uniform physical and chemical state over a long period of time so as not to disintegrate when exposed to weathering and other destructive processes. Individual particles must be tough and firm, possessing the strength to resist physical stresses and chemical and physical changes, that may cause swelling, cracking, softening, and leaching. The aggregate should not be contaminated by excessive clayey material, silt, mica, organic matter, chemical salts, and surface coatings. Physical Properties: The quality of aggregate depends upon its physical and chemical properties. These, in turn, may be inherent mineralogical and textural features of the rock or may be the effects of later changes such as tectonics, mechanical or chemical weathering, or incrustations. The physical properties most significant for concrete use are: 1) abundance and nature of fractures and pores, 2) particle shape and surface texture, and 3) volume changes which may occur because of freezing and thawing or wetting and drying. An aggregate is considered to be physically sound if it is adequately strong and capable of resisting the agencies of weathering without disruption or decomposition. Minerals or rock particles that are physically weak, extremely water absorptive, and easily cleavable are susceptible to breakdown. The use of such materials in concrete reduces strength or leads to early deterioration by promoting weak bond between cement and aggregate, or by inducing cracking, spalling, or popouts. Severely weathered, soft, micaceous, or porous materials may cause localized stresses to develop in concrete by swelling and shrinking during wetting and drying or freezing and thawing cycles. Physical Suitability of the Various Rock Types. Sedimentary rocks have a wide range in physical and chemical qualities. Sand- stones and limestones, if hard and dense, are ordinarily satisfactory, but many sandstones are friable and excessively porous and commonly are clay-bearing. Shales generally make poor aggregate material, being soft, weak, and absorptive. Most igneous rocks are satisfactory, being normally hard, tough, and dense. Tuffs and certain flow rocks may be extremely porous and have high water absorption and low strength. Metamorphic rocks differ in character. Most quartzites are massive, tough, and dense. Fine-grained marbles are usually durable, but coarse-grained marbles have low abrasion resistance. Gneisses are ordinarily very tough and durable. Some schists contain micaceous minerals that are undesirable because they are soft, laminated, and absorptive. Micaceous minerals are susceptible to splitting along cleavage planes and thereby impair particle strength and durability. Some schists and slates in particular are thinly laminated and tend to assume flat slabby shapes that lack strength-and do not pack well. Any or all of these rock types may be rendered undesirable because of harmful exterior coatings. Weathering processes, particularly the action of ground waters, deposit these coatings. The most common coatings are calcium carbonate, clay, silt, opal, chalcedony, iron oxide, manganese oxide, and gypsum. Particles with these coatings are undesirable as aggregates because the bond between particle and coating may be weak, and decreasing the strength of the aggregate-cement bond.

Jan 1, 1994

By John A. Herbst, K. Rajamani

Process improvement is probably the most widespread objective of mineral process plant operators in the late 1980's. An important part of such improvements is dynamic optimization which involves reacting to inevitable plant disturbances in such a way that productivity is maximized at every instant of time. This paper describes the way in which mathematical models can be and have been used in dynamic optimization. Both off-line and on-line model applications are described.

Jan 1, 1989

By R. H. T. Garnett

Recovery performance may be measured in absolute terms or in relative ones that relate the actual mining outcome to what was expected. Consideration is possible in terms of the control exercised by the operator. The eventual mineral output is the only figure known with complete certainty. The paradox is that, while performance is judged against the sampling, the reverse also applies. The R/Efactor and its four component factors are the best overall measures of performance. The choice of equipment for sampling and mining is very important. The sampling process may introduce errors and the sample density may lead to poor mining block selection. The resulting recovery performance is most visible on a regression curve. Changes in the cutoff grade must also be taken into account to avoid unrealistic production targets. Estimation methods incorporating different mathematical assumptions and techniques may cause over-or underestimation of the grade and volume. If the selective ability of the mining equipment does not match the size of the reserve blocks, the performance will be compromised. The treatment plant efficiency, the throughput rate and the degree of bedrock clean-up also affect performance. The maximization of throughput does not yield the optimum results. Marine conditions, which are outside the operator's control, affect not only operational availability but also performance. Examples are provided from actual operations for various commodities, showing the relative magnitude of the different effects upon performance.

Jan 1, 1999

By J de Cuyper, S. Ramachandran, L. A. Vazquez, N. L. Grauerholz, W. Freyberger

A novel process is described for the selective flotation of scheelite from low-grade (- 0.5% W03) tungsten ores having appreciable quantities of calcareous and siliceous gangue minerals. Specifically developed for the Tempiute, Nevada facility of Union Carbide, the process yields tungsten concentrates exceeding 15 percent W03 with at least 85 percent recovery. This condition was not achieved through conventional processes. This process consists of conditioning the ore pulp with judicious amounts of lime, followed by soda ash and sodium silicate as modifiers. The scheelite is then floated using a mixture of oleic and naphthenic acids as collector. Contrary to the common observation as to the deleterious effects of calcium in fatty acid flotation systems, lime addition is found to be beneficial in achieving satisfactory results. The process has also shown excellent results on a Brazilian scheelite ore.

Jan 1, 1976

By Andrew Hall

Many Latin American countries are facing a scarcity of water. As such, infrastructure decisions are quite different from those made in parts of the world that experience a positive water balance. In the latter case, the water treatment approach tends to be ?treat and discharge.? For Latin American regions facing the challenges that go with a negative water balance, the focus is on resource optimization and reuse. Historically, the water challenge has had a significant impact on economic development in Latin America, especially in sectors such as mining, where water usage is high. At the same time, countries such as Chile and Brazil are major development targets for mining and oil and gas operations. Given the water supply challenge, industry is increasingly turning to technologies and processes that maximize water recovery and reuse. With sulfide precipitation and ion exchange water treatment processes for example, it is possible to treat and recover more than 99 percent of water for reuse onsite. These technologies have been applied successfully in other regions of the world where water conservation practices are essential to economic survival.

Jan 1, 2012

In 1989, United States mine production of barite decreased 13% while world mine production decreased by 8.6%, according to the US Bureau of Mines. Consumption, sold or used by grinding plants, decreased by 21.2%. And imports decreased by 12.8%. The value of domestically produced barite, fob mine, increased 17.4%, according to the Bureau. The declared value cif US port of all imported crude barite during 1989 increased from $38.10/t ($34.56 per st) in 1988 to $40.27/t($36.54 per st). Nevada continued to be the leading producer of barite with 77% of the total, followed by Georgia and Missouri. The Bureau of Mines estimates 75% of the domestic mine production was used as a weighting agent in drilling fluids. The remaining 25% was used in barium chemicals, glass, or as a filler. Most of the production from Missouri, Georgia, and Tennessee was used in the nonoilfield sector. Of the total consumption used by grinding plants and chemical manufacturers, it is estimated that 80% was used in drilling fluids. The other 20% was used in the non-oilfield sector, including barium chemicals and fillers in paper, plastics, and glass. The tonnage consumed in the drilling fluids market decreased due to the lower average rig count during 1989. The average number of rotary rigs operating was 869, 7.2% less than the average of 936 in 1988. Crude barite imports were down 12.8% from 1988. Imports accounted for 73.8% of the barite consumed (apparent) in the US. China continued to be the leading exporter of crude barite ore to the United States with 63% of total crude ore imports. India followed with 27.4%, Peru 4.3%, Chile 2.9%, and Canada and Mexico, each with 1.1 %. About 97% of the imported barite ore was used in the oilfield sector.

Jan 1, 1990

By L. G. Austin, R. S. C. Rogers

INTRODUCTION Coal is geologically a sedimentary rock with distinct bedding planes containing a mixture of petrographic constituents. Yet. because of its chemical nature, it also has some of the characteristics of a polymeric material. In addition, it is extensively precracked to give a macropore structure and also has a substantial internal volume of microporosity. Add to this the mineral constituents dispersed in the coal in a variety of forms and sizes. and it can be readily appreciated that coal is a complex and heterogeneous material. It has to date not been possible to predict the particle size distributions produced by breakage of coals from a priori application of the principles of fracture mechanics. However, there is a substantial body of data resulting from empirical observation of size distributions produced under various conditions, primarily from grinding mills. It is the function of this review to outline how this empirical information can be used to predict product size distributions for those systems which have been studied systematically, and to suggest future avenues of research using similar methodology. FRACTURE THEORY APPLIED TO COAL It is, of course, possible to devise experiments for slow crack propagation in a coal. However, the evidence is that coal breaks by brittle fracture in the mills and mining machines of industrial importance and therefore the theory of brittle fracture is sufficient to illustrate the important features of the fracture of coal. In order to produce size reduction a solid must be stressed by the application of force. The force can be a tensile (stretching), compressive, or shear force, and the three dimensional stress pattern in the solid represents the tensile, compressive, and shear forces per unit area acting in any direction through any point in the solid. As an illustration consider the case of a simple one-dimensional tensile stress: then stress is defined as a=F/A where F is the force. A is the cross-sectional area of the solid normal to F and strain. E, is defined as the fractional change in the length of the solid. so that E= x/L where x is the extension of an original length of L. Coal behaves as an elastic material over short times (although viscoelastic creep can occur if the stress is maintained over long times) and if it is not stretched too far the coal returns to its original shape when the stress is removed; otherwise catastrophic failure occurs and the coal fractures at a stress termed the tensile strength. The failure under stress of an elastic material is termed brittle fracture. Elastic material fails at small stain and the stress-stain relation to where brittle fracture occurs is the empirical Hooke's law. a= YE, where Y is Young's modulus. The work done on the solid to take the solid from zero external stress to a stressed state by slowly increasing F up to a final stress u is the integral of the stress times the strain. This reversible strain energy is stored in the solid and. using Hooke's law. is u /2Y per unit volume of solid. If the solid is immediately loaded to u the work done is [EAuL] which Is a2 /Y per unit volume, that is, twice the reversible work.

Jan 1, 1988

By G. M. Wilemon, B. J. Scheiner

The Bureau of Mines conducted investigations on extracting phosphate values from fine-particle wastes generated during the mining and beneficiation of phosphate ore by leaching dried wastes using a H2SO4-methanol mixture. Although phosphatic clay waste contains up to a third of the phosphate originally present in the ore, recovery of these values represents a significant challenge due to the fine grain size of the material, the particles averaging less than one micrometer in diameter. Waste samples obtained from two Florida producers yielded phosphate extractions of 71 and 84 pct, respectively, when leached under ambient conditions and at a stoichiometric acid ratio of 1.4:l. Elevated temperatures did not improve the amount of phosphate extracted. Undesirable A12O3, Fe2O3, and PlgO impurities were largely rejected; higher grade wastes gave acids that meet established industry impurity standards and lower grade samples yielded acids that marginally fell short of the standard. Separation of the crude acids from the insoluble residues was accomplished via vacuum filtration through either filter paper or commercial filter cloths. Both filtration rates and solids retention were improved by the addition of 0.5 lb/ton of poly(viny1 acetate) (PVAc) or poly(ethy1ene oxide) (PEO) to the methanol-acid slurries. These results show potential for substantially increasing the reserves of an important domestic resource.

Jan 1, 1989

By William W. Edgerton

Establishing geotechnical baselines on soft ground projects that require the use of closed-face tunnel boring machines (TBMs) is difficult. It is hard to see the face when mining and the excavated material is combined and mixed, all of which makes baseline quantifications challenging. In an attempt to meet underlying objectives of minimizing bidder contingencies, allocating or sharing risks and paying for conditions only if they occur, nongeotechnical baselines (i.e., functional baselines) have been developed. These have been used on the District of Columbia Water and Sewer Authority?s Clean Rivers (DCCR) Blue Plains Tunnel (BPT) project. This article examines the development of such functional baselines and how they were implemented on the BPT project.

Jan 1, 2012

During 1997-2001, an EC funded project investigated the environmental consequences of the use of industrial waste and sewage sludge based artificial top soils (ATS) in rehabilitating large coalmine waste dumps in the Saar region of Germany. Both the laboratory leaching tests and field lysimeter data analysis carried out by the research partners have shown that the amount of dissolved heavy metals in the leachate was low, and generally below the regulatory limits. However, the dissolved amount of nutrients, especially mineral nitrogen, was found to be relatively high. The hydrological properties of waste rocks and ATS mixtures were established through history matching of the laboratory column tests and the field measurements. 1D column models and 3D field models were used to numerically simulate pollutant transport at the ATS rehabilitated waste dumps. This paper presents the findings of the numerical modelling research carried out for the characterisation of hydrological and pollutant transport properties of rehabilitated coalmine waste dumps in the Saar coalfield.

Jan 1, 2003

By John Relser

The production processes that are developed in the mining and minerals industry are manufactured to be exposed to very aggressive environments. Chemical, abrasion, and impact expose structures and equipment, steel or concrete, to a significant deterioration. This causes damage and adds high costs to operations that can be reflected in the destruction of equipment and structures in the arrest of the production process, which becomes very costly. Also, there is the potential for personnel accidents, which would require large sums of compensation for an employee, thus directly harming the image of the mining operation and company. Manufacturers of paints and coatings that have major centers for research and development (R&D Labs) distributed globally have developed high-tech products for durable protection from the elements for structures and equipment used in the mining industry. The difference between these paintings and coatings and what is normally known as conventional paints (e.g., those called domestic or decorative), is its chemical composition, structured around polymeric components that have highly resistant, chemical and physical properties to cope with extreme conditions to which they are exposed. With this, and only this, longer life of components can be achieved for equipment and structures used in the production processes of the mining industry. Today, in addition to the important features mentioned, some manufacturers of the paints and coatings dedicated to this highly modernized process have invested large sums of money in developing new products that add operational elements to the painting process. These coatings provide added value and significant performance to companies mining operations and that we can describe in three fundamental concepts:

Feb 1, 2014

By F. Touboul, M. Thiercelin, K. BenNaceur

Introduction The need to develop accurate predictive hydraulic fracturing simulators arises from the consideration of vertical containment for the fracture. Fracture height growth from a pay zone into adjacent layers has been shown (see Cleary [I]) to depend on three sets of parameters for the different strata: - elastic properties, - closure stress variations, and, -fracturing fluid leak off, and poro-elastic stresses. Qualitative analysis of the effects of these parameters has been reported in the literature. The first effects were described by Van Eekelen, using simple elasticity considerations [2]. The effect of stress variations was described numerically by Simonson and a1. [3] and experimentally by Thiercelin [4]. Effects of back stresses induced by fluid invasion on fracture propagation were considered by Cleary [5]. In order to couple these effects, a numerical code al- lowing the simulation of three dimensional growth of a hydraulically induced fracture has been developed with the ability of representing the effects of heterogeneities on fracture lateral and vertical extension. The model is based on a new variational formulation of the boundary integral representation of three-dimensional elasticity. The fluid flow and elasticity equations are solved using a moving mesh representation which offers enough flexibility to enable the simulation of any closure stress distribution. Simpler models representing fracture height growth (P3DH models) have been developed [6] [7] that approximate the fracture by a series of one dimensional segments, and the limitation of such approaches is examined in this paper. 1 Description of the model 1.1 Fracture Geometry Hydraulic fracturing simulations involve the coupling of solutions to elastic deformations, fluid flow in the fracture, and fluid leak off into the formation. Since the use of direct solution techniques (i,e,,3D finite elements) is prohibitive, the method used in this study is baaed on a boundary integral representation of the 3D elasticity equations. 1.2 3D Models The classical representation of the problem of a fracture in an infinite medium by boundary integrals is [8]: [ ] where u is the unknown displacement field, r n is the traction operator, I? is the fracture surface, and K is the Kelvin tensor of fundamental solutions to the elasticity operator. Using the notation: [ ] for the displacement discontinuity (or fracture width), one can attempt to solve the boundary integral relation using surface integrals (91 or the displacement discontinuity technique, first introduced by Crouch [lo], and extended to three-dimensional problems [Ill. However, numerical problems arise since the Kelvin tensor has a singularity in

Jan 1, 1986