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By C Jincheng, L. Liang, L. Wenjun

"Considering overgrinding in a grinding process, the grinding characteristics of comminuted hematite products using a HPGR and a conventional CC were comparatively studied. The major properties including particle size, grinding kinetics and grinding technical efficiency (Et) were investigated. Individual size distributions (ISDs) of -2.0mm in a HPGR product showed a more significant “double-peak” characteristic than a CC product. As a result, HPGR products were finer and had a wider full-size distribution because of the greater proportion of fines. The parameters m and zi in m-th order grinding kinetics were analyzed by the partial-derivative method and the critical time tc(tc = exp (1/ zi)) was obtained. zi mainly affected the breakage rate when t < tc; otherwise, m mainly affected the breakage rate. In these tests, tc was considerably higher than the grinding times, and HPGR products yielded a higher zi-value than the CC product for the same sieve size. This indicated that HPGR products had a higher breakage rate and needed a shorter grinding time for a certain grinding fineness. Et was calculated by simulating the size distributions of batch grinding products. HPGR products gave a lower Et at a decreasing rate than the CC products for -2.0 mm feed and -0.5mm feed, and then showed a slightly higher Et for -2.0+0.5 mm feed. This indicated that overginding in HPGR full-size products was more serious under the condition of coarse grinding, whereas the efficiency was higher and overgrinding weakened significantly in HPGR coarse products because of screening-out fines. Based on the above research, a new process of “ultra-crushing in HPGR – classified grinding” was advanced, reducing ores tonnage into first stage ball mill significantly, improving grinding efficient and weakening overgrinding in the whole grinding process.INTRODUCTIONIn mineral processing, comminution accounts for a substantial portion (approximately 60~70%) of the energy consumed in plants. As an ultra-fine crushing equipment,the application of the HPGR for industrial comminution has been paid close attention because of its low specific energy, low steel consumption, high capacity and high ratio of reduction, among others (Schonert, 1998; Norgate & Weller, 1994; Fuerstenau & Kapur, 1995). HPGRs comprise two counter-rotating rolls that draw feed material into the roll gap. One roll is fixed to the mainframe, while the other movable roll is mounted on slides and positioned by hydraulic rams. The specific pressing force (SPF) (i.e., total force divided by projected roller area) is typically in the range of 3~9 N/mm2 depending on the application, while pressures of up to 1000 N/mm2 have been measured within the operating gap (Maxton , Morley, & Bearman , 2003)."

Jan 1, 2016

By Michael E. Henderson

The U.S. Bureau of Mines (BOM) constructed the Hydraulic Transport Research Facility (HTRF) to investigate the hydraulic parameters relating to the transport of coarse coal. To achieve these goals in a timely and efficient manner, the Bureau contracted to Boeing Services International, Inc. (BSI) the responsibility of operating the HTRF and providing technical support. This data report is a summary of the testing and data results for the period from 6 September to 9 September 1983. The testing covered herein is for coarse 2-in by 0 (minus 50 mm) Pittsburgh Seam run-of-mine (ROM) coal in a 12-in (300 mm) pipeline, at velocities ranging from 8 to 16 ft/s (2.4 to 4.9 m/s) and at concentrations ranging from 15 to 50 pct.

Jan 1, 1985

By P. D. Kovscek

The Bureau of Mines has tested a low-thrust water-jet-assisted rotary drill. This work was performed to evaluate the performance of a water-jet-assisted drill operated at thrust levels typical of a handheld manual-thrust operation. Prior work by the Bureau had indicated that using water-jet assist with high-thrust drilling applications would increase drilling rate. Small-diameter holes were drilled in five different types of rock. Thrust and water pressure were varied as the drill rate was monitored. The test results indicate that drilling rates increase with increasing water pressure and thrust. The water jet has more effect on reducing the specific energy when drilling in the harder rocks than in softer rocks. Variation in drill rate for a given rock sample is attributable primarily to the material heterogeneity within the sample. One rock type (Greenwich sandstone) could not be drilled efficiently with the water-jet-assisted drill.

Jan 1, 1988

By Catherine T. Aimone-Martin, Meyers Joseph A.

A new strain-based criteria is being adopted for rock blasting in New York City (NYC). This criteria is based on several years of research involving vibration measurements of tall structures during blasting within several feet from buildings designated historic and Landmarked. This research has demonstrated that tall, heavy structures show little upper-structure vibratory response during hard-rock, urban blasting carried out in NYC. The Fire Department of New York City (FDNY) permits rock blasting and regulated limits for ground vibrations using the U.S. Bureau of Mines (USBM) safe blasting criteria. However, these regulations are often superseded by a 0.5 in/s (12.7 mm/s) limit imposed by the New York City Department of Buildings for historic and Landmarked buildings that are adjacent to the majority of blasting projects in the City. This onerous limit is often exceeded resulting in frequent stop work orders that increase the cost and time of rock excavation projects. The

Jan 1, 2019

By B. M. Satish

The aim of the present work is to study the effect of annealing on the vibration damping capacity of high-chromium (16%) ferromagnetic steel. The alloys were prepared from raw materials of 99.9% purity melted in a high frequency induction furnace under high vacuum. The samples were heat-treated in vacuum at various temperatures (800 to 1200°C) for 1 hour followed by slow cooling (120°C/h). The inverted torsional pendulum method was used to evaluate the vibration damping capacity. The results indicated that the vibration damping capacity of the alloys is influenced by annealing and there exists a critical annealing temperature after 1000°C. The damping capacity increases quickly below the critical temperature since the magnetic domains move more easily.

Jan 1, 2009

By Gary E. Sherman

To aid the U.S. Army Corps of Engineers In their Resource Development Navigation Study, the U.S. Bureau of Mines (Bureau) examined the potential for mineral development near ten Alaska port sites. This report presents the results for the first three sites: Bethel, Kivalina (Red Dog), and Omalik Lagoon. The mineral deposits near Bethel are primarily gold and mercury; the nearest deposit being 55 mites away. Because of the expense of constructing and maintaining a road over the poorly drained lowlands, the potential of Bethel as a port site in the near-term is considered to be low. The Kivalina site currently serves the Red Dog mine and has the potential to handle material for similar deposits in the area. Results from a lead-zinc mine model indicate that potential for additional mine development exists in the area. Coal is the major deposit type found near the Omalik Lagoon site. Due to environmental constraints, development of a large-scale mine producing coal for export is considered unlikely. A small-scale coal mine model was used to examine the feasibility of producing coal for regional use. This alternative may be feasible but would require conversion of heating/generating equipment in the area.

Jan 1, 2011

By J. -F. Blais, M. -O. Simonnot, P. Charbonnier, J. Mocellin, Université de Lorraine INRA, G. Mercier

"Huge amounts of air pollution scrubber sludge have been generated during ferromanganese production using blast furnace. These residues have been historically deposited in ponds near steel making plants. They are very rich in zinc, manganese and lead (5 to 40 %) and also contain aluminum and iron. Considering the market value of these metals, brownfield sites can now be used as secondary resources. These ponds also have to be cleaned up to meet the environmental regulations.We have developed a hydrometallurgical process to recover Zn, Mn and Pb in order to produce valuable compounds of Mn and Zn and recover the final Pb residue by pyrometallurgy. The Zn and Mn compounds need to be pure enough to be economically valuable. Batch laboratory tests were carried out to determine suitable selective leaching conditions. The investigated operating conditions were acid concentration, pulp density and temperature. Optimal conditions to maximize zinc extraction (100 %) and manganese extraction (95.9 %) were found using sulfuric acid and sodium metabisulfide. The final residue contained 14.8 to 23.8 % of Pb. Then, Zn was recovered in the form of ZnO or ZnS by precipitation and Zn metal by electrowinning, while Mn was recovered as MnCO3 with a fairly acceptable concentration of impurities.INTRODUCTIONFerromanganese has been produced by pyrometallurgy in much of Western Europe for centuries. Use of wet scrubber to remove pollutant and dust particles from gas stream was common for most of these operations. Those residues contain high concentration of Zn, Mn and Pb. They have been left to decant in settling ponds installed close to the steel production plants. They now constitute heavily contaminated artificial soils. Those sludges are so contaminated with Zn, Mn and Pb that they can be used for metal production. Currently, no method is available to decontaminate these residues and recover Zn, Mn and Pb. Therefore, an approach considering these brownfield sites as secondary resource is in development. Doing so would achieve two goals, decontaminate the site and produce metals.. (Huot, Faure, Biache, Lorgeoux, Simonnot, & Morel, 2014a; Huot, Simonnot, Marion, Yvon, De Donato, & Morel, 2012; Huot, Simonnot, Watteau, Marion, Yvon, De Donato, & Morel, 2014b)."

Jan 1, 2016

By A. Dadgar

The adsorption kinetics of AuBr4 on Dowex ® -21K ion-exchange resin were studied and found to be independent of the initial gold, bromine, and base metals concentrations. A commercially-available undivided hypochlorite generating cell was used to generate bromine from simulated mixed halide (Br-/CI-) solutions. Electrolyses were performed with solutions containing very low Br&apos; ion concentrations. The current efficiencies were 80-90%, and Br- ion utilization was maximized. A detailed economic assessment was made considering the capital and the operating costs for a 1000 mtpd gold ore processing plant. The toxicity and discharge levels of bromide, bromine, and cyanide were compared from a detailed analysis of the published literature data. Comparing bromine vapor with hydrogen cyanide gas for a given length of exposure, the lethal concentration of bromine is about 3 times less than hydrogen cyanide. The toxicity of sodium bromide is similar to that of sodium chloride. Acute poisoning to bromides and chlorides is rare because of their low toxicities. The allowed discharge levels of Br-, Br2, and CN- in fresh water are 250, 0.1, and 0.005 mg dm-3, respectively.

Jan 1, 1992

By H. Craig Boyle, Craig H. B. Leitch

"The Trout Lake stockwork molybdenum deposit is located in the Selkirk Mountains of British Columbia, 50 km southeast of Revelstoke. The property is being explored by a joint venture between Newmont Exploration of Canada and Esso Minerals Canada.The deposit is associated with a small granodiorite stock of Upper Cretaceous age (76 Ma) which has variably altered the surrounding schists, argillites and marbles of the lower Paleozoic Lardeau Group to hornjelsic biotite schists and skarn. The intrusive is composed of a small stock and an intersecting network of northeast- and northwest-trending dykes at surface that coalesce downward into a larger stock. There are two main phases of intrusion, with an earlier quartz porphyritic granodiorite cut by an intra-mineral ""quartz diorite"" porphyry. A strong sub-vertical north-trending fault controls the distribution of the mineralized stock work and displays post-mineral movement.Molybdenite, accompanied by pyrite and pyrrhotite, is mainly present along the margins of veins in a well-developed quartz stock work, but occasionally is strongly disseminated in microfractured intrusives. The stock work is strongest in and around the contacts of the intrusive and its apophyses, and occurs over a vertical range of more than 1,000 m. As defined by the 0.10% MoS] contour, the main mineralized zone is up to 300 m long by 200m wide. Preliminary drill-indicated reserves, currently being revised, are approximately 50 million tonnes of 0.23% MoS2, within which are several zones of higher-grade material. Hydrothermal alteration, as defined by quantitative X-ray diffraction studies on composite core sections, is composed of a central quartz/K-feldspar/albite/minor biotite zone coincident with molybdenum mineralization, which is overlapped by a slightly later, antipathetic quartz/ sericite/pyrite zone. Ankeritic carbonate is also a common alteration mineral, but only traces of fluorite, and no topaz or sulfosalts, have been observed. Analysis for trace elements such as Sn, W, Bi, Sb, As, Hg, U, Ag, Au, Mn, Cu, Pb, Zn and F has been limited except for Sn and W, which appear to be zoned inside and outside the Mo zone respectively; the other elements do not show detectable patterns thus far."

Jan 1, 1983

By H. D. Freeman

The occurrence of gold in refractory gold ores varies widely and affects the recovery process. The determination of gold and the composition of the associated minerals are important in selecting an appropriate processing scheme. However, locating the gold in an ore sample is a difficult task which requires perseverance, luck, and experience. Our experience has led to the development of a relatively fast and reliable means of deter-mining the mineralogy of ore samples through analysis combining an energy-dispersive x-ray analyser coupled to a scanning electron microscope (SEM). In some cases, a wave length dispersive spectrometer or microprobe is used to further quantify the various mineral compositions. The SEM/microprobe analysis identifies the source of problems that may arise during the recovery of gold from refractory gold ores.

Jan 1, 1981

By Claude P. Heiner

mountain region to M tht Coast points for domestic consumption and for export are shown in Table 11. There is considerable disparity in rates from both Rock Springs, Wyo., and Castle Gate, Utah, to the four coast cities where the slack coal is to be used for purposes other than export. The rate on coal to be exported is the same from either starting point to any of the four coast cities even though there is a difference of as much as 341 miles in the shipping distance. It is interesting to note that the freight rate between Sunnyside, Utah, and Fontana, Calif., on coking coal is $5.05 per ton and that coal up to 8 in. can be moved on this rate if it is suitable for coking. This rate was published late in 1942 on a contemplated annual movement of more than 500,000 tons. There have been decreases in freight rates since 1923 on movements of slack coal from Utah into Seattle and Portland due to pressure on the railroads and to greater. quantity of coal shipped. It is the author,&apos;, opinion that a movement of slack coal in excess of 3 million tons of coal per year from Utah to any point in central California would justify a freight rate equal to that puhlished for Fontana, Calif.. or $5.05 per ton. The movement of 3 1/2 million tons of coal per year on the basis of 240 mine working days per year would require that 14,600 tons be handled each mine working day. If it is assumed that shipments could be arranged for a 6-day week, the average railway movement would he 11,200 tons, or approximately 3 trains containing fifty-five 70-ton coal cars per day. Such movements of coal would require railroad equipment represented by the investment amounts stated in Table 12 and entail the services of 250 men. Table 12 ... Railroad Equipment and Investment Required To Move 11,200 Tons of Coal a Day from Utah to California Railroad Equipment Cost 2800. 70-ton coal cara at $6.000 each $16,800.000 32 locomotives at $310.000 each. 9.920.000 Miscellaneous eauiument:.......... .5;000:000 Total........................ $31,720,000 It therefore appears that, under presently known mining methods, the lowest price at which coal could be sold f.0.b. the mine in amounts of 3 1/2 million tons per year for generation of power in central California would be $4.60. It also appears that the lowest freight rate that could be expecled between intermountain points and the central California area would be $5.05 per ton, making a total cost of coal delivered at a plant site of $9.65 per ton. Conelusions The following are the author&apos;s conclusions: 1. Coal mines in Utah and in the Kemmerer and Rock Springs districts of Wyoming could increase annual production by 6 1/2 million tons per year. 2. Under present conditions coal could probably be delivered to any steam electric plant in central California at a price not to exceed $9.65 per ton. 3. The use of coal at such a price, while higher than the equivalent present price of fuel oil, is entirely feasible. 4. There are adequate railroad facilities for movements of large quantities of coal from the intermountain region to the Rest Coast. 5. In a national emergency it probably would be extremely difficult, if not impossible, to obtain sufficient oil to meet requirements of the greatly expanded West Coast steam electric generatsing capacity. 6. The intermountain region contains ample coal reserves to supply all conceivable demands for West Coast power generation for a number of generations. 7. Increasing demands of labor threaten to lessen, if not eliminate, savings in cost of coal production through the use of new mining machinery. 8. Continuation of experiments in socialism by the Federal Government through construction of hydroelectric generating plants, particularly those unrelated to land-use reclamation, defies justification. Rates under this concept of a governmental function are subsidized through greater taxation of its people. Private capital is available to construct steam plants, or hydro plants where feasible, and should be permitted to continue in order to preserve the principles of our free enterprise system. DISCUSSION (L. C. McCabe and Robert P. Koenig, presiding) C. C;. BALl*—I was asked to lead off the discussion, but it is not with the thought that I might be able to add anything to the paper. The thoroughness with which it was prepared rather forestalls the asking of many questions. Your treatment, Mr. Heiner, is a very valuable contribution. I do want to suggest—that although you have limited your study to this specific question, with certain geographic limitations, many of the things in your paper apply just as well to the eastern coals. I want to agree 100 pct with your final conclusion concerning government-subsidized construction. Id. C. McCabe*—It is certainly worthwhile to take stock occasionally to see where we are going in problems of this nature. I agree with Mr. Heiner that ultimately the only reliable source of fuel that the West Coast has is coal hut the time factor is the difficult element to evaluate. Just before I came here I discussed this subject with N. B. Hinson, Vice President and Executixe Engineer of the Southern California Edison Company, and Chairman of the West Coast Inter-Power Exchange Committee. He has given much thought to utilities&apos; fuel supply and it was very helpful to me in preparing a discussion of the paper to talk with him beforehand. Stock taking and forecasting of future development are essential to the continuing success of any enterprise. Mr. Heiner has called attention to the unprecedented growth of central and southern California and to the increased demands for fuel and power which have accompanied it. He discusses the increased fuel oil and natural gas requirements and the probable limits on the future use of these fuels and of hydroelectric power. In contrast to the calculable limits of these sources of electric energy, the author points to the availability of enormous reserves of coal in the Rocky Mountain States adjacent to the Pacific Coast which can be utilized for power generation. That there will be increased use of coal for power generation in the area under discussion is generally accepted hut it is in the timetable of such development that there is not complete agreement. In a recent report, Mr. Hinson reviewed the future power outlook for the Pacific southwest area. He pointed out that the use of steam plants in connection with water power plants in this region has made the maximum use of hydroelectric energy possible, and that the correct balance between hydro and steam generating plants produces the most economical overall system. Steam plants in the area which had been installed to protect against deficiency in hydro energy in dry years were used to carry war loads. Fortunately, no dry

Jan 1, 1950

SOFCs with thin electrolyte of two types: SDC (15um) single-layer and YSZ (5um) + SDC (15um) bi-layer were fabricated by screen printing and co-firing on Ni¬YSZ cermet substrates. Using in-situ sintered Sm0.5Sr0.5CoO3 cathode the SDC-cell shows high performance at low temperature, 1180mW/cm2 peak power density around 650°C, while the YSZ+SDC bi-layer cell generates about 340mW/cm2 at 650°C, and good performance at 700-800°C with almost theoretical OCV value. Many Zr-content micro-islands were found on the SDC electrolyte surface. The influence of co-firing temperature and thin film preparation methods on the Zr-islands&apos; appearance was investigated.

Jan 1, 2005

While coal was mined in New Mexico in 1860, production was on a small scale during the period considered here, and Table 77 contains all the data found. [ ]

Jan 1, 1942

By H. L. Martin

A joint federal-provincial approach in gathering basic information from industry on mine production, concentrator operations and ore reserves, initiated during 1978, is a major step toward the goal of achieving better government-industry communication through a common data base. Information from questionnaires sent out by provincial governments is shared with the federal government; correct interpretation is ensured by mine visits conducted jointly by provincial and federal representatives. Initial focus is on nonferrous metal mines. The federal Department of Energy, Mines and Resources (EMR) is responsible for a national analysis that is aimed at the early detection of worrisome developments-and their reasons-in the flow from resources to reserves and from reserves to supply of these metals. The heart of the national analysis is the annual construction of a "monitoring curve", showing each metal&apos;s aggregated mine production as it would decrease over time if no new reserves and production capacity were to be added from the year of analysis. For a given metal, a comparison of monitoring curves from year to year can reveal early signs of supply stagnation. In anyone year, a monitoring curve in conjunction with foreseen needs for Canadian mine output will show the production gap that would have to be filled from reserves and production capacity yet to be developed. The production gaps for copper, nickel, zinc and lead, the four leading base metals mined in Canada, are shown for the 20-year period ahead, in the context of production achieved during the past 20 years. It is shown that reserve levels commensurate with likely future production levels would require that average annual reserve additions during 1978-98 exceed the average annual additions during the preceding 20 years. Reserve levels of all four metals have declined in recent years. A review of significant discoveries in the last five years suggests that this fall in reserves is not the result of a lack of exploration successes, but of stagnation in development for various economic reasons.

Jan 1, 1979

By Paul H. Johnson

Resource Engineering and Development, Inc. is designing and building a portable 150 to 225 TPD, flotation-cyanide leach plant with unitized, skid-mounted components. This plant design, with its portability, low capital investment, and high recovery of silver and gold from many partially oxidized ores, is well suited to treat many small, high-grade deposits, old waste dumps, and old mill tailing piles. A description is given of flotation and/or cyanide leach tests run on about 17 partially oxidized, newly mined ores; waste dump materials; placer slimes; and old mill tailings.

Jan 1, 1981

By A. J. Basu

An overview of the evolution of computerized mine planning and design has been given, emphasizing the need for a knowledge-based system for planning and design of underground coal mines. An outline for the development methodology and procedure has been provided. Problem structuring guidelines have been used to incorporate intelligence and integration to the design modules. A skeletal model for a mine planning and design expert system has been prescribed, and the development process has been documented in detail. A feasibility prototype has been developed to test the structure of the skeletal model and to ensure completeness of the design process. The feasibility prototype development and its contribution toward proto typing has been addressed in this paper. At present, prototype development is underway. The prototype is expected to be avail-able for testing and implementation in early 1991.

Jan 1, 1991

By D D. Deacon

A brief description is given of the requirements which No. 4 Shaft has been designed to meet and of the methods by which two-stage winding of rock has been accommodated in a single shaft sunk to a depth of 7,421 ft. This is followed by a consideration of the factors which led to the decision to sink the shaft as rapidly as possible. Introduction T HE No. 4 Shaft of Hartebeest-fontein Gold Mining Company, Ltd., has been sited to serve the deep southern area of the mine, some 1,500 claims in extent, between the elevations of 6,250 and 7,300 ft. below surface. From this area, some two-thirds of the mine production will ultimately be obtained. Above the 6,-250-ft. elevation, an existing shaft hoisting system, situated adjacent to the reduction plant, is of adequate capacity to cater for all ore hoisted to surface for milling. No. 4 Shaft will therefore be required to provide downcast ventilation of 1,000,000 c.f.m., together with surface hoisting facilities for men, material and development rock and underground hoisting

Jan 1, 1965

By Frank G. Horino

The Bureau of Mines studied the uniaxial compressive strength of model rock pillars as a function of the angle and spacing of noncohesive planes of weakness. The model pillars were prepared from NX 2-l/8-inch diameter drill core of limestone, sandstone, and granite, and the planes of weakness were diamond saw cuts ground flat and smooth. The angle of the planes of weakness, measured from the horizontal, varied from zero to 57° in approximately 15° increments. When two planes of weakness were used, the thickness-to-diameter ratio of the wafer was 1/4, 1/2, and 1, Approximately 400 model pillars were tested in uniaxial compression. The results indicate that the uniaxial compressive strength of model pillars decreases rapidly as the angle of the plane of weakness increases from 30° to 57°, and that the spacing of these planes of weakness has only a minor effect on the strength. The effect of the number of horizontal planes of weakness, with a spacing of 1/4 and 1/2 of the diameter, upon the compressive strength of model pillars was also investigated. These results indicate that as the number of planes of weakness increases the compressive strength of the pillar decreases. Normalizing the data provides useful estimates of model pillar strengths for any rock type.

Jan 1, 1968

By F. Elgersma

A high purity electrolysis solution is essential for hydrometallurgical zinc winning processes. For this reason ferric iron containing compounds such as jarosite are precipitated as iron and impurity collector during the calcine leaching. Jarosite thus forms a chemical waste and creates environmental problems. This research contributes to the development of a wet jarosite treatment process, where less contaminated jarosite is produced which can act as an iron source. The present work studies jarosite precipitation kinetics and the uptake of zinc cations in batch and continuous experiments. The distribution coefficient for zinc in continuous experiments is constant for a wide ratio of zinc over ferric ions in the solution. Addition of NH, + ions in batch experiments accelerates the conversion rate equivalent to the driving force increment. Addition of 50,2-ions above the stoichiometric ratio increases the conversion rate less then could be expected from the increase in the estimated driving force. Zinc ions tend to retard the conversion rate. An increasing reaction temperature increases the conversion rate. Below 75 ?C the conversion rate approximates zero.

Jan 1, 1990

By R. V. Higgins

The results of two separate but related studies are given. In the first study, four equations were tested; the object was to determine which would produce a curve that would best fit data points that represent a trend of declining oil production in 90 California fields. Two conventional equations (the Arps and semilog) and two novel equations (extreme-c and double semilog) were tested. The curves were first fitted to the initial 9 years of the 15-year production data and then extrapolated for 6 years to determine how well the extrapolated curve would fit the data points. The generated curves were also extrapolated beyond the last data point to predict rates of future production. The results of the first study showed that no equation was clearly superior to the others in all respects. The semilog equation resulted in the best fit to production data for the first 9 years, but the Arps and extreme-c equations produced a better fit for the extrapolated data for the period of 9 to 15 years. The Arps and extreme-c also gave more realistic production rates when extended to the point where cumulative production equaled reserves. A second study was made to determine if the least-squares technique applied to the Arps equation would result in more accurate extrapolations. The merits of the logarithmic and the nonlogarithmic forms of the Arps hyperbolic equation were also tested. For the logarithmic expression, it was found that one of the constants of the Arps equation reached a value so small or so large that the equation was not applicable to the data of 40 of the 90 California fields. The nonlogarithmic form of the Arps equation was applicable to neither the same 40 fields nor to a few additional ones. When the data and the Arps equation were compatible, the use of the least-squares technique as compared with other methods improved the extrapolation accuracy somewhat.

Jan 1, 1971