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By A. C. Maffei, M. V. Lins Gonçalves

Ore concentration processes are a function of the respective particle size distribution; however, most of them do not use an efficient operational method to determine it. From a practical point of view, the surface area can be calculated for any size analysis. The physical principles for determining the size distribution in each method are different, for the results will not be compared directly. During the development of the research project of the sulfide ore flotation method using inert gas, different methods for calculating the specific surface area have been used, such as sieving, sedimentation/X-ray, laser diffraction and BET, i.e. specific techniques to determine the specific surface area of copper and gold ore concentrates. The statistical method of minimum squares was used to achieve practical correlation equations among them. Regarding these two ores, if one knows a specific surface area value using one of the methods above, one can predict the result of the others. Diminution of the reagent consumption was so controlled and it could be even decreased by using inert gas.

Jan 1, 2003

By Sean Gallagher

Bolting large sheets of wire mesh screen (WMS) to the roof of underground mines prevents injuries due to rock falls. However, WMS can be heavy and awkward to lift and transport, and may result in significant spinal loading. Accordingly, six male subjects (mean age =45.8 years + 7.5 SD) were recruited to lift WMS in a laboratory investigation of the biomechanical demands. Biomechanical modeling was used to estimate external moments about L5-S1 for sixteen lifting tasks, using two sizes of WMS. Full-size WMS involved a two-person lift, while half-size WMS involved a one-person lift. Lifts were performed under 168 cm and 213 cm vertical space. Restriction in vertical space increased the maximum L5-S1 extensor moment from 254 to 274 Nm and right lateral bending moment from 195 to 251 Nm. Lifting full sheets of screen (as opposed to half sheets) resulted in an average 33 Nm increase in L5-S1 extensor moment. The L5-S1 extensor moment was increased by an average of 44 Nm (18%) when lifting screens positioned flat on the floor compared to an upright position. Relevance to industry: Large flexible materials are commonly lifted in industrial work environments, and may involve the efforts of two or more workers. The current study examines the low back loading associated with lifting large flexible screens and presents recommendations to reduce spine loading.

Jan 1, 2009

By M. Shamsuddin

Information on total estimated uranium reserves and domestic requirements have been collected, A survey has been made on the possibilities of recovery of uranium from low grade and complex ore deposits, e.g., marine phosphorites, shales, coal, sea water, etc. In order to assess the potential for uranium recovery from uraniferous phosphorites, available thermodynamic data of uranium minerals, compounds and aqueous species have been collected. The existence of uranium complexes with chloride, fluoride, carbonate, phosphate, sulfate, etc., in ground waters have been evaluated at different pH's. There seems a great need to study the relative stability of these complexes in order to judge the applicability of solution mining technology for selective leaching of uranium from phosphorites. A typical flow-sheet demonstrating recovery of uranium from wet-process phosphoric acid has been included in this report. Some essential features of the economics of uranium recovery from uraniferous phosphorites have been briefly considered and recommendation have been made for further studies.

Jan 1, 1980

By P Goblet, S A. Séguret, E Cordier, A Galli

In salar-type deposits, lithium grades can be measured by bailers introduced at different elevations in the drill holes at locations where, later, the brine will be pumped out to recover the metal. When they are duplicated, these a priori rudimentary measurements may show large differences without indicating whether this is due to the procedure itself or to some physical causes linked to the dynamic behaviour of the salar (seasonality, rainfall, underground flow etc). In the reservoir presented in the paper, the problem is complicated by the double lack of stationarity of the lithium grades: the grades not only increase importantly with the depth but at the same time their fluctuations decrease, making it necessary to use non-stationary geostatistical techniques to simulate them. Reservoir simulation is developed in two steps: first, geostatistical simulations of the lithium grade create possible realisations of the reservoir; then, each geostatistical simulation is followed by a pumping simulation that calculates, at each drill hole of a given extraction scenario, the lithium produced each year over 40 years. For the set of 100 simulations produced in this way, a scenario reduction is made to choose the five most representative simulations where more complex calculations will be carried out (for example, changing hydrogeological parameters such as porosity and permeability, or the elevation of the filters, the number and the location of the pumping and the reinjection drill holes etc). The paper first presents an analysis of the geostatistical model sensitivity to the grade uncertainty when measured by bailer. Among the 100 measurements at our disposal covering the future production domain, 50 per cent are duplicates measured at the same place but at different times. They are randomly sampled to produce five subsets of 75 values, which will constitute the future 3D conditioning points for the geostatistical analysis and the simulations. For each subset, trend, standard deviation and variogram models are fitted, leading to five sets of 20 geostatistical simulations of grades. In this way, the reliability of the different parameters involved in the procedure is evaluated, as well as its impact on the pumping results. Then, a reconciliation study is conducted between the non-stationary nugget effects encountered in the 3D variograms of the lithium grade and a pure statistical analysis of 25 duplicates measured at different locations and/or different times. The result is that if the nugget effect reaches 20 per cent, which is the case of three conditioning subsets out of five, the reconciliation is good and the nugget effect of the variogram model represents the bailer uncertainty, ie the measurement error. Since the geostatistical simulation incorporates a nugget effect, it handles the bailer uncertainty and the impact on the produced metal is included in the evaluation. The final conclusion is that, after the hydrogeological pumping simulations, the initial differences between the five geostatistical models do not influence the final results: lithium grades measured by bailers can lead to a robust evaluation of the extractable resources, a conclusion that conflicts with conventional wisdom.CITATION:Séguret, S A, Goblet, P, Cordier, E and Galli, A, 2017. Bailer uncertainty evaluation in a lithium salar deposit, in Proceedings Eighth World Conference on Sampling and Blending , pp 395–402 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2017

By D. M. Doyle, P. J. Hannon

"The Canada/Nova Scotia Mineral Development Agreement (M.D.A.) is a subsidiary of a five-year Economic and Regional Development Agreement, signed on June 11, 1984. The objectives of the M.D.A. are to strengthen and diversify the Nova Scotian mineral industry and to coordinate federal and provincial policies and programs. The agreement outlines the activities and responsibilities of each government, including the division of the cost (60:40, federal: provincial) between governments. The agreement established a framework for joint planning to avoid overlap or duplication of programs.The M.D.A. programs are broadly divided into five sectors (Table 1 and Fig. 1): Geoscience, Minerals Technology, Development, Firm Specific and Public Information. Each sector is administered by a subcommittee composed of one federal member and one provincial member. The subcommittees report to a Management Committee. The Canada/Nova Scotia Mineral Development Agreement (M.D.A.) Management Committee is made up of Dr. Jack Reeves from EMR and Dr. Richard Potter from the NSDME.The Geoscience subcommittee, co-chaired by Peter Giles (NSDME) and William Poole (EMR), manages the regional geologic, geochemical and geophysical studies in the province. Included in this sector are studies into mineral deposits and the basic geological relationships between mineral deposits.The Mineral Technology sector is co-chaired by the authors, Don Doyle (CANMET) and Pat Hannon (NSDME). This sector of the M.D.A. conducts studies into mineral processing, sampling, deposit byproduct commodities and project feasibility analysis."

Jan 1, 1987

By J. van Lookeren

In the case of a reservoir where the oil underlies a large gas cap and overlies bottom water, production can be inzproved considerably if wells are perforated below the water-oil contact rather than opposite the oil-bearing section. The theoretical arguments for this improvement, which in some cases may be tenfold, are supported by experimental evidence. INTRODUCTION Reservoirs frequently consist of one sand body containing an oil layer underlying a thick, gas-bearing section and overlying bottom water (Fig. 1). Wells in such reservoirs are customarily opened up opposite the oil-bearing interval or, rather, opposite the lower part of this interval (Fig. 2). More often than not, it is inefficient or prohibited to blow off large quantities of gas with the oil. This im-psses a severe limitation on the drawdown, which results in low oil-production rates. Because of the small difference in specific gravity between oil and water, the latter will easily cone upwards, so that the production of water together with the oil is not prevented by this completion method. In such a situation wells should be opened deeper, in the originally water-bearing zone. The gas can be shut off by not perforating over the upper part of the interval (Fig. 3) or by a tubing hung close to the bottom of the interval (Fig. 4). Initially much water will be produced, but when steady-state conditions have been established (as depicted in Figs. 3 and 4) larger drawdowns are permissible than in a conventionally completed well, and correspondingly higher oil-production rates will result. Water cuts are only slightly higher because of the small effect of gravity on the water-oil flow distribution. CALCULATIONS The ratio of improvement has been estimated by means of approximate calculations. The completion depicted in Fig. 4 is the most convenient basis for these calculations. By postulating that vertical flow gradients can be disregarded, the Appendix shows that the well-known Dupuit formula can be obtained except for some complication due to the presence of two fluids rather than one. The Appendix makes the reasonable assumption that, for suitable boundary conditions, the oil layer occupies a constant fraction of the total fluid height throughout the reservoir. The oil- and water-production rates can thus be related to the liquid levels in the borehole as follows:

Jan 1, 1966

By Walter C. Woodmansee

The only reported mineral production in 1977 was small output of alluvial gold, valued at an estimated $54,320.2 In addition, marine shells are gathered for use in lime manufacture, although output was not reported. Proposed development of a bauxite mine and smelter, involving Rennell and Vaghena Islands, was deferred in June. Conzinc Riotinto of Australia Ltd. (CRA), in partnership with Mitsui Mining & Smelting Co. Ltd., and the Solomon Government, with- drew from the project, and Mitsui, which conducted a feasibility study and metallurgical testing of the bauxite, decided to defer further work because of slack demand for aluminum in Japan and difficulties in arranging financing. The Mitsui feasibility studies reportedly indicated that the project could be viable despite technical difficulties and relatively high initial investment costs. The project was to produce 1.5 million tons of bauxite and 600,000 tons of alumina per year from reserves totaling 60 million tans at 45% to 50% A1203.

Jan 1, 1981

By Michael A. Piepenburg

The East Side Access (ESA) Project will extend Long Island Rail Road (LIRR) into midtown Manhattan via 11 km of tunnels, a new terminal station and associated support facilities. In addition to the hard-rock tunneling currently underway in Manhattan, soft-ground tunnels in Queens will traverse beneath Amtrak?s Sunnyside Yard and Harold Interlocking, the busiest rail interlocking in North America. This paper details ESA?s coordinated approach to interfacing with both Amtrak and LIRR with regard to the planned tunnels, shafts and related construction beneath or adjacent to the operating railroads. This interface includes integration of railroad staff, extensive presentations, reviews and agreements with the railroads regarding settlement mitigation, real-time automated geo-instrumentation monitoring, ground improvement, and geotechnical/environmental controls.

By Véronique Falmagne

The mining sequence at Noranda?s Bell-Allard mine calls for two mining fronts retreating toward a central pillar known as the Retreat Zone between pyramids A and C. It is clear from numerical modeling and rock mass characterization that the induced stress level in the pillar will exceed the rock mass capacity. A mining plan was developed including the re-dimensioniong of stopes in the Retreat Zone, additional ground support and instrumentation in order to ensure the safety of the workforce and to maximize ore recovery while minimizing production delays. The mining strategy consists in allowing the rock mass to fracture and fail progressively while maintaining control of the existing openings with the appropriate support. A systematic analysis of rockbursting and caving hazards was conducted for all accesses and stopes in order to plan ground support and instrumentation needs.

May 1, 2003

By Juan M. Antorena

A dynamic testing program was performed to evaluate installation procedures, assess capacity of 610-mm (24-inch) diameter open ended steel pipe to evaluate set-up and provide minimum pile tip elevation based on the dynamic testing results. The program was performed for a marine terminal project consisting of a 570-meter (1900-foot) long, overwater railroad trestle. The project location is Santa Marta, Colombia, South America. The subsurface profile generally consisted of 4m (12 ft.) of water and soft to hard silty clays. The piles were installed to an approximate tip elevation of -22 meters (MSL). Three piles were initially dynamically monitored during installation and then later monitored during restrike driving to evaluate pile drivability and bearing capacity including time related capacity increases due to soil "set-up". Knowledge of change in pile capacity with time after end of initial driving is important for design of pile foundations.

Jan 1, 1995

The response was good-one of the best the SAIMM has had to its various questionnaires. 231 replies were received from 2768 members representing a response of 8,35%. For fellows and Members together, the response was 13,7%. The spread of responses based on respondents' work situation appeared to be well balanced with some bias from those in consulting organizations. Members' perceptions of their employers' positions withrespect to environmental management looked somewhat optimistic, but it is encouraging to note that they reported that more than half were developing environmental management systems. Training of varying degree was taking place at al levels in their organizations. Members saw their Institute as an important agent inlifting environmental awareness, literacy and responsibility not only through the journal and symposia, but also by liaison with government departments and educational institutions. Most respondents saw environmental legislation both from local and overseas sources as affecting their organizations, their products and services with the emphasis on corporate image, core business and sales.

Jan 1, 1995

Inn mining communities throughout the western United States, cows have always been part of the landscape as they graze on surrounding rangelands. Until recently, mining companies regarded these animals as something to be kept off their properties — especially any freshly reclaimed lands. During the last few years, though, this situation has begun to change. Today, cattle can be seen in a handful of mine settings, moving up and down the slopes of mine tailings and waste rock. These animals are being used by several companies to do some of the reclamation work once performed by large earth-moving equipment, mechanical spreaders, rippers and seed drillers. This is because cows can contour slopes more naturally and produce and spread soil nutrients in ways that tractors and ripping machines cannot.

Jan 1, 1999

By O. D. Gonzalez

Existing measurements for the steady-state permeation of hydrogen in a iron above 100°C have been examined for contribution of determinate errors. The analysis leads to a recommended equation for the permeability of hydrogen in a iron: o= (2.9 ±0.5) x 10-3 exp - (8400 ± 400)/RT cu cm (ntp H2) cm-1 sec-1 atm-1/2 THE permeability of a iron to hydrogen has been the subject of numerous investigations over the past 40 years, and at present there are thirteen sets of published results for the rate of steady-state permeation of hydrogen in a iron above 100°C. The numerical values in each set of results are entirely self-consis-tent, but the spread among the sets is too large to be attributed solely to experimental error, i.e., to error other than in the specimen itself. Several reasons have been advanced to explain the disparities, but to date the relative importance of experimental inaccuracy to the spread remains uncertain. The purpose of this report is to examine in detail the sources of determinate errors inherent in the experiments and to assess as far as possible the contribution of the errors to the results. The ultimate goal is the selection of values for the permeability and heat of permeation most nearly representative of hydrogen in a iron. The analysis is limited to those experiments in which the permeation rate was observed at steady state—a condition in which traps for hydrogen within the metal are filled to a fixed level15 so that the trapping mechanism is not reflected in the rate of passage of the gas. Furthermore only data are examined in which surface processes are judged to have little or no influence on the flow. It is hoped with these restrictions to obtain values of the permeability and the heat of permeation which will be as closely related as possible to the mechanism of lattice diffusion. I) DEFINITION OF TERMS; UNITS In this report the data for permeation are given in terms of a coefficient oj permeability, ?, which is defined by the equation: jt=?A/?x{p1/2-po1/2) [1] where jt is the total flow of gas normal to the surface of a membrane of planar geometry, e.g., a disc, of area A and thickness ?x; pi and po are the pressures in the input and output sides, respectively. For flow radial to the walls of a membrane of cylindrical geometry, e.g., a tube, the corresponding equation is: where 1 is the length of the cylinder, and ri and ro are the inner and outer radii, respectively. The flux normal to the surface is given by Fick's law: j= -D(dc/dx) [3] At steady state the concentration gradient will be constant, and integration of Eq. [3] gives for the total flow through a disc of area A and thickness Ax: h =-DA(co - ci) [4] where c, and ci are the concentrations of solute at the output and input surfaces, respectively. When surface control is absent, co and ci are given by Sievert's law c = Kp1/2, and substitution therewith into Eq. [4] gives directly Eq. [I] where ? = DK. Integration of Fick's Eq. [3] in cylindrical coordinates will give Eq. [2] where again ? = DK and is thus shown to be independent of geometry (provided that surface control is negligible). The coefficient of permeability, or simply the permeability,* must be expressed in proper units. In *The term permeability will refer in this report always to the coefficient defined above; permeation will be used to specify the general phenomenon of gas passage through a membrane. this report ? will be expressed in the units of cu cm (ntp H2) cm-1 sec-1 atm-1/2. The variations of D and K with temperature are given by D = Do exp(-Ea/RT) and K = KO exp(-?Hs/RT) where E, is the activation energy for diffusion and AH, the heat of solution, each usually expressed in calories per mole of solute. The variation of permeability with temperature will thus be given (for conditions where surface control is negligible) by ? = ?o exp(-?Hp/RT) where ?0 = DoKo and ?Hp = Ea + ?Hs. The units of ?0 are the same as those of 6, and??Hp will be expressed in calories per mole H. 11) SUMMARY OF PERMEABILITY RESULTS Table I gives the values reported to date for the permeability of H2 in a iron in terms of ?o and ?Hp. Except where noted the parameters listed were taken directly from the numbers reported by the various investigators with only a change in units. The temperature limits within which the listed ?o and ?Hp hold are given in column 7; the limits marked in parentheses in this column indicate the entire temperature range covered in each investigation. The listed values of ?o and ?Hp are those giving a linear plot of ln? against T-1 at the higher temperatures in each set of measurements, and thus presumably represent the case for which surface control was negligible. Column 6 gives values of 9 at a representative tem-

Jan 1, 1970

Experimental studies on viscosity of titanium bearing slags have been reviewed and the assessed data were used in extending the capability of the structurally related viscosity model for silicate melts, developed by the present authors. Experimental data on ternary and higher order systems containing CaO, MgO, MnO, FeO, Al2O3, TiO2, Ti2O3, SiO2were assessed and used. The newly extended viscosity model represented the viscosity behaviour over broad temperature and composition ranges. The structural role played by TiO2and Ti2O3in silicate network structure is discussed with respect to their effect on viscosity of melts. Keywords: viscosity model, TiOx containing silicate melts, silicate network structure.

Jan 1, 2004

By P J. Minehan

The investigation of the potential of the Webb/Baynes block of the Buller coalfield for anode carbon manufacture has generated much information on the physical beneficiation characteristics of the Buller coals in general. A further 36 drill holes of the block in question and several other samples have been analysed by sink/float analysis, either at a single density or over a range of densities. In addition, many samples have been beneficiated on a laboratory shaking table or by flotation. The ash content can be reduced by a variable factor. The reduction factor of between two and four by sink/float analysts is understandably less for tabling where separation is not perfect. All Buller coals behave similarly, there being greater ash reduction factors for higher ash coals.

Jan 1, 1983

By P Holtham, J Meng, E Tabosa, W Xie

Turbulence and its distribution are of great importance in flotation, and have received considerable attention recently. However, there is no mature technique to measure turbulence in three-phase (liquid-solid-gas) industrial flotation cells due to the opaque, highly aggressive and abrasive nature of the slurry involved. Previous research has shown that the piezoelectric vibration sensor (PVS) is a promising tool for turbulence measurement in industrial flotation cells. The PVS is a robust device that converts mechanical vibration to electrical signal, from which turbulence information can be extracted. An improved calibration method has allowed development of a frequency model to calculate the force applied to the sensor. Experimental results and comparison with laser doppler anemometry (LDA) have shown that the PVS can measure fluid kinetic energy, which is related to turbulent kinetic energy, a parameter used in the literature to represent turbulence in flotation. Laboratory measurement in a two-phase (water and air) 60 L cell and with slurry in a 3.5 L cell gave good stable results and mostly consistent trends between the measured turbulence profile and cell operation. When applied in a 300 m3 industrial cell filled with water, the addition of air or slurry to the cell resulted in a shift in the turbulence profile. This is expected because a change in fluid density will change the force applied to the sensor. It is therefore concluded that the piezoelectric sensor is an easy-to-use and robust technique that is fully capable of measuring turbulence in industrial flotation environments.CITATION:Meng, J, Tabosa, E, Xie, W, Runge, K C and Holtham, P, 2014. Development and application of a piezoelectric sensor for turbulence measurement in industrial flotation cells, in Proceedings 12th AusIMM Mill Operators’ Conference 2014 , pp 457–470 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 1, 2014

By Jafar Khademi Hamidi

The Zagros long tunnel is one of the main components of Sirvan water transfer project in western Iran. It is approximately 48 km in length and consisted of two lots. The second 26 km lot of this tunnel is under construction by a 6.73 m diameter double shield (DS) TBM. The tunnel passes through several formations with wide range rock mass qualities. During the tunnel alignment, changes in rock quality were highly frequent from poor to very good. The encountered geological conditions required TBM operation to change frequently from hard rock to soft, dry to flowing, sticky to nonsticky ground (and vice versa), more often than expected. In the course of tunneling, the machine has encountered nearly many adverse geologic conditions. The most important problems have been sudden high volume water inflow into the tunnel, sticky ground, and gas seepage, all of which resulted in reduced TBM advance rates. This study will high-light two difficult ground conditions including large water ingress and sticky ground and also the related problems encountered by the TBM along 8 km of excavated tunnel. In sticky grounds, cleaning of the clogged cutter head caused many delays and contributed to additional downtime. Application of some operational modifications, including decreased TBM thrust showed satisfactory results in such cases. While reduced thrust resulted in reduced penetration rate, but the overall TBM advance was greatly improved by the increase utilization rate and elimination of down time related to cleaning of the head. To cope with high water inflow, application of preventive measures such as pre-grouting has proved to be a more efficientsolution. The sealing of ground water inflow also decreased seepage of dangerous H2S gas and other chemicals such as hydrocarbons accompanying the groundwater.

By David C. Oyler

Three long horizontal holes were drilled from a directionally drilled surface hole at the Emerald Mine near Waynesburg, Pa. The purpose was to adapt the technique of directional drilling for use in draining methane from coalbeds. A 504-m (1,652-ft) long, 76-mm (3-in) diameter, circular arc pilot hole was drilled, using a downhole mud motor, to enter the Pittsburgh coalbed at a vertical depth of 305 m (1,000 ft). The hole was reamed to 222 mm (8-3/4 in) and was cased to a measured depth of 486 m (1,595 ft). Three 76-mm (3-in) diameter horizontal drainage holes were then drilled, totaling 2,909 m (9,544 ft) of horizontal hole. Improvements in drilling methods increased the average drilling rate from 20.4 ill (67 ft) to 64.9 m (213 ft) per day. The cost of drilling the directional and horizontal holes (using a Government-owned drill rig) was $1,169,530, a figure inflated by inexperience and by delays caused by lost-circulation problems and fishing operations. An estimated total drilling cost of $960,000 (including rental of a drill rig) for an improved system, was determined by a detailed cost analysis. Initial gas and water production from November 1979 through May 1980 was low because of caving of the horizontal holes drilled in shale near the bottom of the casing.

Jan 1, 1982

By K Ehrig, J Griffith

An extensive suite of elements are routinely assayed on all resource drill core samples to assist in deposit scale resource definition, local mine scale delineation of ore zones, and ore characterisation for the planning and scheduling of mining and processing of ores at Olympic Dam. This paper discusses a deposit scale geochemical relation that can be used by mine geologists to find more high-grade ore at the local mine area scale at Olympic Dam.A 3D grade shell representing 0.8 per cent Cu was created for a mine area using drill hole assay data. This defined the geometry of the ore zone. The Cu-grade shell was then overlain onto the existing resource block model to evaluate the relationships between the Cu-grade shell, copper and other elements. The strongest correlation was between copper and manganese. The block model showed a dramatic decrease in the concentration of manganese just below the below the Cu-grade shell.Several drill holes that intersected the Cu-grade shell were selected to evaluate the copper manganese relation at the drill hole scale. As expected, the individual drill holes displayed a strong inverse relation between copper and manganese. A geochemical footwall was then modelled representing 0.1 wt per cent Mn. Using both the Cu– and Mn-grade shells, several drill holes were designed/drilled and all hit high-grade copper.For the vast majority of the deposit the inverse relation between copper and manganese is valid; however, in areas with intense chlorite alteration (related to amounts of mafic to ultramafic rocks) this relation is not as strong, due to increased manganese in the rock mass. Even though using the copper manganese relation as a drill targeting method was not always as reliable in a few small areas of the deposit, it demonstrates the value of using existing assay data integrated with the resource block model to discover local mine scale geochemical relationships which can be used to more effectively design drill holes to discover high-grade ore at Olympic Dam.CITATION:Griffith, J and Ehrig, K, 2017. Using existing data to improve the delineation of ore at the Olympic Dam Fe-oxide Cu-U-Au-Ag deposit, in Proceedings Tenth International Mining Geology Conference 2017, pp 321–326 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 20, 2017

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967