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By Kenneth L. Myers

The net balance of the inflow and outflow of water in a tailings storage facility has major economic implications in any large mining and milling operation. In a net precipitation environment it can control the ultimate size and storage capacity of a facility or dictate the need for an expensive treatment and discharge program. In a net evaporation environment it can control the extent of the water rights acquisitions required for makeup water and dictate the number and size of expensive wells and pumping and delivery systems. The elements considered in a water balance analysis include the anticipated production rate, the water content of the slurry used to deliver the tailings, inflow from precipitation and snowmelt, and losses from evaporation and seepage. The mine can exert significant control over only one of these elements: the production rate. All others are subject to considerable uncertainty from month to month and year to year. The traditional approach is to analyze in a spreadsheet environment by making simplifying assumptions and using monthly mean or "average" values for precipitation inflows and evaporation losses. Often the analysis will be repeated with values subjectively assigned to represent a "wet" year or "dry'' year. The probabilistic approach uses the same basic spreadsheet model in conjunction with a probabilistic simulation add-in program allowing probability distributions to be substituted for any of the deterministic variables. The resulting analysis shows the full range of variation possible for each parameter of interest (i.e., available return water, makeup water required, storage, seepage losses) and estimates the exceedance probabilities for each. The potential uses and advantages of the probabilistic approach are discussed.

Jan 1, 1992

By J. D. Bennett

The degree of injury and days lost from work due to an injury are examined for selected electrical sources, occurring in conjunction with falls of the injured miner or with selected machinery, that could have been eliminated by use of diesel equipment. Although the number of electrical source injuries that could have been prevented is small relative to the total number of injuries during the period examined, many lost-time injuries could have been precluded and thousands of days lost from work could have been avoided.

Jan 1, 1984

By E. C. Hopkinson, A. H. Youmans, R. A. Bergan, H. I. Oshry

A new log has been developed for quantitative formation evaluation which is based on a measurement of the length of time slow neutrons survive before they are captured in the rocks and fluids. The logging instrument employs a cyclically pulsed neutron generator and a gated scintillation counter which is synchronized with the source. The source emits short, intense bursts of 14 mev neutrons once every 1,000 microsec and is quiescent between bursts. During the period the source is quiescent, the detector is electronically actuated for two independent preselected intervals. A comparison of the counting rates during these two intervals gives a measure of the rate of decay of the slow neutrons and of the associated gamma radiation. The average neutron lifetime in most earth formations is in the range from 50 to 500 microsec. It can be measured during a continuous logging operation at conventional logging speeds. The design of the logging instrument is described and the results of tests are compared with theoretical predictiom. Formulas are developed which give the relationship between log response and formation properties. It is shown that the method is particularly sensitive to formation fluid salinity, and that salt water saturation can be measured accurately in either cased or open hole. The measurement can be made independent of borehole size, fluid type, casing and tool position in the hole by properly selecting the intervals during which the measurements are made. The results of tests with a prototype logging tool are given. INTRODUCTION A new nuclear logging system has been developed which employs the Accelatron,* an accelerator-type neutron source, and accurately measures formation brine saturation in an entirely new way. It has produced a type of formation log with better sensitivity, greater sampling depth and simpler quantitative interpretation than any other nuclear log thus far suggested. The new Neutron Lifetime Log* employs a pulsed electromechanical neutron source and a synchronously gated radiation detector. A prototype instrument has been field tested during recent months to demonstrate the operability of the apparatus and the feasibility of the method. Tests in wells and simulated boreholes have confirmed theoretical predictions and have shown that formation param ters can be measured independent of casing and other borehole parameters. Preliminary results of field tests have indicated that the log may have important and widespread applications. BASIC PRINCIPLE OF NEUTRON LIFETIME LOG The Neutron Lifetime Log is based on the fact that neutrons emitted by a source in a well are rapidly but not instantly captured by the material around the source. Their capture is a matter of statistical probability; the greater the number of capturing nuclei and the greater the "capture cross section", the greater is the probability that a neutron will be captured quickly. The average life of a thermal neutron in vacuum is about 13 minutes, but in common earth materials, the average neutron life ranges between extremes of about 5 rnicrosec for rock salt and perhaps 900 microsec for quartzite. The Neutron Lifetime Log responds to variations in this average neutron life. The theoretical basis for a log of this general type has been well understood by nuclear logging experts in many laboratories both in America and in Russia, and develop mental work along these lines has been in progress for many years. The Russian literature has reported both theoretical and experimental work1,2 but in this country there have been no published reports of progress toward a practical logging instrument. The logging instrument is designed to measure radiation produced by slow neutrons during selected intervals when no neutrons are being emitted by the source. The source is arranged to emit neutrons in bursts or pulses. During the quiescent interval between the pulses, it is possible to observe the exponential "decay" of the neutrons and the neutron-induced radiation as the individual neutrons progressively disappear due to capture by atoms in the formation or the borehole. When a short pulse of 14 mev neutrons is emitted by a source in a borehole, the individual neutrons are slowed to thermal energy within a few microsec. Thus, a cloud of "slow" neutrons is formed around the source within 10 to 50 microsec after the pulse. This cloud is most dense within a few inches of the source, and is progressively less dense out to a radius of about 3 ft, where radiation from the source is practically undetectable.

Jan 1, 1965

By AIME

The following corrections (in italics and bold face) were received too late for the September issue of Transactions: Page 270, Abstract, line 1, spelling should be goethite. Page 270, column 1, authors' box, authors' affiliations should read: L. A. BAKER, formerly Principal Research Scientist, is Pellet Plant Superintendent, Cliffs Western Australian Mining, Cape Lambert, W. A., Australia. C. G. THOMAS is Experimental Officer, Minerals Research Laboratories, C.S.I.R.O., North Ryde, N.S.W., Australia. R. J. CORNELIUS and K. S. LYNCH are General Superintendent, Product and Process Development, and Superintendent, Pellet Plant, respectively, Hamersley Iron Pty. Ltd., Dampier, W. A., Australia. G. J. ARMSTRONG, formerly Chief Metallurgist, Hamersley Iron Pty. Ltd., is Mill Superintendent, Samin Ltd., Burra, S. A., Australia. Page 271, column 2, line 41, should read "highest possible spalling temperature and to adjust the. . :' Page 275, column 1, line 1, should read "(LOI) figures are shown in Table 1 and vary from 2.61..." Page 275, column 1, line 16, spelling should be goethite. Page 276, column 2, line 6, should read "Predicting Grate Speed and Production Rate: The cor-..." Page 276, column 2, line 8, should read "basis of Blends A, B, C, D, and Plant Ore 1, shown in Table..." Page 276, Table 3, heading under "Prediction Method" should read Blend E. Page 277, column 1, line 38, should read "=293 tph of specification pellets (see Table 1 for loss-..." Page 277, column 2, replace caption for Fig. 14 with the following: Fig. 14-Example of calculation of hood temperature profile during downdraft free-water drying, given plant free-water drying time. Page 277, column 2, replace caption for Fig. 15 with the following: Fig. 15-Example of calculation of hood temperature profile during drying, given plant goethite drying time.

Jan 1, 1974

By J. C. Wynn

J.R. Hillebrand From the abstract, "A realistic ore deposition model to serve as a conceptual framework." Further, on page 246, "The first area of study was the Josephine peridotite, now identified as an ophiolite terrane, located in northern California and south-western Oregon (Fig. 3). Here, it was felt that we could test the models shown in Figs. 1 and 2 and, if successful, expand the model and test it in other chromite districts in the US and around the world." My comments refer only to chromite deposits in Europe and the Middle East. First, I question that may chromite deposits occur in the idealized ophiolite section shown in Fig. 1. Second, although some podiform deposits (referring to morphology) have been important (Guleman, Turkey, for example), the stratiform deposits are of greater importance in tonnage and frequently grade. Examples include Nada, Yugoslavia; Bulqiza, Albania; Xerolivado, Greece; Saranovsk, Russia; and Abdasht, Iran. Reply by J.C. Wynn Mr. Hillebrand raises two issues that deserve a serious response. One issue is basically subjective and the other is ultimately political. First, the question of where (and how many) podiform chromite deposits are found in the idealized ophiolite section of Dickey (1975). The Dickey model is still perhaps somewhat controversial (Panayoutou, 1980), but our experience in the Josephine ophiolite of northern California (Wynn, 1980; and Albers, 1983) shows that the model works well there. Virtually all the chromite is found in dunite lenses in the tectonite peridotite (harzburgite). Since there are few complete ophiolites exposed in the world, the model will probably never satisfy everyone. The degree of acceptance is a function of any individual's subjective experience. Second, it is well known that stratiform chromite contributes more than 95% of the chromite reserves presently known in the world, and it could be reasonably argued that there is no point in exploring for or exploiting podiform deposits further. The title of the paper, however, was in part 'strategic minerals geophysical research'; chromite is considered a strategic and critical mineral of the US and many other industrialized nations. Stratiform deposits in South Africa and Zimbabwe account for most of the chromite reserves in the world. Unfortunately, experience in modern times with substantial price fluctuations and even resource cartels dictates the wisdom of identifying and maintaining a national chromite reserve, irrespective of the cost. An improved exploration methodology is an essential element in this strategic objective. References Albers, J.P., 1983, "Geological and Geophysical Studies of Chromite Deposits in the Josephine peridotite, California and Oregon," US Geological Survey Bulletin 1546 A-D, 118 pp. Dickey, J.S. Jr., 1975, "A Hypothesis of Origin for Podiform Chromite Deposits," Geochimica et Cosmochimica Acta, Vol. 39, pp. 1061.1074. Panayiotou, 1980, Proceedings, International Ophiolite Symposium, Cyprus, 1979, 781 pp. Wynn, J.C., 1980, "Exploration Geophysical Methods and Strategies, and Their use to Locate and Assess Small Mineral Deposits," Chapter 12 of Meyer and Carmen, eds., The Future of Small Scale Mining, McGraw-Hill, New York, pp. 75-83.

Jan 12, 1983

By E. C. Potter

It is not the purpose of this paper to enter into the minutiae of a subject so vast, upon which volumes have already been written and volumes more might still be written, but simply to pass in review the characteristic features of that practice, which, dating from the blowing-in of the Edgar Thomson "A" furnace in 1879 and continuing down to the present day, has given to American blast-furnace operations a new significance. The blowing-in of " A" furnace marked the beginning of a new era in the science of iron-smelting if, indeed, it was not the very birth of science as applied to this industry in the United States. American blast-furnace practice in its generic sense and world-wide significance dates from that day, and really all that is valuable, all that is remarkable or worthy of discussion, is embraced in the experiences and achievements of the past fifteen years. Back of that we find only the dead level of mediocrity, or worse, a dispoition to " let well enough alone;" a general, almost universal, employment of " rule of thumb " methods. The application of scientific principles and methods was rare and, indeed, previous to the introduction of the Bessemer process in the early seventies, science had no place in controlling the operations of the American blast-furnace. The old practice consisted mainly in dumping raw materials in at the top of the furnace and tapping out iron and slag at the bottom, for the successful consummation of which the furnace-manager directed his best energies toward keeping the furnace as free as possible from "gobbing" with, alas ! but indifferent success. The burdening of the furnace was based largely on Mark Twain's receipt for " Johnny-cake," altered to suit the circumstances, viz.: a lot of ore, a lot of fuel and about a quarter of a lot of flux. The possible capacities of furnace-plants were not nearly realized. Enormous wastes were permitted, unheeded because not understood. In the use of fuel quantum suff. was always the rule. Increase of product was not thought of because it was not deemed wise or safe to attempt

Jan 1, 1894

By H. G. Schneider

The Smackover oil and gas field lies in Ouachita and Union Counties, Ark., in the south-central part of the state, in T.15 and 16S., R.15, 16, and 17W. It is 10 miles north of El Dorado, the principal business and railroad center in the south-central part of the state, and extends from the town of Smackover in all directions. Productive territory having an aggregate area of nearly 55 sq. mi. has been developed. It extends 6 miles from north to south and 12 miles from east to west. The field may be divided into two parts: the east district, which includes the area east of the town of Smackover, and the west district, which includes the area west of the town of Smackover. In relation to the neighboring productive fields of Arkansas, the Smackover field is 9 miles north of the El Dorado oil and gas field, 8 miles slightly west of north of the East El Dorado oil and gas field, and 16 miles east of the Stephens oil field. Smackover was discovered in May, 1922, when the Oil Operators Tnist drilled well No. 1 on the J. T. Murphy farm, in the southeast quarter of sec. 8, T.16S., R.15W. This well is located almost on the top of the Norphlet dome and was drilled to the Nacatoch sand. It had an initial open flow volume of 30,000,000 cu. ft. of dry gas per day, and a rock pressure of 950 lb. per sq. in. In July, 1922, the V. K. F. Co. completed the first oil well in sec. 29, T.l5S., R.l5W., on the north side of the Norphlet dome, and 3 miles north of the first gas well. This well started the active development of the north and northwest sides of the dome.] The field was extended westwards, when oil was discovered in the Nacatoch sand, during October, 1922, in sec. 4, T.l6S., R.l6W., 51/2 miles west of the original gas well. This opened up the so-called "light oil district," which is located on a structural terrace, for which the name

Jan 1, 1924

By Pharis E. Williams

The ability of voids, microballoons, and even solids to sensitize explosives has been known and used for many years. This phenomenon has generally been studied and reported under the terminology of "hot spots" because of the increase in local pressure and temperature when a shock wave encounters such sensitizers. A method for treating this phenomenon in detonation theory or in a detonation model has been studied for almost the same length of time. Perhaps because of the complexity and non-linearity of the void, or microballoon collapse, several of these studies have used the expediency of including additional terms in the burn rate law to account for the influence of hot spots. The detonation model proposed here considers the sensitization due to discontinuities in the shock impedance to be a mechanical phenomenon to be accounted for in the mechanical equations governing the detonation and not in the burn rate law. While this is not a new contention, the method for handling this non-linear phenomenon within the proposed model is new. The model also includes a method which accounts for the manufacturing variables of emulsion matrix cell size, microballoon size and type, as well as energetic additives.

Jan 1, 1992

By Leahy G. J, Moxon N. T, Nicol S. K

Experimental work is described in which extremely dilute aurocyanide liquors are treated with novel surface-active complexing agents to produce a hydrophobic aurocyanide species. Subsequent aeration of these liquors causes accumulation of such species at the air-water interface and the aurocyanide complex is transferred to a froth concentrate. A detailed performance assessment of this process is made and this knowledge used in the design of a pilot plant facility. Early results indicate the feasibility of the selective recovery of aurocyanide ions from reclaimed residue dam water (approximately 0.2ppm Au) with upgrade ratios of the order 180:1. A further study was made applying ion flotation to the recovery of gold from a carbon-in-pulp (CIL) feed liquor (approximately 1.0ppm Au). The probable economics of this process compared to conventional CIL processing is also described. Successful development of countercurrent ion flotation for concentrating solids-free gold solutions may offer a lower cost alternative to existing gold ore processing technologies, or in more secondary applications such as concentrating dilute gold solutions or heap leach runoff. The technology may also have more generalised applications to other heavy metal process- Ing.

Jan 1, 1991

"The Merensky Reef is a platinum group minerals (PGM) bearing reef in the Bushveld Igneous Complex in South Africa. The reef has been treated by bulk PGM and sulphide flotation with the aim of maximisingthe valuable minerals recovery and gangue minerals rejection.Synthetic water with a calcium concentration of 80 ppm and 500 ppm was prepared and the flotation results obtained were compared to a simple electrolyte in order to determine the effect water quality has on pentlandite and pyroxene surface alteration and, ultimately, floatability. During the study, the possible effect of interactions between the minerals investigated and Ca2+ ions in the presence of sodium isobutyl xanthate was studied at pH 6 and pH 9 by means of zeta potential determinations, microflotation tests and ToF-SIMS analysis.The results obtained on 1:1 pentlandite-pyroxene mixtures showed that the quality of process water plays an important role in flotation. The flotation recoveries of pentlandite and pyroxene were lower in synthetic process water compared to those obtained in a simple electrolyte solution."

Jan 1, 2003

By D. Caiden, C. S. Covil, P. J. Chamley

The paper describes the background to alternative delivery models, drawing on international experience, and introduces Project Alliancing/Contract Partnering, common risks and risk sharing on tunnel projects. A plea for early contractor involvement in design is made before describing some whole life design implications for tunnels. The paper concludes with four short case studies; Channel Tunnel Rail Link in the UK, Hull Waste Water Tunnel in the UK; Island West Sewage Transfer Station in Hong Kong, and the New Southern Railway in Australia.

Jan 1, 2005

By Lee Sieng Kai

This paper presents the result of the analysis of strain-dependent concrete modulus from full-scale static axial compression load tests conducted on more than 200 instrumented cast-in-place barrettes and bored piles over the past 12 years, covering commonly adopted grades of concrete for heavy foundation construction in Malaysia and Singapore. The concrete modulus values, Ec, analysed were directly back-calculated from the material of the instrumented test piles by means of placing a layer of vibrating wire strain gauges near the pile head region. The best fit curve for back-calculated concrete secant modulus versus measured axial strain follows non-linear behaviour for both categories of test pile samples analysed. The result of the analysis seems to suggest that using average constant modulus value would generally lead to a significant error in load distribution computation, particularly at high stresses region.

Jan 1, 2006

By Ernie Doell, Trung Nguyen

"In early 1995 Cluff Mining commissioned a newly constructed high density tailings thickener at its Cluff Lake uranium mill. The 85 ft diameter high density thickener is one of the first of its kind in North America, and incorporates the novel paste technology in its design to produce densified (in the range of 60 -65% solids) mill tailings suitable for stable deposition in the tailings management area. This paper discusses the impetus behind the installation of such an unconventional thickener, and the many trying experiences in making it operational.IntroductionCluff Mining, a wholly owned subsidiary of Cogema Resources Inc., is the operator of a uranium mine and mill complex at Cluff Lake which is located in northern Saskatchewan. Since 1980, the company has developed and mined out several different ore bodies within the Cluff Lake region for the production of uranium concentrates, commonly known as yellow cake. Based on the known ore reserves, the Cluff Lake operations are projected to last till the early 2000's.Tailings from the Cluff Lake mill have been discharged to a tailings management area consisting of a tailings pond and two facilities for primary and secondary treatment systems. The tailings pond has an impervious bentonite lined dam, and it is divided into a solids and a liquids holding areas. Until the beginning of 1995, the mill tailings were discharged in two separate lines to the solids pond; one line carried the slurry residue of 45-50% solids (w/w) from the CCD circuit, and the other discharged raffinate tails containing less than 1 % (w/w) gypsum precipitate. Supernatant in the solids pond is treated in the primary treatment system prior to discharging to the liquids pond. Figure 1 shows the site plan of Cluff Lake tailings management area.It has been estimated that by the end of 1995 the solids pond would be filled to about 60% of its design capacity, and probably would be full before the year 2000. Therefore, Cluff Mining had to consider a more efficient tailings disposal method that could extend the service life of the existing Cluff Lake tailings management area. A high density tailings thickener was believed to be the most practical and economical system for tailings disposal at Cluff Lake mine."

Jan 1, 1996

By Raja V. Ramani, Ralph W. Barbaro

This paper presents an application of a Mixed Integer Programming (MIP) model to the problem of locating a centralized coal preparation plant and determining the production schedule for the mines. The system used for illustrating model application is hypothetical but realistic. It consists of three mines, two potential preparation plant sites, heavy media processing plant, and one market. The goal is to maximize the total profit of the system while satisfying the coal delivery schedule over a three year period meeting both quantity and quality requirements (ash, sulfur, and heat content). In addition to the base case, four different scenarios are analyzed. These four modifications are: (1) removing the flotation circuit from the preparation plant and sending all of the fines directly to the clean coal, (2) lowering the quality of coal from one of the mines, (3) applying discounts to the unselected site to improve its competitive position, and (4) adding a new mine. A detailed discussion of the base case and the effect of these four alternatives is presented.

Jan 1, 1983

By David L. Rife

Fluid inclusions have been studied since the mid-1800s. In 1858, the famous English geologist H. C. Sorby, stated that ". . . there is no necessary connection between the size of an object and the value of a fact, and that, though the objects [inclusions] ... are minute, the conclusions to be derived from the facts are great."' This statement philosophically emphasizes why fluid inclusions should be studied. Fluid inclusions supply the economic geologist with "hard" data on the chemical environment and mechanisms of transport for ore fluids. Such studies enable geologists to understand more about their complex nature. The information that can be obtained from fluid inclusions is as follows: 1) Fluid inclusion "filling temperatures" measured with the microscope heating stage, reflect the hotness of an ore fluid at the time of its entrapment and are one of the most accurate methods of geologic thermometry. 2) Ore fluid densities indicate the extent to which ground water becomes mixed with ore fluids. Density is determined from the composition of inclusions, the ratios of gas to liquid (at room temperature), and from

Jan 1, 1973

By R. M. Moon

Neutron scattering has played a crucial role in advancing our understanding of rare-earth materials. It has provided a detailed description of the rich array of exotic magnetic structures; it has confirmed the accuracy of theoretical wave functions for the 4f electrons; and it has provided fundamental data on the collective magnetic excitations in these materials. The fundamental property of the neutron which has been exploited in this work is the magnetic interaction which exists between the magnetic moment of the neutron and atomic magnetic moments on individual rare-earth atoms. This interaction produces scattering of neutrons in a manner closely analogous to the scattering of X rays by atomic charge distributions. In a material exhibiting long-range magnetic order, Bragg diffraction peaks will appear at scattering angles determined by the periodicity of the magnetic structure. The Bragg intensities are determined by the magnitude and relative directions of the atomic moments. The rare-earth metals and alloys are characterized by sinusoidal modulation of magnetic moment components which can be combined in various ways to produce a variety of magnetic structures. The periodicity of these modulations is frequently not related simply to the underlying periodicity of the chemical structure. The major features of these structures are explained by the combined, and sometimes competing, exchange and crystal-field interactions. At a more fundamental level, neutron diffraction also gives information on the spatial distribution of a magnetic moment in a rare-earth atom. This moment comes from the 4f electron shell, and accurate measurements of the neutron scattering amplitudes have been used to check the accuracy of atomic wave function calculations for the 4f electrons. It was found that relativistic Dirac-Fock calculations are in excellent agreement with the experimental results. Collective excitations of ordered magnetic systems are described in terms of spin waves, which are sinusoidal modulations in space and time of the direction of the ordered moments. Inelastic neutron scattering is used to measure the energy and wave length of these collective excitations. Analysis of these data gives direct information on the interatomic interactions responsible for the magnetib properties of these materials.

Jan 1, 1992

By H. Rossmanith

This contribution introduces the fundamental concepts of wave propagation and fracture mechanics which form the basis of electronic blasting, i.e. precise initiation timing using electronic detonators. The concept of Lagrange diagrams will be frequently used for the calculation of the delay time between blast-holes in a row and rows of blast-holes. The effect of burden and structural geology will be briefly touched. It is found that the advanced blasting technology based on the use of electronic detonators introduces a change of paradigm. It will be shown that knowledge in wave propagation and fracture mechanics is essential for the successful application of the new blasting technique in industry. In particular, the delay time, the wave speeds in the rock mass, the shape of the wave pulse and the acoustic impedance mismatch have become decisive parameters in advanced blasting. Utilizing the wave speed and wave shapes of detonations, large scale tests Utilizing the wave speed and wave shapes of detonations, large scale tests in various countries (Australia, Chile, etc.) have shown that optimal delay timing requires shorter delay times in conjunction with allowing for a wider drilling pattern and the use of a reduced amount of explosives, i.e. a lower powder factor. This seemingly contradictory arrangement is fully justified by using scientific principles in blasting, and converting blasting from an art to a scientific discipline.

Jan 1, 2003

By T. G. Joseph, K. Barron

A strain-softening constitutive relationship is introduced that describes the post-failure stress-strain curve for rock regardless of whether the rock is intact or broken. The core of this relationship is an “apparent friction” concept that relates the post-failure apparent cohesive and frictional characteristics of the rock to the strain. The relationship can be determined for a given rock via a series of triaxial strength tests establishing the peak strength and corresponding strain for a range of confining pressures, together with the determination of the base angle of friction via a simple tilt test. The postulates and assumptions used in deriving this relationship are verified from results of tri-axial tests on both intact and broken rock. This strain-softening relationship is then applied to coal. Having determined the post-failure stress-strain curve for coal specimens, this information can then be used in a finite element program, such as Phase 2, to examine the post-failure characteristics of coal pillars. Using example data, the strength of coal pillars of different width/height ratios are estimated and compared with well-known empirical pillar size-strength relationships. In addition, the post-failure stress-strain behaviour of a coal pillar is compared with an empirical relationship reported in the literature.

Jan 1, 2003

By Y. C. Kim, F. Szidarovsky

The technique of linear kriging as a grade estimation method of mining blocks is reason¬ably established in the mining industry. During the kriging process, negative kriging weights ([]i) are sometimes encountered. Due to negative kriging weights, negative block grades may be obtained in some extreme situations, which makes no practical sense. To guarantee nonnegative weights, an additional constraint is required in the kriging system of equations. Unfortunately, the nonnegative weight constraint results in a set of nonlinear system of equations. In this paper, a derivation of the resulting set of nonlinear equations is presented and a numerical algorithm is developed for the solution of the equations. Because the algorithm developed does not remove negative weights arbitrarily, optimal nonnegative weights are always guaranteed. Results obtained using the developed algorithm were compared with those using the standard linear kriging, in terms of computer, time and the estimation results. Both the computer time and the kriging variance were found to be higher with nonnegative constraint, as expected. However, some systematic pattern was observed in the kriged values (i.e., over-or underestimation) with or without the nonnegative constraint. The study also demonstrated when one should generally expect negative kriging weights in practice, and what practical impact the negative weights can have on the kriging estimates.

Jan 1, 1987

By M. H. Cullender

The performance characteristics 01 gas wells producing from formations which fail to stabilize within a relatively short period of time are obscured by the interrelation of the coefficient (C) and the slope "n" of the conventional back-pressure curve q = C(P2 f- p2s)n An empirical method is presented whereby the characteristic or true slope (11) of the back-pressure curve may be determined for a particular gas well. For those gas wells which do not stabilize within a relatively short period of time, the coefficient (C) is considered as a variable with respect to time and as a constant only with respect to a specific time. Thus, the back-presrure performance of such a well is presented as a series of parallel curve5, each curve representing the performance of the well at the end of a given time interval. Through use of the method presented, a simple presture gradient is developed and maintained within the drainage area around a producing gas well during the test period in order that the variation of the coefficient (C) with respect to time does not obscure the true value of the lope. INTRODUCTION The back-pressure method of testing gas wells as set forth by Schellhardt and Rawlins1 is dependent upon the requirement that a series of flow rates and corresponding pressure data be obtained under stabilized conditions. These data arc then plotted on logarithmic coordinates of flow rate (Q) vs difference in squared pressures (P2f — P2s) in order to determine the constants (C) and (n) for Equation 1. With respect to this method of presenting the performance characteristics of a gas well, it should be pointed out that although Equation 1 is an empirical relationship, the form of the equation was justified to a considerable extent by an independent development by Muskat and Botset.2 This development was theoretical in nature; however, certain assumptions with respect to the type of flow existing (viscous vs non-viscous) were madc which may or may not be correct. As the use of the method presented by Schellhardt and Rawlins spread through the industry, it became evident that the method of testing was applicable for those wells which approached stabilized prbducing conditions within a relatively short period of time. Performance characteristics could not be determined by this method, however, for wells which approached stabilized protlucing conditions slowly over a considerable period of time. This characteristic of "slow stabilization" has generally been associated with gas wells producing frorn reservoirs of low permeability. As the demand for natural gas continued to grow through the years, a great number of wells were completed in reservoirs of low permeability which exhibited "slow stabiliz:~tion" characteristics. Consequently, the problem of determining the true performancc characteristics of these wells became more apparent. It is with this problem in mind that the isochronal performance method of determining the flow characteristics of gas wells is presented.

Jan 1, 1956