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This pamphlet and the enclosed video describe a safe, effective and economical method for removing dust from work clothes. Background Information Dusty work clothes can increase a worker’s exposure to respirable dust. Respirable dust is usually considered to be particles having an aerodynamic diameter of 10 microns or less and able to enter and deposit in the gas-exchange region of the human lung. A former U.S. Bureau of Mines report documented a 10-fold increase in worker dust exposure on a number of separate occasions from dusty work clothes.* It was found that once clothes become contaminated, they are a continual dust source until cleaned. The only MSHA approved method to clean work clothes requires a HEPA-filter vacuuming system which is very time consuming and difficult to perform effectively. Therefore, most workers use a single air hose (not MSHA approved) which can elevate dust levels for the worker, co-workers, and the work environment. A substantial amount of engineering technology has been developed that, when applied, can significantly lower respirable dust exposures of workers at mineral processing plants. But even with these improvements, some workers continue to exceed their permissible exposure limit. Elevated exposures increase the potential for developing debilitating or fatal lung diseases. ?e clothes cleaning method described within is an example of a continuing effort to reduce the potential for developing these lung diseases. Information about engineering research by the former U.S. Bureau of Mines and NIOSH can be found online at www.cdc.gov/niosh. ?is website can also be used for obtaining NIOSH information about health hazards associated with crystalline silica.

By Aram Grigoryan

This paper addresses the challenges of designing the underpinning of major sub-way station with 4 operating tracks. No. 7 subway extension crosses under the existing 42nd street subway station on the 8th Avenue line. Understanding the history of the original construction, of the current structures and their condition were instrumental in developing a feasible underpinning design that is integrated with the design of the new tunnels. The existing 8th Avenue subway station has a lower abandoned level. Several alignments and corresponding underpinning schemes were studied. The design allows new tunnel construction under the station without interruption of station operations.

By M. K. Larson, B. G. White

Researchers at the National Institute for Occupational Safety and Health (NIOSH) are investigating the causes and mechanisms of roof failure in underground mines. It is expected that a better understanding of these causes and mechanisms will lead to better layout and support designs that will help prevent accidents and fatalities associated with fall of ground. Two numerical experiments were conducted by NIOSH researchers using the Fast Lagrangian Analysis of Continua (FLAC) computer modeling program with a strain-softening continuum to simulate fracture zones. Two models, one of a round hole in a plate and one of a rectangular opening, were constructed and boundary conditions were applied to simulate far-field shear. The Particle Flow Code in Two Dimensions (PFC2D) computer program was used to look at the effects of far-field shear in generating fractures around an underground opening, but these models are preliminary until boundary conditions, strengths, and stiffnesses are matched to the FLAC models. Results showed that shear zones propagated from the opposite corners of openings in directions that appeared to be determined by opening shape and far-field stress. Tensile failures also formed and extended away from these shear zones. The consistent direction of shear deformation with respect to far-field shear provides a plausible explanation for preferred directions of shear as seen in geologic environments.

By Suthan Pooranampillai

This paper presents a case study of the use of single axis cement deep soil mixing (CDSM) to deal with static settlement and seismic stability of the foundation soils under a reinforced soil slope (RSS) embankment up to 50 feet high. As part of the widening of Interstate 5 (I-5) to allow High Occupancy Vehicle (HOV) lanes in Tacoma, Washington, a new approach and span over the Puyallup River will be constructed. During the soils investigation and design phase of the project, low plasticity silts (ML) inter-bedded with silty sand layers and organic silt where identified as being potentially liquefiable. CDSM was selected to address the embankment foundation concerns and allow for future trenchless installation of utility lines beneath the embankment. The presence of a confined, artesian aquifer within the design depth of the CDSM led to the installation of a depressurization system to avoid an upward gradient through the wet soil-cement. In addition to addressing the design approach, the paper discusses the challenges associated with quality assurance of CDSM within the time constraints of an ongoing project. The limited recovery rate of conventional triple tube coring in the soil-cement and double tube wet sampling led to the use of sonic coring to provide a near continuous core of the soil-cement.

By P. Tim Johnson

Relentless increases in demand for nickel and vanadium for uses such as steelmaking, catalysts and battery materials, plus the growing financial and environmental costs of their primary extraction, have led to much interest in potential secondary sources of these metals. The presence of such metals in heavy fuel oils, bitumen and related materials offers both opportunities and challenges for potential extraction methods, especially with the growing production and importance of metal-rich fossil fuels around the world. For several decades, Tetronics’ DC plasma smelting technology has been used for the recovery of metals such as nickel and chromium from stainless steel melt dusts and other wastes in compact, environmentally-friendly and efficient plants. This paper explores the suitability of DC plasma smelting as part of a wider flowsheet with feed preparation and aluminothermic reduction techniques for smaller-scale extraction operations based on this important niche secondary source of these key metals.

By Ali Ekrem Aritan

Exposure to hand-arm vibration (HAV) among the labor force in the mining industry can result in permanent vibration diseases such as behavioral disorders, visual impairment, osteoporosis, pain (mostly in the hands, wrists, and shoulders), circulatory system disorders, and malnutrition. In this study, the vibration exposure of excavator operators working regularly in 25 different natural stone quarries was measured. In addition, the relationship between vibration exposure and rock properties was investigated. Gloved and ungloved vibration measurements were performed and revealed that antivibration gloves reduce excavator operators’ vibration exposure by 7.10–25.95%. Samples from each quarry were characterized with rock mechanics tests. The correlations between the hand-arm vibration measurements and the natural stone physical–mechanical properties (uniaxial compressive strength, Shore hardness, Knoop hardness, apparent density and total porosity) were determined to be over 70%. One finding of the study was that the health risk in excavators cannot be reduced sufficiently by the sole use of antivibration gloves. Furthermore, the excavation of any rock with a Knoop hardness above 121 is associated with an 81% risk of HAV. To increase awareness of the danger of vibration exposure for natural stone miners, training programs should be provided, and technical and operational changes should be implemented.

By Zhi-xiang Cui

Dongying Fangyuan Nonferrous Metals Co., Ltd. has developed a new technology to produce anode copper from concentrates through only two furnaces. This new technology is called the Two-Step Copper Smelting Process. This paper presents the commercial application of the Two-Step Copper Smelting Process and its operating conditions. The key features of the Fangyuan Two-Step Process are as follows: (1) feed materials, including concentrates and flux, are mixed without pretreatment and fed into the Submerged Lance Smelting (SLS) furnace; (2) high grade white metal (WM) produced by the SLS furnace is transferred via WM conduit into one of the two Submerged Lance Converting and Refining (SLCR) furnaces; and (3) the two SLCR furnaces blow alternatively to maintain continuous operation of the whole production chain. The new smelter started operation in October 2015 with a processing design capacity of 1.75 Mt/year of mixed feed and has been operating for over 30 months.

By Ulf Nyberg, Changping Yi, Daniel Johansson, Håkan Schunnesson

To investigate the non-ideal detonation properties of aluminized emulsion explosive, a series of tests for an emulsion explosive with 5% aluminum powder additive were carried out with mortar confinement. The velocity of detonation (VoD) and the curvature of the detonation front for different charge diameters were obtained from the tests with a high-speed camera. The burning process of the aluminized emulsion explosive has been modelled with the ignition and growth (I&G) flow model in the LS-DYNA code. A routine based on the optimization program LS-OPT code was developed to identify the parameters in the burning rate function with the detonation velocities and the front curvature radii from two tests. A Perl code was implemented in the routine and was used to calculate the VoD, fit the detonation front and obtain the detonation front curvature radii. The calibrated parameters were used to predict the VoDs and the detonation front curvature radii for the rest cases. The results indicate that both the VoDs and the detonation front curvature radii from the numerical modelling are in good agreement with the experimental results. The numerical results also indicate that the variety of the burn fraction and the peak pressure with the change of charge diameters is reasonable with the calibrated parameters.

By F. G. Miller, R. C. McFarlane, T. D. Mueller

During the process of gas storage in pressure-depleted oil reservoirs, it has been observed that in some instances additional liquid oil is recovered and that the composition of the storage gas is materially altered. A mathematical study was made of the dynamic behavior of such a depleted oil reservoir undergoing gas injection. The important variable considered in this study, not included in previously published work, was that of compositional effects on the phase behavior of two-phase flow. Pressure, saturation and component composition profiles were developed for a linear, horizontal and homogeneous porous medium containing oil and gas but undergoing dry gas injection. Special new techniques were developed to overcome the problems of numerical smoothing which arise in the solution of the equations representing such systems. The method of solution includes the development of partial differential equations describing the behavior of the system, representing these equations by finite difference approximations, making certain simplifying assumptions and, finally, applying methods of numerical analysis with the aid of a high-speed digital computer. In an example calculation, results using the mathematical model are compared with field observations made on a gas storage project in Clay County, Tex. This field project involved a depleted oil reservoir used 'for gas storage and gas cycling purposes. As a result of these processes, the reservoir yielded substantial amounts of secondary oil, both in the form of stock tank oil and as vaporized products in the produced gas. The methods derived in this study may be applied to a variety of oil reservoir problems which are dependent on compositional effects. In recent years the number of oil reservoirs being used for gas storage purposes has increased greatly, and there has been at least one published account of additional oil recovery resulting from gas cycling a depleted oil reservoir after repressur-ing with dry gas for storage purposes. Additional oil recovery from oil reservoirs resulting from gas storage operations could become an important secondary recovery process. This is especially true since the use of natural gas in large metropolitan areas continues to increase and more gas storage volume near these areas is needed. These facts provided the motivation for the work reported here. This paper reports on a study of the inter-relations of composition, saturation and pressure changes which occur when hydrocarbon gas is injected into an oil reservoir system. From an understanding of the process, prediction methods may be developed for use in forecasting the secondary recovery products from gas storage operations in oil reservoirs and, consequently, .the economics of such projects can be developed. The process of storing hydrocarbon gas in an oil reservoir and the cycling process both involve the transient multi-phase flow of oil reservoir fluids with changing fluid compositions. There is a scarcity of work published on the subject. One of the first laboratory models developed to study a problem similar to the one posed here was published in 1948 by Standing, Lindblad and Parsons. l They developed a model to study gas condensate recovery by gas cycling, including the effect of heterogeneous reservoir permeability. Their results showed the compositional effects of injecting a gas of known composition into a two-phase condensate reservoir of known composition. A major finding of their study indicated that maximum oil recoveries from gas cycling projects result when low cycling pressures are used. Previous to their work it was generally considered

By M. J. Nicol, R. P. Colborn

An investigation into the kinetics and mechanism of the oxidation of iron (11) by oxygen in aqueous chloride solutions By R. P. COLBORN Pr. Eng., Ph.D. (Natal) and M. J. NICOLt B.Sc. Hons., Ph.D. (Rand) A reaction mechanism for the oxidation of ferrous chloride by molecular oxygen is developed. and the appropriate constants are evaluated. The effect of a number of cations and anions on the rate of oxidation has been tested.

By Henry M. Howe

My attention has been drawn within a few days to a series of articles in Volume XVIII of the Engineering and Mining Journal, 1874, by Mr. J. A. Church, in which it is stated, among other

By Katerina Kryst

Antimony and bismuth are two of the elements that need to be removed from copper electrolyte to ensure a trouble free operation as well as to maintain copper cathode purity. One method to control these impurities is the use of aminophosphonic ion exchange resins. Antimony is present as both Sb(III) and Sb (V). Sb(V) is very difficult to remove from these resins, requiring excess amounts of highly concentrated hydrochloric acid. In industry this affinity of Sb(V) for the resin causes a buildup of Sb(V) and degrading resin performance due to continual reduction of resin capacity. A new method for regeneration of aminophosphonic resins loaded with Sb(V) has been developed, which utilizes catalytic regeneration of the resin. Ion exchange can then be utilized for continual control of Sb and Bi in copper electrolyte.

By C. F. Gates, H. J. Ramey

Recent literature shows that pronounced increases in oil recovery can result from the use of miscible systems in recovery operations. This literature also points out certain problems associated with maintaining miscibility, e.g., compositional changes resulting from alterations in pressure and temperature or from zone dilution. The purpose of the work described in this paper was to study miscible zones for possible use in waterflooding operations and examine the manner in which these zones break down. The fluid system selected for study was oil—terNary-butyl alcohol—water, which, because of its narrow range of miscibility, is ideally suited for investigation in short, linear systems. The laboratory-observed effects on oil recovery and zone stability of a number of variables are reported. Among the variables investigated were miscible zone size, viscosity ratio, length of travel, and interstitial water saturation. Results obtained with this system show that interstitial water adversely affects recoveries because of premature phase break. Salinity of the water further aggravates Ais situation. This effect, although pronounced for this system, would probably occur in any fluid system containing an alcohol. As expected, viscosity ratio has a decided influence on recovery efficiency and zone stability. The results also show that use of a suficieno zone size, even though the system has poor phase characteristics, yields higher oil recoveries than are obtained from straight water floods. Length-of-travel studies showed a square root relationship between zone growth and path length for favorable viscosity ratios. No such clear-cut dependence was observed under unfavorable viscosity conditions. INTRODUCTION As new oil reserves have become increasingly more difficult and expensive to find and develop, the oil industry has devoted more and more time and money to finding more efficient methods for exploiting known reserves. The increasing number of water floods is one manifestation of this attempt to improve oil recoveries from existing fields. Since considerable quantities of oil are by-passed by the waterflood process, it is only a partial answer to the problem. The search continues. Of late, several proposed processes have received the critical attention of investigators. Among them are gas drives, in situ thermal reactions and miscible displacements. The present paper is concerned with miscible displacements in conjunction with water floods. Recent literature1- reports that, under proper conditions, oil recoveries from LPG floods, propane sweeps, condensing gas drives, etc., approach 100 per cent of the oil in place in the region contacted by the flood. This literature also points out some of the problems associated with these processes, one of the main ones being the maintaining of miscibility. Compositional changes resulting from pressure and temperature variations or from zone dilution give rise to phase breaks and loss of miscibility, the conclusion being that, after loss of miscibility, much of the beneficial influence of the zone is lost.' The results of the subject work show that, if sufficient zone material exists ahead of a phase interface, considerable improvement in oil recovery can be obtained. In order to increase our understanding of the behavior of miscible systems as they degenerate into immiscible processes, a laboratory system having rapid deterioration characteristics was needed. The fluid system oil—ter tiary-butyl alcohol (TBA)—water possesses these properties and was the system investigated. Although these fluids are different from those generally employed in miscible studies, an understanding of their behavior can be applied to other miscible slug processes. However, under conditions where mass transfer maintains a miscible system through multiple contacts, e.g., enriched gas drive or high pressure gas drive, the observed behavior of alcohol zones would not be applicable. The variables of interest were zone size, viscosity ratio, length of travel, initial water saturation, rate and core characteristics. Of these, only the effects of the following on zone breakdown and oil recovery are reported in detail: (1) zone size, (2) path length, and (3) initial water saturation. The effects of viscosity ratio and core characteristics are discussed in conjunction with other variables. Although initial water saturation is not envisioned as important to the phase behavior of hydrocarbon systems, e.g., LPG, it is important in alcohol systems. The properties of the fluids and cores used are given in Table 1. As previously stated, this fluid system was selected because of the limited range of miscibility

By John D. Thornley

Alaskan villages typically store a one-year supply of fuel to reduce significant delivery costs. Alaska Village Electric Cooperative (AVEC), an electric utility cooperative providing power to 51 Alaska villages, has made a concerted effort to upgrade and improve their undersized and aging facilities. The Village of Stebbins, located south of Nome on Norton Sound is receiving upgrades to its AVEC bulk fuel facilities. Stebbins offered unique challenges from a foundations perspective due to the nature of the soil. The geotechnical investigation found the soil below roughly a third of the footprint of the bulk fuel facility to be thawed with seasonal freezing and the remainder was found to be warm permafrost with ground temperatures of between 30°F and 32°F. This is a unique and challenging arctic engineering design issue because foundations are designed differently for frozen ground conditions. Driven piles were selected because of site constraints, such as the design flood elevation and the change from thawed to frozen ground conditions. The pile design specified that the pile embedment depths would be selected based on the results of pile driving analyzer (PDA) testing during construction in the thawed ground and maintained within the frozen ground portion of the footprint. Difficulties during pile driving in the frozen ground resulted in several piles becoming severely damaged, requiring subsequent removal. This resulted in a reevaluation of the means and methods for pile installation. Additional fieldwork was performed to further characterize the subsurface soils and their frozen nature. Options for installation of piles in difficult areas were evaluated including ground thawing, predrilling, and reducing embedment depths. Presented within this paper are the findings from the initial and subsequent field explorations, discussion of the design methodology, and the decisions that led to successful installation of piles at this challenging remote village.

By Michael J. Sapko, Eugene M. Bazala, Eric S. Weiss, Kenneth L. Cashdollar

The data presented in this report are the results, to date, of an ongoing Pittsburgh Research Center Disaster5Prevention research program on the explosion hazards associated with blasting operations in noncoal mines. Laboratory and experimental mine tests have shown that oil shale and sulfide ore dusts can be ignited given the proper predispersed dust concentrations, particle size, and kerogen or sulfur content. Methane (CH) gas may also4be present in deep oil shale formations and can pose a significant added hazard to underground blasting operations. The most common explosive used for blasting in oil shale had been ANFO, a combination of ammonium nitrate and fuel oil; blasting in sulfide ore had used ANFO and/or dynamites. Tests conducted at the cannon gallery at Lake Lynn Laboratory near Fair chance, Fayette County, PA, provided a means of evaluating the relative incendivity characteristics of new and existing explosive products. Three explosives—a pumpable emulsion-ANFO blend, a packaged water gel, and an emulsion blasting agent—exhibited low-incendive qualities compared with other more highly incendive products such as ANFO and some dynamites. Based on the data collected during numerous full-scale blasts in oil shale and sulfide ore mines, the low-incendive products significantly reduced or eliminated the ignition hazards while at the same time providing effective fragmentation of the rock. Based on the positive results from the gallery and field testing, low-incendive explosives, coupled with good blasting procedures, show promise in reducing dust and/or gas ignitions associated with blasting operations in oil shale and sulfide ore mining applications.

By D. vas As, Constance M. Vleggaar, P. D. Toens

A facility at the National Nuclear Research Centre, Pelindaba, for the calibration of gamma survey meters used in uranium-prospecting operations by P. D. TOENS, D.Sc. (Fellow), D. van ASt, M.Sc. (Visitor), and CONSTANCE M. VLEGGAAR, B.Se. (Visitor) Ground radiometric surveys in uranium prospecting have in the past suffered from two serious shortcomings. Owing to varying instrument sensitivity and the often arbitrary height at which readings are taken, it has been impossible to compare results obtained in different surveys and, moreover, to relate such readings to actual U30s concentrations. A set of calibration sources designed to overcome these problems has recently been constructed on the site of the National Nuclear Research Centre, Pelindaba. A discussion of the standards applied and the instrument calibration procedure is presented.

By Vivas

Goldcorp is one of the largest gold producers in the world with projects in South, Central and North America. Goldcorp?s flagship operation is Peñasquito, a world class, polymetallic deposit that started production in 2010 and is one of the largest mines in Mexico. Since the early stages of the project, Goldcorp has used the most advanced technologies available to maximize its value. However, the implementation of optimum mine plans has been challenging to put into practice. This is due to the fact that the mine operation involves more complexity than the plans usually reflect. This challenge is an industry-wide issue that presents opportunities for improvement. This article discusses the mine planning methodologies and procedures used to connect long-, medium- and short-term planning strategies in order to bridge the gap and produce optimum mine plans that can be practically implemented in the field.

The first session of the Institute was held at the Smithsonian Institution, on Tuesday evening, February 22d. The members were welcomed to Washington and to the Smithsonian by Prof. Joseph Henry. President Holley responded to the cordial welcome of Professor Henry, and then read an introductory address on the subject of Technical Education. Following the discussion on President Holley's address the following persons, duly proposed and indorsed by the Council, were elected members and associates of the Institute : MEMBERS. Emile R. Abadie,. .. .. St. Louis, Mo. R. J. Anderson,.....Pittsburgh, Pa. Commander L. A. Beardslee,. .. Washington, D. O, Charles Bender,. .. .. New York City. Charming M. Bolton,. .. . Richmond, Va. Thomas E. Bowman,. .. . Silverton, Colorado. Calvin E. Brodhead,. .. . Bethlehem, Pa. M. L. Brosius,. .. .. . Lewistown, Pa. Harvey H. Brown,. .. .. Cleveland, Ohio. James A. Burden,.. .. . Troy, N. Y. J. P. Clemes,. .. .. . Sonora, Mexico. N. H. Cone,. .. .. . Nederland, Colorado. W. F. Durfee,.. .. . New York City. Robert Frazer, Jr.,. .. . Ashland, Pa, Joseph E. Galigher,.. .. . Bingham, Utah. William Golding,.. .. . Steel Works P. O, Pa. Samuel E. Griscom,.. .. . Pottsville, Pa. Gen. E. Burd Grubb,.. .. Beverly, N. J, Arthur R. Guerard,. .. .. Charleston, S. C. Edward Hart,.. .. .. Easton, Pa. Prof. Lewis M. Haupt,. .. . Philadelphia. E. S. Hawley,.....Buffalo, N. Y. John W. Hoffman,.. .. .. Philadelphia. Nelson P. Hulst,.. .. . Milwaukee, Wis. H. C. Humphrey,.. .. . Philadelphia. Ed. P. Jennings,.. .. .Ithaca, N. Y. B. F. Jones,......Pittsburgh, Pa.

By D. P. Richards

Tunneling in carbonate sedimentary rocks such as lime stones and dolomites can be difficult when solution channels or voids are anticipated. Addressing the risk aspects associated with these formations can be done effectively through the Geotechnical Baseline Report (GBR) by properly characterizing the ground and ensuring that the Owner?s and the Contractor?s interests are represented and protected. This paper presents a review of tunneling difficulties in these rocks and includes a review of site investigations, geologic characterization, and presentation in the GBR. Key construction issues are also discussed, including appropriate excavation technology, mechanisms of face support and groundwater control, and quantifying grout takes.

By J. D. Testerman

A statistical technique to identify and describe naturally occurring zones in a reservoir and to correlate these zones from well to well is described. The technique is particularly useful in describing a reservoir where cross flow between adjacent strata is important in determining reservoir behavior. Although it has been used primarily for permeability zonation, the technique is general and can be used to correlate any reservoir property or related data, such as the information contained in well logs. INTRODUCTION One of the first problems encountered by the reservoir engineer in predicting or interpreting fluid displacement behavior during secondary recovery processes is that of organizing and using the large amount of data available from core analysis. Permeabilities pose particular problems in organization because they usually vary by more than an order of magnitude between different strata. Due to the sheer volume, it is almost always necessary to group data and to use an average value to represent a number of measurements. Perhaps the most common method now used to group permeability data is the capacity-fraction technique, which ranks permeabilities in order of magnitude, regardless of the physical location of the permeabilities within the reservoir. The cumulative per cent capacity is plotted against cumulative per cent thickness. This plot is divided into an arbitrary number of zones, generally of equal thickness. Five zones (or averaged groups of data) usually are obtained, each of which is treated as homogeneous in subsequent calculations. The division so obtained has no physical meaning; strata in the same zone, calculation-wise, are usually not adjacent in the reservoir. Reservoir engineering techniques being developed will handle crossflow that occurs between adjacent communicating reservoir strata because of imbibition and gravity segregation. Since crossflow occurs between physically adjacent layers within the reservoir, a new zonation technique recognizing the actual location of strata within the reservoir is necessary. Similarly, the recognition of natural zones is important for predictions of oil recovery by processes involving diffusion. One such process is miscible displacement, where predictions of lateral diffusion within the reservoir must recognize the actual location of the invaded zones in relation to the rest of the formation. Natural zones must also be adequately recognized to account for heat transfer within the reservoir during thermal exploitation. Because of the complexity of the problem, statistics appear to offer the only practical hope of dividing a reservoir into physically-meaningful natural zones. This paper presents a statistical technique for identifying these natural zones and for ascertaining which ones are likely to be continuous between adjacent wells. The zones defined have minimum variation of permeability internally and a maximum variation between zones. The technique is general and can thus be applied to reservoir properties other than permeability. The method will guide the reservoir engineer in estimating which zones are likely to be continuous between wells. However, a statistical correlation based on permeabilities in two different wells is no guarantee that the zones so defined are, in fact, continuous. Rather, the assumption of continuity must be consistent with geological data concerning the depositional environment, as well as justified on the basis of engineering judgment in combination with statistics, just as judgment is required with conventional zonation methods. CALCULATION PROCEDURE The reservoir zonation technique is a two-step operation. The steps are individually described, and a sample calculation is presented in the Appendix. ZONATION OF INDIVIDUAL WELLS First, the set of permeability data at a single well is zone, into Zones. These zones are selected so that variation is minimized within the zones and maximized between the zones. The equations4,6 used to zone the data are where B = the variance between zones, , = the number of zones, i = the summation index for the number of zones, j = the Sumation index for the number of data within the zone, mi = the number of data in the ith zone, k,. = the mean of the permeability data in the ith zone, k . = the over-all mean of the data in the well, W = the pooled variance within zones, N = the total number of