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By Hossaini SMF

After reviewing the various approach es,namely, empirical,analytical.observational and numerical, a logical systematic approach is proposed for the estimation of compressive strength of coal pillars. In this approach first,uniaxial compressive strength of coal in pillars is estimated,taking into account the size effect and the effect of discontinuities. Next,the compressive strength of coal pillars is estimated by determining the stress distribution in the pillar and the Bieniawski strength criterion. The results appear to be compatible to the ones obtained by Wilson's method. The traditional pillar design equations give improper answers for deep workings.

Jan 1, 1991

By M. L. Fuller

DURING the last several years many papers have appeared dealing with the structure of highly polished metal surfaces. The awakening of interest in this subject is due to the applicability of the electron diffrac-tion technique to the study of surfaces. The original theory of Beilby1 considered the surface of polished metals as of the nature of a super-cooled liquid or a vitreous, amorphous solid. The electron diffraction effects from polished metals have been interpreted by many to be a direct experimental proof of the correctness of the Beilby theory. This inter-pretation has been strongly opposed by others, so that at the present time the subject is in an uncertain and controversial state. In the present paper new, and hitherto unpublished, electron diffrac-tion effects from polished zinc are described. These observations indicate that the polished surface of zinc is crystalline.

Jan 1, 1938

By R. A. Ritter, J. P. Batycky

A numerical technique has been developed to permit estimating the pressure gradient associated with laminar flow of thixotropic liquids through long Pipelines. For this purpose the pipeline is divided into a number of radial and longitudinal increments within which rheological properties of the fluid may be considered as constant at any time. Then, provided only that the fluid flow curve is defined at every duration of shear, it is possible to predict the instantaneous pressure gradient at any cross-section along the pipeline for each desired flow rate and pipe size. The technique consists of an iterative integration of shear rate to establish the appropriate value of the wall shear stress at each location. Consistency of fluid in the increment is determined by the flow history of that increment, while the radial flow associated with variations in velocity profile is accounted for by adjusting the width and radial position of the increment. A number of pressure profiles, computed at each of several flow rates, provide a convenient basis for pipeline design and pump selection. INTRODUCTION In recent years considerable attention has been given to predicting pressure drop associated with the isothermal laminar flow of time-independent non-Newtonian fluids in pipes and annuli. 6,11,12 The approach generally has been to develop analytical relationships between flow rate and pressure drop based on simple constitutive models which hopefully provide an approximate description of the rheological properties of the fluid. Analytical solutions are highly desirable since the influence of all pertinent parameters can be readily determined. Unfortunately, however, this approach is restricted to simple flow geometries and- frequently leads to erroneous results due to inadequacies in the model. In certain cases a solution may be obtained through applying appropriate numerical techniques.l,14 For example, a digital computer program is available for predicting the velocity profile and pressure drop encountered by any Newtonian or time-independent non-Newtonian fluid flowing under laminar conditions in a cylindrical pipe or annulus.l In this paper the consistency behavior of the fluid need only be described in terms of basic rheological data. Analyzing flow systems involving fluids with time-dependent rheological characteristics is considerably more complicated since substantial changes in consistency may occur because of sustained shear action. This sensitivity to shear frequently persists for several hours. Consequently, variations in pressure drop and/or flow rate resulting from the aging process and addition of unsheared or partially sheared fluid to the system must be considered for purposes of pipeline design. This paper outlines a numerical method for predicting the transient and steady-state laminar flow behavior of a thixotropic liquid in a pipeline of arbitrary length (i.e., at a specified constant flow rate, the instantaneous pressure gradient may be determined at any time after start up and at any location along the pipeline). Several such pressure gradient profiles, computed at several flow rates, may be combined to produce a complete portrait of the system response. This flow portrait provides a reasonable basis for pipeline design and for selecting a suitable pump characteristic. TIME-DEPENDENT RHEOLOGICAL BEHAVIOR The most familiar time-dependent rheological properties are those exhibited by thixotropic liquids. Many of these materials, particularly thixotropic crude oils, generally display an apparent yield stress in that a finite pressure gradient is required to initiate flow. Then, under the influence of sustained shear at a constant shear rate, the consistency systematically decreases to some final limiting value. The shear stress obtained at

By B. J. Arnold

Froth removal rate is perhaps the most important parameter in scaling up from laboratory tests to plant froth flotation circuits. The WEMCO froth factor, the percentage of the froth height over the lip of the cell, accounts for the difference between laboratory and plant froth removal rates. As laboratory tests are generally run with a high pulp level, laboratory results are directly comparable to plant results only when a high froth factor (high pulp level) is run in the plant. When a plant does not have a high pulp level, laboratory results must be modified by using a ratio between laboratory and plant kinetics to predict plant results. This ratio, which accounts for the froth factor is important in testing any new reagents or reagent dosage levels. CQ Inc. researchers have used predictive scale-up equations using this froth factor coupled with equations for kinetics and the residence time distribution in the froth flotation cells. These equations show that modifying the froth factor in the plant can have a large impact on flotation cell yield and reagent use. EQUATIONS DESCRIBING FROTH FLOTATION Scaling up from laboratory- to plant-scale coal froth flotation has been the subject of much research and debate over the years. Determining the proper rate equation to describe flotation kinetics and an equation to describe the residence time distribution in a bank of flotation cells have been particular areas of study. As shown in Tables 1 and 2, various rate equations and residence time distribution equations have been proposed in the literature. These equations consist of one or two parameters giving the rate constant(s) in units of time-1 and a parameter for recovery at infinite time, [Roo]. Dowling, Klimpel, and Aplan (1985) evaluated the rate equations in Table 1 for their ability to fit froth flotation kinetic data and found that all of the equations give reasonably low standard errors. Several of these equations, however, proved to have superior confidence limits for the parameters. Other equations have also been proposed to describe the recovery versus time profile. Most recently, Diao et al. (1992) proposed a first-order form with a sine wave distribution. As indicated in Table 2, investigators have suggested many equations to describe the residence time distribution in continuous froth flotation. To measure the water residence time distribution in a bank of cells, a soluble tracer is often used, with the level of tracer being measured over time at the tailings discharge. This response is then put on a dimensionless basis as described by Austin et al. (1984) in order to compare mixing behavior between cells or under different conditions. Coal flotation cells are generally of the flow-through or hog-trough variety allowing for some degree of backmixing and short-circuiting. While the water residence time distribution (see Figure 1) at the end of one cell in a bank of 1.4 cu ft WEMCO froth flotation cells may approximate perfect mixing conditions (Arnold, 1989), the water residence time distribution at the end of a bank of cells does not. Figure 2 shows the RTD for various flotation cell types compared to that for perfect mixers in series. To better describe the water residence time distribution in coal froth flotation cells, Van Orden (1986) used an equation similar to the perfect-mixers-in-aeries equation. This

Jan 1, 1993

By Charles Will Wright

The application of the camera as an adjunct to topographic mapping began practically with its invention, and it has been employed with varying success since that time. With the exception of the camera to be described, the plate-camera has been universally used in this work, thus giving a projection of the area photographed on a flat surface. From such projections or photographs, by the rules of geometry and of perspective, points defining topographic features and seen from at least two camera-stations may be projected upon a ground-plane—the map.' In 1904 I employed the plate-camera for this purpose in Alaska, but found that the labor necessary to plot the maps, even in a general way, was long and tedious. In 1905 a small Eastman panoramic camera was fitted with spirit-levels, a sight-alidade and a transparent scale, introduced inside the camera to register the degree-points in the sky-line of the film-negative ; also, arrows to indicate the horizon-line. This was, on the whole, successful; but the details in the topography were not brought out in the views with sufficient clearness, aid the photographs were too small. These difficulties were overcome by obtaining a larger and more carefully constructed instrument, which was satisfactorily employed in the field during the year 1906. A panoramic view is made up of an integral number of perspective views upon flat surfaces, and logically is the most accurate and direct means to obtain an impression of a field of * Published by permission of the Director of the U. S. Geological Survey. Stanley, H. M. Photographic and Co-ordinate Surveying, Bans., xx., 740 to 766 (1891). Also, Flemer, J. ,4. Phototopographic Methods and Instruments, Report U. 8. Coast and Geodetic Survey, pt. 2, app. 10, pp. 619 to 735 (1897).

Jan 1, 1908

By Stephen Krickovic

THERE is today no proven continuous mining machine that can be used under all the varying conditions found in most bituminous coal mines. During the last five years, however, both the machines and methods of using them have been improved. Coal operators can now exercise a fair degree of selectivity, except those who must struggle with thick and hard partings and operate in seams less than 40 in. thick. It must be realized, then, that more than one type of continuous miner may be used advantageously in the same coal mine. Although this appears to violate the standardization generally sought after, the gain can more than offset added maintenance and, to a lesser degree, operating problems.

Jan 12, 1957

By P Griffin

Mill relining is a major contributor to overall plant downtime. Reducing the number of mill liner pieces removed from and replaced in the mill has a direct impact on the overall reline time and in turn, mill availability. To improve the mill availability of Ridgeway OperationsÆ 32 foot SAG mill, a number of initiatives were implemented in terms of liner design. These included the conversion of the shell from 40 to 30 rows, reducing the number of pieces from 80 to 60 each shell reline and reducing the number of pieces from 48 to 32 per feed end reline. In addition, modifications were made to the discharge end of the mill to extend the life of the outer pulp lifter and discharge cone, thereby reducing the frequency of change out. The standard radial outer pulp lifter was converted to an angled design. The discharge cone was converted to the BullnoseTM design supplied by Bradken. This paper discusses the design changes made and the expected benefits to the Ridgeway Operations in terms of mill availability improvements.

Jan 1, 2007

By M Stewart, J Vann, A Bu, D Frederickson

The Golden Gift is a recently discovered deep deposit below the main operating areas of the Stawell Gold Mine. At an early stage of the project, diamond drilling was used to define the mineralisation on sections approximately 100 - 150 m apart. The project economics were sensitive to both grade and tonnage. There were consequently two significant risks on resource quantification: risk on tonnage (ægeological riskÆ); and risk on grade (ægrade riskÆ). The degrees of freedom inherent in the geological model were considered to be potentially high because of wide drill spacing and likely structural complexity. To quantify geological risk three geologists familiar with Stawell mineralisation independently interpreted the deposit. This generated three plausible, different geological volume models. Conditional simulation was then used to quantify grade risk. Conditional simulation requires the user to define input statistics (histogram and variogram model) and a geological envelope. Based on global mean grade of an ordered set of simulations, æpessimisticÆ, æmedianÆ and æoptimisticÆ simulation cases were defined. The result was a 3 x 3 risk matrix with geological risk (the three interpretations) on one axis and grade risk (also three cases) on the other axis. An interesting result was that geological and grade risks were of a similar order of magnitude. Therefore a risk analysis of grade by geostatistical methods within a fixed geological model is of limited value, especially if the drill spacing is wide. After completion of this study, with additional drilling, the geological degrees of freedom at Golden Gift reduced substantially. A second Golden Gift risk study used a refined geological model to build a set of simulations to be used in preliminary mine design. A third simulation study in the deeper parts of the Magdala ore deposit, a well-drilled part of the mine with production history, demonstrates that the geostatistical simulation method used at Golden Gift is a robust and useful tool to quantify grade risk.

Jan 1, 2003

By Robert Corson

Zinc has a large solubility in Fe and a completely filled ?d? shell. With the discovery of dramatic increase of the magnetostriction in Fe by Ga addition, an examination of element Zinc that is adjacent to Ga in the periodic table is of significant interest. In this work, the effect of binary alloying of Zn with Fe on the magnetic and magnetostrictive properties is examined. The FeZn alloys were processed using powder metallurgy and vapor phase synthesis, and Zn contents were varied from 5% to 30%. An examination of the influence of different processing parameters and the Zn content on the resulting alloy properties is presented. The alloys were characterized using X-ray diffraction and SEM. Magnetostriction measurements were carried out at different pre-stress levels. Magnetic properties were measured using a vibrating sample magnetometer.

Jan 1, 2006

By Knasmillner

During blasting body wave interaction with geometrical surfaces induces Rayleigh-waves which propagate along free surfaces, e.g. crack faces or delaminated rock layers. These Rayleigh-waves carry most of their energy within a very shallow surface layer and propagate with very little attenuation in real rock materials. Upon interaction with a crack front a very strong mixed mode stress intensity factor may result and lead to fracture initiation. On the basis of experimental photomechanical results the history of dynamic stress intensity factors Kt and K2 will be studied in Detail.

Jan 1, 1990

By Brimblecombe P

Morwell Open Cut is a continuous mining operation employing 5 buck- etwheel excavators, I bucket chain excavator and 54 conveyors. The combined bunkering capacity at both client Power Stations represents less than 12 hours maximum coal demand. This creates an extremely dynamic operating environment, which is further complicated with significant variations in both excavating and transportation plant capabilities. To achieve set objectives, including- I adequate reserves, 2 coal supply reliability, 3 cyclic plant maintenance, 4 minimal cost of coal, scheduling of the operation requires constant monitoring and reappraisal. Investigations are in progress to develop a computer based scheduling tool capable of simulating the complex operating environment. A review of computer scheduling packages currently available within the State Electricity Commission of Victoria has found limitations making most unsuitable for the task. The type of package found to be most suited is a knowledge based system ('Expert System')capable of operating within a set of rules defined by the user. Work is proceeding on the development of a knowledge base to test the effectiveness of Personal Computer based `Expert Systems'.

Jan 1, 1989

By Bernard G, Limpach R, Ulveling L

A major aspect in competitive ironmaking is to replace metallurgical coke by injecting alternative cheap fuels. Whereas in the past, heavy oil injection as well as on a lower scale natural gas injection have proved to be reliable, the progressing high price level of these fuels has prompted international interest in looking for alternative cheaper fuels, especially pulverized coal. Theoretical analysis and practical operations showed that for constant adiabatic flame temperature, potentially more coke may be replaced by injected coal than by heavy oil, because of less endothermic cracking of hydrogen components. Since about 1974, the ARBED-Group has been looking for alternative fuels and in 1976 came to conclusion to select for first trials pulverized lignite for the following reasons:

Jan 1, 1981

By C. O. Brawner

FACTORS THAT INFLUENCE STABILITY AND STABILIZATION METHOD The most effective stabilization method and design can only be developed if the cause(s) and mechanics of the slide are known. Therefore, it is important that the stability be evaluated by an engineer who has had extensive rock stability experience. The most important factors that influence stability are structural geology, ground water, blasting and the mining method or methods. Structural Geology - The majority of failures in rock slopes occur along discontinuities in the rock (joints, bedding planes, shear or fault zones, etc.). Therefore, on all surface mining projects, the development and maintenance of a comprehensive structural geologic mapping program should be a first priority program that is considered a part of the operations function. This program should include mapping all major features - faults, shear zones and through going joints. All structural features which could influence stability should be mapped and presented in a structural domain format for the entire mine (Canmet, 1977). Where planes, wedges or blocks will be undercut by the mining excavation, shear strength and strain to failure tests should be performed on the joints, fault gouge and gouge-rock contact surfaces. These tests must be performed on the samples in the direction of potential slide movement and must determine the range of peak and residual shear strength values. A preliminary assessment of friction angle can be obtained from measurements of failed surfaces in the field (Figure 1) or from core sliding tests (Barton, 1981). An assessment must be made of the past geologic history of

Jan 1, 1983

By M. J. Ross, D. A. Norrgran, J. A. Wernham, J. N. Orlich

INTRODUCTION Laboratory testing for magnetic concentration circuit design is a requirement, just as it is for most other types of concentration. Natural variations in raw materials allow on1 y the broadest of generalities to be made regarding magnetic separation. Further, magnetic fields are geometry dependent, leaving fundamental models of a separator overly dependent upon the exact conditions for which the models were derived. Despite this, an understanding of the basics of magnetic separation and of the problem to be attacked can result in rapid progress towards the final circuit design with a relatively simple testing program. Magnetic Separation Basic Principles A magnetic field can readily be understood in terms of lines of flux. A familiar demonstration of these lines of flux is the pattern of iron filings on a sheet of paper when a magnet is placed underneath. Lines of flux2 are measured in Gauss (1 line/cm2) or Tesla (10000 gauss). Regions of high field strength have a greater number of lines. Field direction is indicated by a convergence of lines. When a particle is placed in a magnetic field it cuts the lines of flux and alters them in one of three basic patterns. These patterns are referred to as diamagnetic, paramagnetic and ferromagnetic. Diamagnetic materials have electronic structures which react to oppose an applied magnetic field. This opposition acts to locally reduce the applied field slightly. The visualization is that lines of flux diverge and go around the particle. Because of this divergence or opposition, a diamagnetic particle will tend to move towards regions of lower flux density. That is to say that the particle will be repelled by a magnetic field. Aluminum oxide and napthalene are examples of diamagnetic materials. Paramagnetic materials have an electronic structure which increases an applied magnetic field. Although these materials also exhibit diamagnetism, they have randomly oriented impaired electrons which align with the magnetic field. The resultant local field enhancement is significantly larger than the diamagnetic opposition. The visual-

Jan 1, 1986

By Manuel D. Viera Flores

Existe un grave problema ambiental que ha pasado desapercibido a lo largo del tiempo y que Metaproject ha venido estudiando los últimos 10 años. Un problema mundial para el sector minero consistente en la acumulación de los neumáticos OTR (Off the Road) fuera de uso, como pasivo ambiental. Metaproject ha estado investigando y desarrollando un proyecto de re- valorización de estos neumáticos, a través de un desarrollo de I&D+i al que hemos llamado “Gestión Sustentable de Neumáticos Mineros”, que permitirá tratarlos como fuente de energía eléctrica potencial.

Sep 1, 2017

By W. B. Greer, J. J. K. Daemen

Introduction The performance of seals in boreholes, shafts and tunnels is an important concern in mine safety, in the control of effluents from operating and abandoned mines and in the underground containment of hazardous wastes (Einarson and Abel, 1990; Mining Waste Study, 1988). Despite the clear need for effective seals, few documented test results are available concerning the performance of in situ seals. Some evidence indicates that horizontal or near-horizontal holes are especially difficult to seal properly (Kelsall et al., 1982). This research involved the installation, extensive hydraulic testing, removal and post-test examination of a 10-cm-long x 10-cm-diam cement grout seal in a near-horizontal borehole in limestone. The work was performed in an underground mine on Marble Peak in the Santa Catalina Mountains, AZ. A test hole was diamond cored in the recrystallized limestone of the Escabrosa formation. The hole is 33.24 m long, 10 cm in diam, and dips at 10.4°. The hole extends between two drifts and thus is accessible from both ends. Seal installation Surveys to assist in selecting the interval to seal consisted of core logging, video logging and constant-head injection tests using a straddle-packer unit. The location selected, 3 m from the lower end of the hole, had low hydraulic conductivity (3 x 10-10 to 3 x 10-9 cm/sec) and was free of significant fractures. The grout used, an expansive Class A cement, was provided by Dowell-Schlumberger, Tulsa, OK. A grout mass about 1.5 m in length was installed, with a dump bailer, above a temporary mechanical plug. Groundwater in the hole, if any, was minimal during placement. After 13 days of curing, the grout mass was partially drilled out from both ends, leaving a seal 10 cm long. Water distribution in rock mass The distribution of water and fluid pressure in the rock mass near the seal appears to be complex. The generally dry condition of the borehole and rock mass suggests that the rock mass near the seal was unsaturated prior to the injection tests of this research. The injection tests presumably created an expanding saturated zone around the seal. However, anomalously high fluid pressures, consistently recorded by one of two piezometers installed near the seal, suggest connection to a source of significant natural hydraulic head. Comparable head variations for closely spaced piezometers have been reported by others (Sowers, 1976). [ ] Seal testing The seal was tested for 3.5 years, using steady constant-head, tracer travel-time, dye-injection, head-buildup and transient constant-head tests. These tests are fully described in Greer and Daemen, 1991. In the head-buildup test, transient flow occurs through the seal (and rock mass) to a closed, water-filled interval of the borehole adjacent to the seal. The test consists of monitoring the rise in head in the closed interval until steady conditions are approached. The test may be analyzed in terms of a one dimensional analytical model to obtain the effective hydraulic conductivity (Ks) and specific storage (Sss) of the seal. Analysis in terms of an axisymmetric three-dimensional numerical model may yield properties of both the seal and rock mass.

Jan 1, 1993

Elastomeric compression gaskets for segmental tunnel liners are capable of fulfilling all sealing requirements for one pass constructed tunnels.Once the segments are mounted and the gaskets are compressed the watertightness of the tunnel is guaranteed at once and for the whole technical life time.The only prerequisite for effective sealing is that tolerances in the tunnel segments be kept within reasonable limits.

Jan 1, 1993

By L M. Foster, J R. Kellett, G A. McMah

The Great Artesian Basin (GAB) contains one of the largest reserves of fresh water in the world. The volume in storage is enormous, being estimated at nearly 65 000 million megalitres (ML). Development of this resource, dominantly for the pastoral industry, began in the late-1800s and quickly accelerated. With exploitation of the resource, artesian pressures declined almost as rapidly. This loss of head is a result of the total discharge from the basin and much of this discharge is waste of water. The waste through uncontrolled bores and inefficient distribution systems still amounts to about 75 per cent of all discharge. However, the volume in storage has hardly been depleted. The major concern is the effect of withdrawal on artesian pressures. Due to the size of the Basin, the relatively flat gradients and low permeability, the movement of water through the aquifers is extremely slow and independent of recharge. Hence, the normal concepts of sustainable yield (ie discharge should equal recharge) cannot be applied to the Basin as a whole as travel times do not allow for the effect of recharge to be seen away from the outcrop areas within management timeframes. The large volume in storage, though, can provide an extensive buffer to the impacts of temporary water needs. This effect should be considered when assessing the acceptability of fixed life projects such as mines and the extracted volumes from their operations. Identifying a sustainable yield involves balancing the acceptability of the economic, environmental and social costs with the associated discharge and fall in head, to arrive at an acceptable balance.

Jan 1, 2003

By Jochen Petersen, Alison Lewis, Cledwyn Mangunda

Run-off and waste water streams high in dissolved metal content are generated in all mining operations. The metals pose a threat to life due to their persistent bio-accumulative toxic (PBT) characteristics. Hence, there is a need to treat mine waste water effectively. Lime precipitation is the technology of choice through which Fe, as the major metal species, is removed as Fe (III) oxyhydroxides with other metals co-precipitated and/or adsorbed. Sulphates are removed as gypsum or incorporated into the Fe phases. The resulting sludge has poor dewatering characteristics and is deposited in landfills, with an inherent risk of returning the Fe back into the water cycle through leaching. This study seeks to understand the mechanisms behind the formation of this sludge in terms of product quality. The relationship between process conditions and product characteristics has been investigated through exploring the effect of Fe (III) concentration on the precipitate product characteristics (particle size distribution (PSD), size, morphology and structure) and quality (in terms of filterability, settling ability, etc.) in a simplified system. Neutralisation of acidic synthetic aqueous Fe (III) sulphate streams containing 50, 400 and 800 mg/L Fe(III), respectively, was effected by mixing it in a continuous stirred tank reactor (CSTR) with dissolved calcium hydroxide for pH control at a residence time of 15 minutes. Precipitate samples analysed for morphology and PSD, using nanoSEM and Zetasizer respectively, showed a general decrease in PSD and zeta potential with increases in feed Fe (III) concentration. These results were used to infer the particle size enlargement mechanisms of Fe (III) oxyhydroxide precipitates under a given set of operating conditions. Preliminary product quality results indicate that a high concentration (800 mg/L) leads to the rapid formation of metastable precursors with poor product quality, whilst a low concentration (50 mg/L) leads to formation of thermodynamically more stable precipitates with good product quality. The approach demonstrates a potential route forward in terms of linking operating conditions to the attainment of desirable characteristics rather than specific precipitate phases which are difficult to identify.

Jan 1, 2016

By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958