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By A. T. Iannacchione

Underground limestone mines typically use the room-and-pillar method of mining in the generally flat-lying limestone formations. In some cases the dip may exceed 5° which can result in unique roof instability problems. Stability may be further exacerbated by the presence of horizontal tectonic stresses. Field studies and numerical model analyses are combined to assess the affect of the dip in various stress conditions. The results showed that where the horizontal tectonic stresses are sufficient to cause intact rock failure, increasing dip results in increased failure potential. The effect of the dip is greater when the maximum horizontal stress is parallel to the dip. Two case studies are presented and evaluated against the findings of stress analysis results. The study showed that the empirical rules of orienting headings parallel to the maximum stress are generally applicable to dipping excavations, except when mining in the up-dip direction. The importance of accurately determining the orientation of the maximum horizontal stress is emphasized because the window of favorable orientations relative to the stress is small.

By Michael Day, Paul Kos, Scott Brinton

A hydrogeologic characterization and impact analysis was performed for a proposed quarry at the Hitch Rack Ranch located in the Little Turkey Creek watershed southwest of Colorado Springs, Colorado. Continuous multiple channel tubing, nested piezometers, stream flow measurements, and mapping of known seeps were used to define the three-dimensional potentiometric distribution and areas of groundwater recharge and discharge. Water balance considerations, mass balance calculations, and potentiometric response to earth tides and barometric fluctuations confirmed that the granite fracture system in the ridge area of the proposed quarry has an extremely low bulk hydraulic conductivity resulting in minimal groundwater discharge to sustain the baseflow of Little Turkey Creek. The Little Turkey Creek valley forms the major conduit for groundwater flow exiting from the upper part of watershed underlain by granite. This conclusion has significant implications with respect to mine planning to minimize projected impacts to the hydrologic system and preserve this recharge component to downgradient Denver Basin sedimentary deposits.

By Niels Verbaan

NioCorp is developing the niobium/scandium/titanium Elk Creek carbonatite deposit. The probable reserve announced by the company in 2017 indicated significant niobium (0.79% Nb2O5), titanium (2.81% TiO2), and scandium (71 g/t), and is composed predominantly of calcite, dolomite, and ankerite. Niobium is mostly (80%) contained in pyrochlore with the balance in various Fe-Nb-Ti oxides, which also host most of the titanium. Scandium is primarily deported in dolomite, with lesser quantities in pyrochlore and biotite. The process flowsheet recovers separate niobium, titanium, and scandium products. Scandium is extracted from whole ore hydrochloric acid leach solutions using solvent extraction and is further refined through a re-leach and precipitation process. Scandium leach residues are treated in a sulphuric acid sulphation process to recover separate niobium and titanium precipitates as well as to solubilize the remaining scandium. Both hydrochloric acid and sulphuric acid reagents are recycled within the flowsheet. This paper will discuss key bench and pilot test results of the niobium extraction and recovery circuits and will present a conceptual flowsheet developed by the project team for NioCorp at SGS Minerals.

By M. Kaitz

A continuing discussion in both the petroleum engineering and economic literature is directed to the difficulties encountered in the use of discounted cash flow rate of return (DCF) as a measure of investment worth. Although useful in most Instances, DCF has been criticized because it is time-consuming in its trial-and-error solution, theoretically invalid, not adaptable to cash flow streams yielding multiple return solutions and not entirely reliable in selecting between mutually exclusive investments. The theoretical invalidity of DCF stems from the reinvestment assumption implicit in the calculation that earnings are reinvested at the DCF rate. The emerging consensus of the economic literature is that the net present value or the present worth of the net cash flow stream (discounting at the average opportunity or cost of capital rate) is more correct and reliable. Other criteria proposed have been ratios of net present value divided by initial investment or by present value of all investments in a project. All of these criteria are simple to determine and explicitly assume a reinvestment rate for [he income generated by a project. This paper develops and discusses a theoretically valid profitability criterion which is simple to compute and retains the appeal of a percent return on investment. It is called "percentage gain on investment" or PGI. It measures the gain an investment is expected to realize over like capital invested in the average opportunity and explicitly considers reinvestment potential. Why add another Concept to the large array of investment criteria now available, any one of which, or perhaps a combination of several, appears to embrace the form's (or individuals) objectives? The answer is that not one of the existing criteria provides both a readily comprehensible and theoretically valid measure of risk coverage that has general application. The proposed PGI does fulfill these requirements. INTRODUCTION An ancient expression warns that "one must yield to the times" — there are better ways of doing things. A review of the petroleum engineering and economic literature on one topic alone, measurement of investment worth, certainly is witness to this truth. In use for a number of years, the DCF has recently received attention, directed mainly to its theoretical invalidity. Several alternatives to DCF have been proposed to provide a valid, simply determined criterion to describe investment worth and to overcome the criticisms previously mentioned. This paper introduces another method called percentage gain on investment (PGI) and is proposed as but one of several yardsticks that should be used in making investment decisions. MEASURES OF INVESTMENT WORTH This paper will consider only those criteria which give weight to the time pattern of future earnings. These criteria are usually compared with an average opportunity rate or cost of capital of the firm to judge the relative worth of the investment. For purposes of demonstration, a 9 percent average opportunity rate will be used throughout this paper. Implicit in the DCF calculation is the assumption that earnings are reinvested at the DCF rate. Some argue, though, that there is no reinvestment assumption,' that the DCF rate is simply that maximum rate of interest one can pay on the investment over the life of the project and break even. The determination of DCF is accomplished by discounting the net cash flow stream at that rate (DCF) which will yield zero. The question is: why should reinvestment potential be explicitly considered in calculating return on investment or other criteria measuring economic worth? Perhaps the answer lies in consistent or equal treatment of future cash flow. It appears entirely illogical to give different present worth value to $1 received, say, 10 years from now, which is the circumstance resulting in comparing projects with different DCF returns. In fact, $1 received in 10 years has the same value regardless of which project generated the income. DCF return thus favors investment projects which are expected to provide early income as compared to those providing long-term income. Not surprisingly, the controversy on reinvestment assumption is an old one. Hoskold' discussed this same problem in 1877. He considered the future income from mineral properties as an annuity or a series of fixed future payments. (As will be demonstrated, his equation can be modified for variable income.) Prior to Hoskold, the value or what one could pay for the mine, was determined with the use of standard, single-interest tables. Here is what Hoskold said with regard to these tables. "This table, and others of its kind, to be found in most works on annuities, is constructed correctly according to

By Sunil Vytla, Akash Adhikari, Purushotham Tukkaraja

Blasting operations produces gases and fumes that may be toxic or non-toxic in nature. A detonation of commercial explosives such as ANFO, emulsion, and dynamite would ideally produce only nontoxic products such as steam (H2O), carbon dioxide (CO2) and nitrogen (N2). However, in the real world, the detonation of explosives produces toxic products such as nitrogen dioxide (NO2), nitric oxide (NO) and carbon monoxide (CO). The focus of this study is the blast fumes entrapped in the muckpile. Fume clearance and workplace re-entry time studies performed in the past have overlooked the toxic gases entrapped in the muckpile. Studies show that as much as 60% to 70% of the fumes or gases produced during blasting underground can remain entrapped in the adjacent rock mass or in the muckpile. The toxic fumes trapped inside the muckpile are slowly released and could be fully uncovered during the mucking process. Exposure to these gases or fumes is hazardous to mine workers. In this study, author have analyzed the nature of fume flow, i.e. accurately predicting where and how the fumes flow after an underground development/tunnel blast. This will help in determining i) precise re-entry times for the workers ii) rate and direction of the fume flow. Computational Fluid Dynamics (CFD), a mathematical simulation technique that predicts fluid dynamics phenomena is used for this purpose. CFD is preferred over physical models because it is inexpensive, once the accuracy is established, a wide range of scenarios can be simulated quickly, and the toxic gas flow patterns through underground openings can be analyzed efficiently. For this study, CFD is performed using SC/Tetra software owned by MSC software company.

By Gerardo Fuentes

The stoichiometry and kinetics of the hydrothermal reaction of enargite in copper sulphate solutions was investigated in the range 140–300 °C, and particle size under 15 and 50 μm. The stoichiometric experiment was performed at 300 °C, using one gram of sample (96% enargite, 4% tennantite) and 100 mL of copper sulphate solution (10 gpl) at 1.2 pH. Enargite reacted completely after 80 min. A solid product was obtained and characterized by XRD. The main product was chalcocite (M) and some traces of djurleite and chalcocite (Q). Tennantite did not react under these conditions. The kinetic experiments were conducted at 140 °C, 190 °C, 250 °C and 300 °C. From fitted data and Arrhenius equation the calculated activation energy (Ea) was 51 kJ/mol. According to the hydrothermal transformations studied, the reactivity of different phases found in the copper concentrates was bornite > chalcopyrite > covellite > sphalerite > pyrite > enargite > tennantite.

That electricity is an important and valuable agent, the limit of whose capacity for utilisation is as yet unknown, is a truism; although enormous advances have been made, the possible developments are yet greater. Mining, along with other industries, shares already to a large extent in the practical utilisation of this agent. Electrical engineers have been employed for several years past in developing and applying electricity to all classes of machinery, and for every purpose where power is required and in no instance, that the writer is aware of, has its use been curtailed in favour of any other agency now known, while extensions are continually made. The first modern electric motor was shown at the Vienna Exhibition of 1873, and it was used to work a pump through a mile length of cable but it was not before 1878, that an electric motor was put into daily commercial use by Messrs. Chretian and Felix to work a beet sugar hoist. This early plant effected a saving of 40 % as compared with hand work.In 1879, the first Electric Railway was constructed for the Berlin Exhibition, and in the same year, Mr. T. A. Edison was running an experimental line at Menlo Park. The first electric line opened for the public, was constructed by Siemens and Halske, in 1881, at Lichtenfelde, and was 11 miles in length.

By C. W. Gennet

Announcement was made in the spring of 1926 that the Boston & Maine R. R. Co. had contracted with the well-known German steelmakers, Messrs. Fried Krupp, for the manufacture of 15,000 tons of basic open-hearth steel rails at the Rheinhausen Works, for delivery to Boston, Mass. The manufacture of rails in the United States has for many years been almost a national pride, and as this feeling is chiefly the result of a long-time liberal and consistent patronage of American rails by American railroads, it is not strange that this somewhat unusual announcement should arouse more than ordinary interest. Since the end of the World War, the importation of foreign rail has been fairly large, principally because the newly created economic conditions have rendered some American competition more difficult, but the tonnage imported, for the most part, has been made up of small orders for miscellaneous use; and the contract referred to constitutes the largest single importation of foreign rail in over ten years. In 1915, the Algoma Steel Co. of Sault Ste. Marie, Canada, supplied the Illinois Central R. R. with 30,000 tons of rails,' and various other American roads with smaller amounts. In 1902, 1903 and 1904, large tonnages of rail from abroad were purchased, the Louisville & Nashville R. R. alone obtaining 30,000 tons from German mills. It is the object of this paper to present, in what is believed to be a new and concise form, figures showing the production and consumption of rails in the United States, and to record some of the testing and inspection results of the recent Krupp rails; also, to direct attention to two quite unique departures from American practice that were regular features of the Krupp process and which are worthy, it is thought, of careful study. Production and Consumption of Rails in the United States Table 1 shows the tonnage of rail produced in the United States and the amount imported, exported, and consumed by years since 1849. That, evidently, was the first year of record, for the statistics of the American Iron and Steel Institute and its predecessor, the American Iron and

By D. Berberick

Hecla?s Lucky Friday Mine is a deep, underground producer of silver, lead and zinc in the Coeur d?Alene mining district of northern Idaho. Main access into, and production from, the mine is via the Silver Shaft, a 5.5-m (18-ft) diameter, concrete lined shaft sunk by J.S. Redpath to an original depth of 1,890 m (6,200 ft) in the early 1980s. The shaft is divided into four compartments (Fig. 1), with sets made of 225 mm x 175 mm (9 in. x 7 in.) hollow structural section (HSS) steel buntons and 150-mm x 150-mm (6-in. x 6-in.) HSS dividers spaced every 4.5 m (15 ft) down the length of the shaft. Two skip compartments on the east side of the shaft are equipped with 125-mm x 150-mm (5-in. x 6-in.) HSS steel guides and 9-t (10-st) skips with three deck trailer cages for men and materials. The west side of the shaft is divided into a manway, and a fourth compartment that was originally designed for a service cage. Shaft services consist of a 250-mm (10-in.) a compressed air line and 150-mm (6-in.) sandfill line along the south side of the shaft, and 250-mm (10-in.) discharge (gray) water and 150 mm (6 in.) fresh water lines on the north wall. The mine?s primary 13.8 kV power lines, as well as communication lines are located on the west wall of the shaft. The production hoist is a 3.7-m (12-ft) diameter, double drum, double clutch, 2,238 kW (3,000 hp), direct current unit equipped, at the time, with thyristor drives. The 30-year-old drives would prove to be problematic during the rehabilitation project, leading to an upgrade to modern ABB drives later in the project, after the shaft rehabilitation was complete. The shaft had been subjected to the typical wear and tear of 30 years of operation, including intermittent sandfill and muck spills, and, in the lower areas, some corrosion. During those 30 years, the west compartment, originally designed for the service cage, could only be accessed from a work deck on top of the skips or from the manway.

By J. Böhlke, B. Friedrich, E. Hecker

The legislation for the disposal of heavy metals contaminated substances is still going to be tightened up in the future. The main criteria for the utilization or deposition of these residues are the content and the water solubility of these metals. Through this, the use of slags from the lead-and zinc-industry in road building may become limited or even not possible at all. From an economic point of view this would lead to Pb/Zn losses and costs for safe dumping. This paper investigates the feeding of the reducing agent via hollow electrode DC smelting and the yield of metal reduction. After carrying out thermodynamic calculations, the process window conditions for electric-arc furnace tests were determined. Doing this, the zinc could be reduced, evaporated and recovered as an oxidic intermediate product flue dust, while the lead was present either in flue dust or in metallic form. The zinc content in the final slag could be reduced by up to 90%. The slag product has undergone an eluation test which allows it to be used as building materials. Keywords: zinc reduction, lead reduction, hollow electrode, slag treatment, electric arc furnace

By Theresa Y. Schulz

It is interesting to study the noise standards that have been promulgated in the US over the last decade or so. These regulations are likely to have long-lasting impact. The Occupational Safety and Health Administration (OSHA) Hearing Conservation Amendment (March 1983) continues to have influence not only in the workplace but in the debate over new regulations. Both the Mine Safety and Health Administration (MSHA) and Federal Railroad Administration (FRA) regulatory preamble documents state the desire to be consistent with OSHA. An examination of Table 1, which compares the major components of the three regulations and the 1998 NIOSH “best practices” criteria, depicts the extent to which that intent is met. There has been some regulatory activity in the last decade which may give some hope for evolution and updating based on the wealth of science that has occurred during the last quarter of a century since the OSHA regulation was enacted. However there has also been some “back-sliding” toward more lenient standards. The MSHA noise standard made regulatory progress in September 2000 by emphasizing engineering and administrative controls, followed by personal protective equipment, in the hierarchy of noise intervention. MSHA’s requirement for technician certification (today only available from CAOHC) strengthened the training requirements for audiometric testing in hearing conservation programs and MSHA also added the requirement of dual hearing protection at 105 dB TWA. There were many subtle differences between OSHA and MSHA based on comments and a desire to clarify some of the vague aspects of the OSHA noise standard, and meet the needs of the regulated mining industry. One example pertains to the ceiling for exposures. OSHA says, “no exposures >115 dBA,” which is interpreted to mean no unprotected exposures above that level, giving credit for the assumed effectiveness of hearing conservation programs, hearing protection devices and administrative and engineering controls. MSHA specified that a “P” code1 violation be issued for any protected or unprotected exposures >115 dBA. The Federal Railroad Administration (FRA) noise standard for railroad operating employees, which went The Modern Evolution of Hearing Conservation Regulationsinto effect February 26, 2007, was expressly based on the OSHA standard but also uses MSHA for comparison. The preamble states that the FRA defers to OSHA as the “primary regulator of noise in the workplace,” but also acknowledges the need for some departure from the OSHA regulation (FRA Preamble II.B). As an example, FRA requires testing at 8000 Hz “because it will allow employers to identify hearing loss sooner.” The FRA rejected MSHA’s hierarchy of noise controls in favor of requiring specific engineering interventions and focusing on appropriate hearing protection which would still allow communication and audibility, and identification of excessive noise through employee-filed “excessive noise reports.”2 Where OSHA has no specific mandate requiring employees to take advantage of the employer-paid audiogram, it has been traditionally a condition of employment and is generally accepted that OSHA-covered workers require an annual audiogram. MSHA addressed this issue in its preamble; however, they made no significant change. MSHA employers are required to offer annual audiograms but MSHA stopped short of requiring employees to comply with annual audiometric testing. The MSHA preamble does allow that mine operators can also make audiometric monitoring a condition of employment. FRA requires employees to

By R. Karl Zipf, David Newman

The objective of this is paper is to review the current state of knowledge and practice in highwall mining (HWM). HWM has become a widely-applied method in surface mining, commonly used alone or in conjunction with contour or slot mining. It provides 800-feet to 1,200-feet of additional recovery when the economic stripping ratio is reached in contour mining or in slot mining when surface access to a reserve is limited. A significant attribute of the highwall miner is its versatility. HWM has been used successfully to mine abandoned pre-reclamation law highwalls, points or ridges uneconomic to mine by underground or other surface methods, outcrop barriers left adjacent to underground mines, separate benches of the same seam where the parting thickness or quality differences between benches render complete extraction uneconomic, previously augered areas containing otherwise inaccessible additional reserves and close or widely spaced multiple seams. The theory and design methods to assess roof, pillar, and floor stability are presented followed by three case histories. Simple design charts for sizing HWM web and barrier pillars are also presented. A recommended web pillar width may be obtained from the design charts given the overburden depth, the HWM cut width, and the mining height. Given the depth and panel width for a set of HWM cuts, another set of charts gives a suggested barrier pillar width. The case histories, from Northern and Southern Appalachia are used to illustrate the application of rock mechanics to quantify the stability of the highwall, roof, web pillars, and floor. The case histories involve 1) mining through a previously augered highwall, 2) mining under back-stacked spoil and 3) selective mining of closely spaced benches of the same seam. Because each site is unique, the appropriate pre-mining geotechnical analyses range from the calculation of roof, web pillar, and floor bearing capacity stability factors to detailed numerical modeling of the auger and underground mine workings. When operating in the vicinity of existing underground mine or auger workings, the determination of ground deformation and strains resulting from highwall mining is a necessary facet of a ground control investigation.

By D. K. Ingram, G. L. Mowrey, T. R. Rehak

Problem: Blasting is a hazardous component of surface mining. Serious injuries and fatalities result from improper judgement or practice during rock blasting. This paper describes several fatal injury case studies, analyzes causative factors, and emphasizes preventive measures. Method: This study examines publications by MSHA, USGS, and other authors. The primary source of information was MSHA’s injury-related publications. Results: During the 21-yearperiod from 1978 to 1998, the mean yearly explosive-related injuries (fatal and nonfatal) for surface coal mines was 8.86 (95% CI: 6.38 -11.33), and for surface metal/nonmetal mines 10.76(95% CI: 8.39 - 13.14). Flyrock and lack of blast area security accounted for 68.2% of these injuries. This paper reviews several case studies of fatal injuries. Case studies indicate that the causative factors for fatal injuries are primarily personal and task-related and to some extent environmental. A reduction in the annual injuries in surface coal mines was observed during the ten-year period of 1989 - 1998 [5.80 (95% CI: 2.71 - 8.89) compared to the previous ten-year period of 1979 - 1988 [10.90 (95% CI: 7.77 - 14.14)]. However, such reduction was not noticed in the metal/nonmetal sector, i.e., 9.30 (95% CI: 6.84 - 11.76) for the period 1989-1998compared with 11.00 (95% CI: 7.11 - 14.89) for the period 1979-1988. Discussion: A multifaceted injury prevention approach consisting of behavioral/educational, administrative/regulatory, and engineering interventions merits consideration. Impact on industry: The mining community, especially the blasters, will find useful information on causative factors and preventive measures to mitigate injuries due to flyrock and lack of blast area security in surface blasting. Discussion of case studies during safety meetings will help to mitigate fatal injuries and derive important payoffs in terms of lower risks and costs of injuries.

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By Steven J. Knoll, Theodore J. Williams, Douglas F. Scott

Highly stressed rock in stopes continues to be a primary safety risk for miners in underground mines because it can result in failures of ground that lead to both injuries and death. Spokane Research Laboratory personnel investigated electromagnetic (EM) emissions in a deep underground mine in an effort to determine if these emissions could be used as indicators of impending catastrophic ground failure. Results suggest that (1) there is no increase in the number of EM emissions prior to recorded seismic activity, (2) some EM signals are generated during blasting, (3) interference from mine electrical sources mask seismic-generated EM signals, (4) EM emissions do not give enough warning (compared to seismic monitoring) to permit miners to leave a stope, (5) the distance an EM signal can travel in the rock is between 18 and 40 m, and (6) current data acquisition systems do not differentiate between EM signals generated from seismic activity and random mine electrical noise. These results preclude monitoring EM emissions as precursors of impending catastrophic ground failure.

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By J. N. Sicking, F. H. Brinkman

A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium-ratio data for reservoir studies of condensates and volatile crude-oil systems. The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and variom reservoir pressures. Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems. In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir. INTRODUCTION As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids—thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated. Unfortunately, because of the complex nature of hydrocarbon mixtures, accurate K-values are hard to obtain. The equilibrium ratios for a particular component will vary not only with the temperature and pressure, but also with over-all composition of the system. The importance of composition is quite critical at elevated pressures, but becomes negligible at pressures below about 300 psia. Therefore, because most phase behavior problems involve the high-pressure region, each fluid system becomes a special case. Experimental programs to determine characteristic K-values are quite difficult and time-consuming. Thus, it is often necessary to resort to approximations of the K-value data. Charts giving K-values for various mixtures and classes of mixtures are available in the literature. However, there are two major difficulties in using them: (1) the K-values of the "plus" component (that mixture of components heavier than the last one analyzed) must be obtained by extrapolation from the K-values of the other components; and (2) the K-values obtained must finally be adjusted by trial and error to agree with observed volumetric data. To eliminate these difficulties, a new method of determining equilibrium ratios was developed. Briefly, after the composition of the system as a whole has been analyzed, the method uses empirical correlations and the gross fluid properties of the system (relative vapor-liquid volumes and densities) to calculate K-values. Because the calculative procedure is long, it is best solved on a digital computer. About one hour of machine time on an IBM 650 computer is required to develop a K-chart for the fluid being examined. DEVELOPMENT OF THE METHOD OF OBTAINING K-VALUES Equilibrium ratios are defined as the ratio of the mole fraction of a component in the vapor phase to its mole fraction in the liquid phase. This statement is expressed in Eq. 1. A typical plot of equilibrium ratios for a particular system is shown in Fig. 1. It should be noted that, at pressures near the saturation pressure, the K-values appear to converge to a common point. This apparent convergence point is called the convergence pressure and is a characteristic of the system involved. Various empirical correlations of K-values have been noted. It has been observed that an isothermal plot of

By Hugh Neill, O&apos

In previous papers,' the author has reported the results of experiments on the straining in tension of a single-crystal test piece, about 0.6 in. long, of vacuum-melted electrolytic iron containing 1.8 per cent. of silicon. The crystal was originally in the "as cast" condition, and was stressed slowly along a tetragonal axis so that slipping along conjugate gliding planes finally transformed the original cylindrical portion into a pair of fracture wedges. One of these fracture wedges was sectioned along the stress axis in a plane at right angles to the edge of the wedge. A metallographic study of this plane of section led to the conclusion that slip had taken place in the (111) direction along (112) planes making a V shape with the stress axis. The present paper describes the results of scratch-hardness tests conducted on the same section, in order to determine the distribution of strain hardness therein, followed by annealing, and considers the resulting variations in hardness. These observations supplement those made by Krivobok2 on similar material reduced 25 per cent. by hammering (i. e., by impact) in the cold. In order to investigate ageing effects, two small crystals of the same alloy were also tested. The Specimens Employed The principal specimen, A, was prepared for the metallographic examination leading to the determination of the slip planes of the crystal. Therefore the work described in this paper was conducted on metal which had been repeatedly etched and had been allowed to rest for about 30 months after straining. It consisted of a section of the fracture wedge and contiguous unstrained head of the test piece taken along a tetragonal axis parallel to the direction of stressing, the plane of section originally being not far removed from the (011). Several subsequent grindings