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By T. A. Pollard, C. R. Sandberg, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By Marshall Pease, R. J. Brandon

A UTILITY that has a large consumption of coal must insure an adequate and sound supply of fuel. The Detroit Edison Co., which has an annual coal consumption of about four million tons and spends approximately $32 million a year for coal, including freight charges, has developed a program for fuel procurement and for evaluation and selection of fuel for reliable and efficient plant operation. Fuel Procurement Coal Purchasing Division: The Fuel Supply Div. of the Purchasing Dept. combines all of the procurement functions in one group, which must maintain adequate stocks of fuel. In addition to its usual purchasing duties, the division also governs transportation, follow-up, invoice and freight bill, in cooperation with the Accounting Dept. The Fuel Div. is comprised of the fuel agent, an assistant fuel agent, a coal buyer and five coal clerks, who follow the movement of each car, initially approve freight bills and invoices, and file claims whenever there is a shortage of one ton or more. The fuel agent reports directly to the purchasing agent of the Company, and all major programs are planned jointly with the chief purchasing officer. The apparent individuality of the fuel section is necessary because of the tremendous volume of coal cars handled each day, sometimes as many as 500, which must be handled promptly to complete the fastest possible move from the mines to the plants. Determining Annual Coal Volume: Through the combined studies of a Production Dept. Load Committee and the Controller's office, accurate predictions of coal requirements for any given year are provided the Fuel Dept. from 12 to 15 months in advance. This is divided into the requirements of all individual power plants and central heating plants. This in turn determines the quantity and quality for plants whose specific fuels vary with the type of equipment installed. In the Detroit area, which has a high industrial load, early estimates of annual coal consumption usually are resolved at the end of the year within 4 or 5 pct of the original plan. Operating in a highly developed industrial area eases the task of estimating primary output; and, with the residential demands increasing in a steady and fairly well-defined pattern, the overall coal schedules are not subject to radical changes during any given year. Selecting Suppliers: At any time, but especially during or before an emergency, the coal supply factor must be made secure. This is particularly true in the procurement of utility fuel. There are always extreme quantities of so-called "bargain" coal available during the buyers' markets, such as recently prevailed. These opportunistic offerings may be considered a means of averaging down overall price, rather than as a steady and dependable supply source. Coal is purchased on contract from mine operators and sales agents who have proved reliable. They are not opportunists who desert for higher dollars in times of duress; they do not fail to fulfill contracts when markets rise or overship when markets dip. The progressive operator today who is willing to expend capital to improve quality and service deserves much more consideration than a matching of short-term pennies. When a company has a high volume of annual needs, all phases of the mine supply must be considered. The mine must be able to produce the quality required at a fair price and be able to sell oversizes of coal in enough volume to screen sufficient nut and slack. It must crush coal and sell mine run at prices in line with competitive nut and slack and be willing to do so when there is no demand for prepared sizes. Determining Price: The public utility is in direct competition with any of its customers who can, if savings are guaranteed, generate their own power. Today, to a greater extent than ever before, private industry must do a better overall job than Government-controlled operations. The price of coal must be realistically balanced with the price paid by almost all industries and the railroads as well. The supply-demand ratio in coal is not difficult to discern. There is access at all times to Govern-

Jan 1, 1952

By H. J. Ramey

Conventional calculation of total system isothermal compressibility for a system containing a free gas phase involves, among other things, evaluation of the change of oil and gas formation volume factors and the gas in solution with pressure. Preferably, this information should be obtained from laboratory measurements made with particular oils and gases. Often, experimental measurements are not available. In this case, it is necessary to obtain pressure-volume-temperature relationships from general correlations such as those of Standing' for California oils. In order to speed estimates of compressibility, generalized plots have been prepared of the change of both oil formation volume factors and gas in solution, with pressure from Standing's correlations. A generalized plot for estimating the change in the two-phase (oil and gas) formation volume factor with pressure is also presented. Usually, the effect of gas dissolved in reservoir water upon the total system compressibility is neglected for gas saturated systems, due to the low solubility of gas in water. Results of this study indicate that the increase in total system compressibility caused by solution of gas in water is often as large as the compressibility of wafer, and can be magnitudes larger for low pressure systems. Generalized results for estimating the change of gas in solution in water with pressure are presented in tabular and graphical form. INTRODUCTION During the past decade, pressure build-up and drawdown techniques have gained an important place in reservoir engineering. Build-up and drawdown analyses are only two special applications of the broad field of transient fluid-flow theory. All solutions of transient fluid-flow problems contain a parameter called the total system isothermal compressibility. This property of fluids and porous rock is a measure of the change in volume of the fluid content of porous rock with a change in pressure, and it may vary considerably with pressure. Evaluation of total system isothermal compressibility is not difficult, but it is tedious and time-consuming. Often compressibilities are estimated roughly, or transient flow methods are neglected completely. The benefits of using accurate system compressibility in properly-executed build-up or drawdown analyses are: 1. Better planning of pressure build-ups may be achieved to avoid unnecessary loss of revenue due to excessively long shut-in periods, or to shut-in periods too short to yield useable data. 2. Better and more reliable estimates of static formation pressures for reserves estimates and rate performance estimates. 3. Reliable information for evaluation of well completion effectiveness, and planning and interpretation of well stimulation efforts. The purpose of this paper is to clarify the nature of the total system isothermal compressibility, and to present useful methods for estimation of compressibility, particularly for systems containing a gas phase. DEVELOPMENT Numerous publications have presented solutions to transient single-phase flow of slightly compressible fluids, stressing pressure build-up applications. In transient flow, a compressibility* term arises to permit volume content of fluids in porous rock to change as pressure changes. The basic nature of the compressibility term is usually taken for granted. Problems arise in practical applications of transient fluid theory because most published works consider only one flowing fluid—in an ideal porous system containing only one fluid. In 1956, Perrine2 presented an intuitive extension of single-phase flow pressure build-up methods to multiphase flow conditions. Later, Martin- established conditions under which Perrine's multiphase build-up method had a theoretical foundation. Perrine has shown that improper use of single-phase build-up analysis in certain multiphase flow situations can lead to gross errors in estimated static formation pressure, permeability and well condition. It is likely that, much pressure build-up data for oil wells should be analyzed on the basis of multiphase flow. For both single-phase and multiphase build-up analysis, the isothermal compressibility term in dimensionless time groups often should be interpreted as the total system compressibility. All real reservoirs contain one or more compressible fluid phases. In addition, rock compressibility can contribute in an important way to the total system compressibility. The proper total system compressibility expression may contain terms for compressibility of oil, gas, water, reservoir rock and terms for the change of solubility of gas in liquid phases.

Jan 1, 1965

By C. R. Sandberg, T. A. Pollard, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe' using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"' pure silwer and Ag-0.5 at. pct ~n;' and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l' Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele'~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,'~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,' Gallaher,' and Gallagher and Wash-burn.' Ives and Ruff' found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By George B. Clark

Many basic engineering principles of all four phases of mining operations, namely, prospecting, exploration, development, and exploitation, can be analyzed better in terms of quantitative geology. Geological data from both field and laboratory will also complement scientific methods now being developed. THE geological data emphasized so successfully in prospecting for new deposits, that is, structural controls, strength of solutions, and type of mineralization, are basically those required for successful exploitation. In the mining of newly discovered deposits the most economical methods should be employed as early as possible to keep the overall cost per unit produced at a minimum and to permit maximum extraction of valuable minerals. A crucial question is: How can geological data be translated into useful quantitative results which will aid in achieving this end? H. E. McKinistry' has suggested that a solution may be reached in one of two ways: 1—the usual approach, use of judgment based on experience; or 2—mathematical calculations and tests on models, both subject to certain limitations. He also suggests that in addition to better use of geology more case data and theoretical data are needed on which to base sound judgment. Further research, therefore, is necessary. Perhaps in this field the emphasis should be on more specialization in mining methods and ground movement by men with thorough training in physics, engineering, geology, and underground mining. These specialists would be equipped to point out the most economical and scientific methods of exploitation. Selection of a stoping method is governed by the amount and type of support a deposit will require in the process of being mined, or by the possibility of employing the structure of the deposit to advantage in mining the ore by a caving method. In addition to these factors there are others which almost invariably influence the choice of an economical method of mining:' 1—strength of ore and wall rocks; 2—shape, horizontal area, volume, and regularity of the boundaries of the orebody, and thickness, dip and/or pitch of the deposit and individual ore shoots; 3—grade, distribution of minerals, and continuity of the ore within the boundaries of the deposit; 4—depth below surface and nature of the capping or overburden: and 5—position of the de- posit relative to surface improvements, drainage, and other mine openings. In the final analysis it is usually necessary to disregard the less important of these factors to satisfy the requirements of the more important. Because of the variation of geological conditions throughout and surrounding the deposit, no mining method will be everywhere ideally applicable to the conditions encountered in one ore deposit. The immediate problem is to interpret the above physical characteristics of deposits in terms of geological characteristics. Very few quantitative geological data are available on the factors related to a choice of mining methods. However, there are many descriptive data in mining and geological literature which collectively show how important an effect details of geology have upon all phases of mining operations. The following categories of basic mining methods were investigated to establish the geological factors that have affected their successful application: 1— open stopes with pillars; 2—sublevel stoping; 3— shrinkage stoping; 4—cut-and-fill stoping; 5— square-set mining; 6—top slicing and sublevel caving; and 7—block caving. It should be noted that the first five of these methods are listed in the order of increasing support requirements. Mines were selected as examples only where geological descriptions were complete enough to warrant their use. A study of the geological factors involved in mining operations led to a choice of the following classifications, employed in Table I: 1—structural type of orebody; 2—dimensions (geometry); 3— country rock (type); 4—faulting, folding, and fracturing; 5—alteration of ore and rock; 6—type of mineralization; and 7—geological factors determining mining method (summary). Of these factors only one yielded results that can be defined from available data in a quantitative manner, i.e., dimensions of the deposit. These are the most reliable guides that can be used in selection of suitable mining methods. They are, in general, the properties of geologic structure most difficult to evaluate by studies of models, pho-toelastic studies, and other laboratory methods, all of which are at present more limited in their applications than the geologic method. Application of geology has proved a reliable guide in other phases

Jan 1, 1955

By J. S. Marsh

OPPORTUNITY to pay tribute to the memory of Professor Henry Marion Howe is a strenuous assignment as well as an honor. Upon recalling Howe lecturers and lectures of the past 25 years, glancing over the list of those earlier, and rereading Howe's books, I arrive at several conclusions: 1—Many lecturers either worked under or knew Professor Howe. 2—It is virtually impossible to pick a subject on which Professor Howe did not touch. 3—There is precedent for a technical paper based upon pursuit of a single subject. 4—There have been listening lectures and reading lectures. There is solid comfort only in 2: the subject field is wide open. I did not know, nor even ever saw, Professor Howe, so can supply no fitting reminiscence. As a college student I was dimly aware that he counted among the giants. Fuller appreciation of his stature came with reading his books and papers, growing acquaintance with some of his associates, and the intrinsic dignity of the climax of the Annual Meeting, beginning at four o'clock of a Thursday afternoon in the auditorium of the Engineering Societies Building in New York. As for producing the technical paper sort of thing, it is my lot to have reached an age and assignment such that to do so would be to filch information from those who did the work and whose story is theirs to tell; for this I have no enthusiasm. As for the final conclusion, Professor Howe was one of the chosen few so highly expert at expository writing that he could produce a lecture or paper that reads as though it would also have listened well. One of his tricks was the free use of words not ordinarily part of the technical vocabulary, provided that such words were likely to communicate most precisely what he had in mind. How wonderful it would be for all who must read reports by the ton if ability at exposition could be taught with the effectiveness open, say to, differential calculus! Perhaps Professor Howe should be required college reading even if for no other reason than to prove that technical writing need be neither dull nor diffuse. My assignment is clearly still strenuous. Another point to consider is the fact that metallurgy is now so tremendously diversified that hope of finding a topic of universal appeal is negligible, even if one were competent enough to be permitted free choice. That which follows is, therefore, a compromise composed of necessity and of the obligation to attempt to avoid boring to slumber those of you who are not especially interested in the general subject chosen. The Iron and Steel Div. is now essentially a process metallurgy division, heavily concerned with the smelting of iron and the making of steel. The American Iron and Steel Inst. figure for present steel capacity of this country is 125,828,310 net tons; how this is divided among processes is indicated by the production totals for 1953, shown in Table I. The glamor girls and boys make the front page and so it is with steelmaking processes. If there is an Antarctic Daily Bugle, it undoubtedly has carried stories of revolutionary development, such as oxygen processes and vacuum melting, and stories of the incomparably rosy destiny of electric arc melting. All such certainly have their place and their future; meanwhile, it is the sturdy and old reliable open hearth that accounts for the bulk of production reported back on the financial page, and it is the old reliable that is most likely to continue to account for the bulk for some perfectly sound raw material, technologic, and economic reasons. This, plus the fact that next year marks a centennial (for it was in 1856 that Frederick and William Siemens conceived the regenerative open hearth), is reason enough to talk about open hearth furnaces, but is not the real one. The real reason is that in some years of association with open hearths, I have accumulated—in addition to a genuine liking and respect for them—certain odds and ends of fact and fancy that this lecture provides a unique chance

Jan 1, 1956

By C. Richard Tinsley

Like most minerals, coal is inherently a demand-limited commodity. The very sedimentary nature of its occurrence implies greater availability potential than demand. But this situation is overridden by economics among fuels, between coals, and within coal blends. Such considerations make coal forecasting a very hazardous profession indeed. THERMAL COAL If one thought that the lead times involved with a mining project were very long, one has obviously not been exposed to the planning process in the electric generation business - a process seriously confounded by shifts in load growth, environmental pressures, capital intensity, security of fuel sourcing, inter-fuel economics, and so on. But as a general rule, the near-term forecasts for thermal coal can reliably be based on a bottom-up, plant-by-plant analysis. Cement plant conversions can also be reasonably estimated next in order of reliability, although they have a much wider spectrum of coal qualities and fuel sources to choose from with a notably higher tolerance for sulfur and ash. Finally, industrial demand can be assembled from the estimates for conversions by pulp/paper plants, chemical plants, etc. The industrial sector is harder to estimate, since it may involve small boilers or dual-fired units. Assessing demand in the Pacific Rim is relatively a straightforward process in the near term because the major importing countries are all located on the Asian continent with either negligible or very minor (yet stable) indigenous coal production, (itself often operated on a subsidized basis). Furthermore, all imports are seaborne. These major importers are Japan, Korea, Taiwan, and Hong Kong with Thailand, Singapore, and Malaysia up-and-coming consumers. The suppliers to this market all have substantial reserves to back up decades of exports to these countries. Australia, the US, Canada, South Africa, China, and the USSR dominate the supply side. The second oil-shock of 1979/1980 has convinced the importers that reliance on oil can be expensive and eminently interruptible. Thus, they are determined to diversify away from oil' to nuclear and coal for generating electricity and for coal for other purposes where possible. This trend is seen to continue even in the face of the oil glut worldwide and oil-price reductions in early 1982. But the importers are also convinced that reliance on one coal source and, in particular, one infrastructure route for the coal chain from mine to consumer can be equally expensive and interruptible. Strikes in the US and Australia; excessive demurrage at certain ports; relegation of coal to a lower priority on multiple-use railroads in the USSR and China; and concern over escalation on high-infrastructure or high-freight coal chains are among the risks worrying the importers. As a consequence, Pacific Rim thermal coal purchases are being allocated among supplier nations, between ports, and within each country. An example of Japan's shift away from Australia and toward the US and Canada is shown in the estimates in Table 1. But the confidence of the import estimates deteriorates sharply beyond the plant conversion timetables and construction schedules in the near term. If part of the second generation of coal-fired power plants can handle lower-energy coals, the field of suppliers could widen to accept sizeable tonnages from Alaska, Wyoming, Alberta, or New Zealand resources. These supply sources generally have some infrastructure or freight advantage to compensate for their lower quality and to compete on a delivered energy-unit basis. These also offer diversification in sourcing. And the possibility of coal liquefaction in Japan further widens the sourcing network. A great number of Pacific Rim coal forecasts have been generated, especially for Japanese thermal-coal imports which are expected to grow strongly in the 1980's. Since the Japanese themselves have not yet settled their energy policy, the exact numbers are hard to call. Nevertheless, at 50 million tonnes of imports in 1990, Japan would consume 50-60% of the total Asian thermal coal imports as shown on Tables 2 and 6. The next most important consumers are the "island" nations of Korea, Taiwan, and Hong Kong (see Tables 3-5). All three are embarking on power plant developments usually with captive unloading facilities, capable of accepting more than 100,000-dwt vessels. Korea, with no-indigenous bituminous coal, is not especially enamoured with US coals, which are deemed too heavily loaded by freight and infrastructure costs -- up to 70% of the delivered price. Thermal coal contracts are presently split to Australia (70%) and to Canada (30%). Korea Electric Power Co. is already considering second-generation boilers capable of burning lower-quality coals than the present standard. Korea does burn domestic anthracite.

Jan 1, 1982

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 Richard J. Borg

The vapor pressure of Cd in equilibrium with CdSb in the presence of excess Sb has been measured using the Knudsen effusion method over the temperature range 276° to 379°C. The free energy of formation of CdSb is given by AF° = -1.58 + 1.53 x l0-4 T, kcal per mole. The enthalpy and entropy are obtained from the temperature coefficient of the .free energy. CADMIUM and antimony have almost imperceptible mutual solid solubility but form a single stable intermediate phase, CdSb. This phase, according to Han-sen,l extends from about 49.5 at. pct to 50 at. pct Cd at 300°C and has the orthorhombic structure. The free energy of formation of CdSb can be calculated from the vapor pressure of Cd for compositions which contain less than 49 at. pct Cd. The appropriate reaction and formulae are given by Eqs. [I] and [2]- CdSb(s, ~ Cd(g)-, +Sb(s) [1] Since Sb is in its standard state, Af - N,,AF'-,, = NcdRT In a,, = NcdRT InP/PO [2] In Eq. [2], P, is the vapor pressure of Cd in equilibrium with the alloy, and Po is the vapor pressure in equilibrium with pure solid Cd. It is implicit in this calculation that the free energy only slightly changes within the narrow limits of the single phase field. Thus, the value obtained from the antimony-rich boundary is truly representative of the stoi-chiometric compound. The results reported herein are obtained from a mixture near the eutectic composition, i.e. 59 at. pct Sb. Only two previous investigations" of the free energy of formation of CdSb have been made. Both relied upon the electromotive force method, and measurements were made over relatively narrow temperature ranges which strongly influences the reliability of the values of AH and aS. EXPERIMENTAL The eutectic composition is prepared by fusing reagent grade Cd and Sb by induction heating in vacuo with the starting materials held in a graphite crucible having a threaded lid. The material obtained from the initial melt is pulverized, sealed under high vacuum in a pyrex capsule, and annealed at 420°C for two weeks. X-ray analysis"gives the following lattize parameters: a = 6.436A, b = 8.230& and c = 8.498A using Cu Ka radiation with A = 1.54056. These values are in fair agreement with the result? previously reported by Al~in:4 i.e. a = 6.471A, b = 8.253A, and c = 8.526A. Vapor pressures are measured using an apparatus which has been described elsewhere,= however, with a single important modification. Knudsen effusion cells are made of pyrex with knife-edged orifices made by grinding the convex surface of the lid on #600 emery paper. Photographs taken at known magnifications using a Leitz metallograph enable the determination of the orifice area. Numerous calibration measurements of the vapor pressure of pure Cd give close agreement with values previously reported5,= thus indicating that no significant error can be ascribed to the substitution of glass cells for metal cells used in previous work. Because the vapor pressure of Cd is reliably established and because it is difficult to obtain Clausing factors for the glass cells, the final values used for the orifice areas are calculated from the calibration measurements of the vapor pressure of pure Cd. Effusion runs are started in an atmosphere of purified helium which is quickly evacuated as soon as the cell attains thermal equilibrium. Less than one minute is necessary to obtain high vacuum after evacuation begins, and the temperature seldom varies by more than 0.5oC from the value obtained prior to pumping out the helium. RESULTS The results of this investigation along with other pertinent data are tabulated in Table I. Fig. 2 is the familiar graph of log P against T-10 K. At least mean squares analysis of the data presented in Table I yields the following equation: log1DJP = 8.790 - 6472 x T"1 [3] The deviations of the individual measurements from the values calculated with Eq. 131 are given in column six of Table I; the average deviation is 4.0% of the calculated value. Although the partial molal properties change significantly with composition within the single phase region, the integral thermodynamic value should remain relatively constant. Hence the results of the following calculations, which use the data obtained for the eutectic composition, are probably representative of the equi-atomic compound. Eq. [4] describes the vapor pressure of pure Cd as a function of temperature and may be combined with Eq. [3] to

Jan 1, 1962

By H. O. Jahns

This paper describes the application of regression analysis for obtaining a two-dimensional areal description of heterogeneous reservoirs from short-term pressure-time data such as that obtained in interference tests. The method replaces the time-consuming trial-and-error procedure commonly used to match field data on an electric analyzer or digital computer with a systematic search which is programmed for a computer. The computer program adjusts the properties of a reservoir model automatically until a least-squares fit is obtained between observed and calculated pressure data. The reservoir is simulated by a single-phase, compressible, two-dimensional model. It is divided into a number of homogeneous blocks whose transmissibility (kh/F) and storage (Fch) values are varied to obtain the least-squares fit. The reliability of these values is determined from their standard deviations and correlation coefficients. Although the method is rigorously applicable to single-phase flow only, multiphase flow can be handled provided saturation changes are small during the test. Possibly the method can also be used to obtain a reservoir description from pressure-production history, but this application is outside the scope of this work. The paper includes, in addition to a description of the numerical procedure, a discussion of some of the problems associated with the method. Rules are given to help in selecting the number of homogeneous blocks and deciding upon their arrangement. The uniqueness of a reservoir description is considered. Finally, the use of the method is illustrated by the interpretation of field data from two interference tests. INTRODUCTION Pressure data from short-term transient tests, such as single-well and interference tests, are widely used to obtain reservoir properties. These tests are usually analyzed by assuming a simple reservoir model; very often, a homogeneous one is used. As a result, analysis of the transient data from each well frequently gives different values for reservoir properties. The problem then arises to combine all these differing results into a more detailed picture of the reservoir. One technique is to simulate the reservoir with a digital computer or with an electrical analyzer and to adjust the reservoir parameters by trial and error until the simulated pressure data are in reasonable agreement with the observed pressure data for all wells. Although this method has been used for both transient tests and pressure-history data, it is time-consuming and subjective. A second technique uses regression analysis to replace the trial-and-error procedure with a systematic search that can be programmed for a digital computer. Use of regression analysis in reservoir description was proposed recently by Jacquard and Jain.1 They divided the reservoir into a number of homogeneous blocks whose properties are varied until a least-squares fit is obtained between observed and calculated pressures. However, they did not consider their technique to be operational, mainly because of ".. .(I) the lack of experience in using the method .. . notably for the improvement of convergence; and (2) limitations imposed by the insufficiency of available computers". 1 While the analysis presented in this paper applies the same general principle used by Jacquard and Jain, the specific method is significantly different. Some differences are (1) the regression problem is solved in a different way which requires less computer time in most cases; (2) a stepwise solution, in which the detail in the reservoir description is increased from step to step, is used to improve convergence; and (3) the reliability of the estimated reservoir .properties.. as measured by their standard deviation and correlation coefficient, is estimated'

Jan 1, 1967

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By J. M. Tobin, L. H. Cadoff, L. M. Adelsberg

The reaction between liquid zirconium and graphite at temperatures above 2000 °C has been investigated. The reaction products were found to be carbon-saturated zirconium metal and ZrC which formed between the graphite and the metal. Parabolic growth behavior was observed for the ZrC Phase at all temperatures of this investigation. The parabolic growth constant at temperatures between 2000° and 2860°C was measured to be 1.83 exp 84,300/RT) sq cm per sec. The reaclion mechanism was proposed to be the rapid carbon saturation of the liquid metal and the formation of ZrC at the metal-carbide interface with diffusion of carbon through the ZrC, the "rate - determining step" of the reaction. The concentration-independent diffusion coefficient of carbon in ZrC, (DZrC), was expressed as 0.95 exp? 78,700/RT) sq cm per sec. This value mas calculated using the temperature-invariant ZrC phase fields proposed in the literature. The [ZrQiq)] — [ZYQiq) + ZrC] phase boundary over the temperature range 2000° to 2800°C was determined and the ZrC + C eutectic temperature was found to be 2890° ± 50°C. ThE Group IV and VB transition-metal refractory carbides are of interest because of their high melting points, high temperature strength properties, and relative inertness in certain corrosive environments. The present-day understanding of these materials, however, is limited by the general unavailability of accurate and reliable physical and chemical property data. This is due primarily to the difficulties associated with the preparation of suitable, high-density, high-purity carbide samples, and the achievement and control of uniform high-temperature environments. Accurate measurement of temperature is also an important factor limiting the reliability of reported data. The Zr-C reaction was selected for investigation because of the high melting point (>34000C) and favorable nuclear properties of the reaction product, ZrC. The direct reaction method afforded an opportunity to obtain kinetic data on the fully dense carbide. In this paper, layer-growth techniques were used to estimate the diffusivity of carbon in ZrC and to investigate the phase equilibria in the Zr-C system at temperatures above 2000°C. EXPERIMENTAL PROCEDURES AND DATA Crystal bar zirconium (99.9 pct Zr), purchased from the Nuclear Materials and Engineering Corp., and ZTA graphite (99.9+ pct) were used in this study. The analyses of the materials are listed in Table I. A schematic of the high-temperature carburization apparatus is shown in Fig. 1. The sample was a zirconium metal charge in a 1/2 -in.-ID graphite crucible which was capped with a tightly fitting graphite stern. The crucible and stem were designed to closely approximate black-body conditions. The graphite crucible was packed in lampblack (outgassed 1 hr at 2100°C) which provided insulation and thermal stability to the system. The inert atmosphere was maintained by a constant flow of high-purity argon or helium gas. The nozzle-diffuser section on the top flange was sufficient to prevent back-diffusion of air into the system. Chemical analysis of the carburized samples revealed oxygen and nitrogen concentrations of less than 44 and 20 ppm, respectively. The sample was heated by induction with a Westing-house 5 kw-450 kc power source. Temperature was measured with a Milletron two-color pyrometer which was sighted into the crucible by reflection from an overhead front surface mirror. Optical losses due to glass absorption and light reflection at air-glass interfaces were minimized by the employment of the dynamic-gas seal. It was found that no correction was required for the front surface reflector. The pyrometer was calibrated periodically against a U.S. Bureau of Standards tungsten ribbon secondary standard. Temperatures inside the crucible were also calibrated against the Zr-ZrC eutectic (1850°C)1 and the Nb-Nb2C eutectic (2335°C)2,3 temperatures and agreed to within ±10°C of these values. The temperature was controlled by manually adjusting the power input; variations of

Jan 1, 1967

By H. Leslie Bullock

From aluminum to zirconium, the quantitative preponderance of quartz as a gangue material is well recognized. lf this material is to be efficiently removed, its variations must be understood. Variations with temperature are especially important. Too little attention has been given to the thermal polarization of quartz. Under closely controlled conditions, electrostatic upgrading is very reliable. For efficient separation, contact charges must be fostered and charges due to radiation, surface coatings, or thermal polarization avoided. This paper lists thermal transition points of quartz and shows their effect on actual separations. Simple separation tests with all factors except temperature held constant are recommended for determining transition points. With silica making up more than 27% of the earth's crust, its oxides comprising more than 59% of all igneous rocks, and quartz accounting for most of the main free oxides, the mining engineer is in constant contact with quartz, which may occur as a valuable mineral to be purified or, far more frequently, as a gangue material to be removed as completely and economically as possible. As a means of effecting such purification or removal, dry beneficiation is becoming more and more desirable owing to local water scarcities, wet waste disposal problems, or freezing conditions. One method that has been gaining particularly rapid acceptance is electrostatic beneficiation, or the separation of dry free-flowing materials by means of opposite surface charges, differences in potential, or differences in conductivity. Electrostatic beneficiation dates back to the 1870's, but only in recent years have newly developed methods and apparatus and a growing knowledge of solid-state physics widened the field for its economical application. Because the term "electrostatic beneficiation" has been rather loosely used in the literature, it has come to include both electrostatic and electrodynamic procedures. Attracting type separators, however, in which oper- ation is based on differences of surface charge or potential, are truly electrostatic, because the separation occurs in a substantially static field set up between oppositely charged surfaces. Separations with this type of equipment may occur at potentials as low as 1000 v and seldom require potentials as high as 30,000 v. In the new contact charge dielectric separators1 the variation in charge is produced by continuous contact and separation of the particles in the moving feed stream and these charges are fostered by the use of non-conducting support and feed surfaces and by handling the feed in the form of streams of appreciable depth. This favors uniformity of feed and allows higher production rates. The distinctive surface charge differences are set up on the separation of the particles according to Coehn's Law,2 which states that equal and opposite charges are generated on the separation of any two materials in contact and that the substance having the highest dielectric constant will be positively charged. The basic contact charge concept is reliable, but all electrical charges are transient and modified by the electrical conditions of the surroundings. Pyro-electric, photoelectric and radiant effects may modify or totally destroy the contact charges necessary for efficient separation, or contact with conducting surfaces may neutralize them. Such hostile conditions must be carefully guarded against, since they have led to many costly failures in the past. The most consistent difference in surface charges to insure good separation is produced by repeated uniform contact and separation of particles in the moving stream. The thickness of the feed stream possible with this method reduces the effect of contact with the supporting surfaces, but as some contact is inevitable, the best results may be assured by having the dielectric constants of the supporting surfaces between the dielectric constants of the substances to be separated. In general, the hard smooth surface of quartz makes it an ideal substance for electrostatic separation from most minerals. For instance, with calcite, starting with a feed containing 1.9% acid insolubles, one can produce a concentrate containing 0.30% acid insolubles with a tailings containing 21.7% acid insolubles and a yield of 92.8%. The color can be held at 92 or above and the tint at 1.7 or lower. Working with specularite iron ore, laboratory work has given a concentrate of 68.8% Fe., with an iron unit recovery of 96.7%. Excellent results are also in pros-

Jan 1, 1969

By E. R. Russell, N. E. Richards

The current ejyiciency of aluminum cells was derived from the metal produced over a period of time and the theoretical faradaic yield. The difference in the actual amount of aluminum in the cathode at the beginning and end of the period must be determined. The weight of aluminum in the cathode was calculated from the dilution of an added quantity of impurity metal. Use of multiple indicator metals, copper, manganese, and titanium, demonstrated that the weight of aluminum in cells can be determined to within 1 pct with routine but careful chemical analyses. Over intervals of the order of 30 days, current efficiencies reliable to within 1 pct can be obtained. INVESTIGATIONS beginning with those of Pearson and waddington ,' through the most recent published work of Georgievskii,9-11 illustrate the direct relationship between the composition of the anode gas and the applicability of analysis of anode gases to the control of alumina reduction cells. McMinn12 noted the lack of an independent method for measuring cell production efficiency over the short term. There is no doubt that changes in the current efficiency are immediately reflected in the composition of anode gases. However, the accuracy of faradaic yields calculated from gas analyses depends upon the degree of interaction between primary anode gas and Carbon.6 A conventional industrial practice of obtaining long-term current efficiency for production units from mass balances and quantity of electricity is generally insensitive to the impact of planned control of any one or more of the influential reduction cell parameters such as temperature, alumina concentration, and mean interelectrode distance. Consequently, there is a real need in the aluminum industry for a procedure to obtain the absolute cell current efficiency over a short term—10 to 30 days—both for the calibration of values obtained from gas analysis6 and for evaluating the effect of controlling specific parameters in the reduction process. The amount of aluminum produced may be determined by considering the cathode pool as a reduction of an impurity metal in aluminum. Analyses over a period will show a decreasing concentration of the impurity due to the accumulation of aluminum solvent. The increase in aluminum inferred from analyses is the amount produced by the cell during the period. Combining weights of the cell aluminum in the cathode at the beginning and end of a specific period, weights of aluminum tapped and the quantity of electricity passed during the interval will yield the current efficiency. Smart,I3 Lange;4 Rempel,15 Beletskii and Mashovets,16 and winkhaus17 have used dilution techniques to determine aluminum inventory in alumina reduction cells. A technique for determining the weight of aluminum in production cells by addition of small amounts of copper to the aluminum cathode was described by smart.13 The precision in values of the aluminum reservoir through dilution of copper in the cathode ranged from about 1 to 3 pct depending upon the quantity of copper added in the range 0.2 to 0.01 wt pct, respectively. Because the method appears so direct and apparently simple, one would not anticipate difficulties in application to industrial cells. The objective of this study was to resolve this problem associated with the trace metal dilution technique for determining the amount of aluminum in a cell. The approach in evaluating trace metal dilution as a basic factor in determining the weight of aluminum in the cell reservoir, and the absolute current efficiency of the Hall-Heroult cell, was to dilute more than one trace metal in the aluminum cathode so that we could discriminate among complications arising from physical mixing, the possibility of separation of intermetallic compounds, loss of the added elements, and chemical detection. EXPERIMENTAL METHODS These experiments are not complex but require standardized procedures. The technique involves addition of the trace metals to the cathode, knowing when these metals are homogeneously distributed in the liquid cathode, timing of the sampling, employing accurate and precise analytical methods, using reliable procedures for monitoring the amount of electricity passed through the cell, and accurate weighing of aluminum removed from the cell during the particular period. More accurate results might be obtained if the increment in concentration of the added indicator metals were of the order of 0.1 to 0.2 wt pct. The method must be applicable to production units and, hence, the contamination of the aluminum minimized. For this reason, the concentration of trace metals in the cathode was kept below 0.07 wt pct and generally at 0.04 wt pct level. Trace quantities of copper, manganese, titanium, and silicon are already present in virgin aluminum and are suitable as additives from electrochemical and analytical points of view. Concentration of silicon is quite dependent upon the characteristics of the raw materials and was not used extensively in this work. Chemical Analyses. All instrumental analyses require calibration against an absolute technique such as a gravimetric, volumetric, or spectrophotometric method which represents the ultimate in sensitivity, precision, and accuracy. On review, the best methods for copper appeared to be optical absorption without

Jan 1, 1969

By E. P. Pfleider, W. G. Pariseau

Even as the rational selection of excavation equipment requires a matching of machine performance capabilities to rock response characteristics, the functional features of transportation systems must be matched to the characteristics of the materials handled in order to secure optimum, trouble-free operation. In particular, ore passes and chutes must be designed for flow in order to insure controlled draw whenever a chute is opened. The alternative to quantitative design is, of course, the well known ad hoc procedure of freeing plugged ore passes, cleaning up spillage from flooded chutes, etc., after installation of the system. Since the voluminous empirical work sporadically undertaken through the years evidently had not led to reliable design methodology, it seemed worthwhile to attempt a rational and complete description of the movement of material through ore passes. The concepts of de- formable body mechanics applicable to gravity-induced flows of granular media or "soils" were involved. Accordingly, the mathematical theory of soil plasticity was adopted as a working hypothesis, and a two-dimensional laboratory model of an ore pass constructed in order to investigate the appropriateness of the theory. The general experimental strategy consisted of formulating the movement of material in ore passes as a boundary value problem in soil plasticity, determining the required boundary values of stress and velocity experimentally, and then using these data for the initiation of a theoretical solution for stress and velocity throughout the moving mass of material. A comparison between the theoretical and experimental constituted the test of the original hypothesis.

Jan 6, 1968

By O. D. Gonzalez, R. A. Oriani

The migration of hydrogen and of deuterium dissolved in a iron and in nickel induced by an applied electrical potential has been measured over a range of temperature. In all cases the intevstitial solute migrates to the cathode. The deduced charges of transport are positive, independent of or slightly dependent on temperature, and markedly larger for the beavier mass. These results are interpreted as showing predominating momenlum transfer between electron holes and the acticated complex of the elementary diffusion act. THE migration of components of a metallic system under the action of an applied electrical potential is called electromigration or electratransport. This phenomenon has been known since 1861 and is becoming of increasing interest to metal scientists because of the opportunity it offers to explore the connections between mass transport and electron transport. Until recently, reliable data have been very scarce because of the difficulties inherent in the measurements. In addition, theoretical understanding has been either nonexistent or rudimentary and at present this situation is only moderately improved. Whereas the prevalent notion had been (and is still widely held) that electromigration directly reflects the state of ionization of a component in its equilibrium state in the metal, it is now becoming clear that the major, if not the sole, factor is the momentum transfer between the charge carriers, themselves in motion because of the applied field, and the metallic components in their activated state. It becomes important therefore to obtain reliable data over a range of temperature on electrornigration in systems where only one component moves, that is, either in pure metals (vacancy motion) or in interstitial solid solutions. Our choice of systems was dictated by our measurements' of the Soret effect in solid solutions of hydrogen and deuterium in iron and nickel. Indeed, the main reason for making measurements on electromigration at all is that we suspected a mechanistic connection between thermal diffusion and electromigration. In our former paper' we proposed that what is common to both phenomena is the momentum transfer between the charge carriers in the metal and the atom as it jumps from one equilibrium position to another. In Soret diffusion, however, there is in addition the dissipation of the energy of the jumping atom via pho-nons. We have since found that similar ideas for this interconnection have been developed by Fiks.2 In the present paper we will discuss in more detail our understanding of the mechanism of electromigration itself, but we turn first to a presentation of the experiments and results. EXPERIMENTS AND RESULTS Let us consider a metallic system in which only one component, m , can diffuse at the temperature in question, and to which are applied simultaneously an electrical potential gradient, grad cp, and a chemical potential gradient, grad p,. One may write3 for the material flux Jm and the electronic charge flux Je by applying the condition, grad = 0, to Eq. [I] and evaluating grad(um/T) for the isothermal case and for activity coefficient independent of composition over the relevant composition range. ere, c is the concentration and D the diffusivity of the mobile component. The experimental technique that we have used to measure Z* for the isotopes of hydrogen individually dissolved in each of two transition metals has been developed from a method used by Wagner and Heller.4 (A somewhat similar method was also used by Herold.5) A wire or thin rod of the metal under study connects two volumes of gaseous hydrogen at identical pressures; hence grad um = 0. A direct current is made to pass through the specimen, serving to maintain the specimen at the desired temperature and also to produce the electromigration of the hydrogen dissolved in the metal in equilibrium with the gaseous hydrogen. Under these conditions, the flux of hydrogen from one volume to the other is given, from Eq. [I] for grad( um/T) =0by

Jan 1, 1968

By R. E. Ogilvie, N. L. Peterson

Diffi-lsion measurements were conducted at all compositims in the bcc solid solution of the U-Nb system employing incremental couples at composition intemals of 10 at. pct. Diffusion coefficients were determined by the Matano method from concentration gradients obtained with the electron-probe microanalyzer. The activation energy for inter-diffi-lsion as a function of compositim shows three distinct regions: 1) 80 to 100 pct U.6= 30 kcal per mole; 2) 20 to 80 pct U, $ - 70 kcal per mole; 3) Oto 20 pet U, Q = i40 kcal per mole. The frequency factor, fi0 and the activation energy $ were found to be roughly related by the following equation: log Do ^9.7 X IO-5Q -6,6. The Kirkendall marker movement indicates that DU is larger than DNb between 16 and 100 pct U and DNb is larger than DU from 0 to 4 pct U. FOR practical as well as fundamental reasons, the rates of diffusion in alloys are of considerable consequence. Most solid-state reactions are largely dependent upon the diffusion of atoms through the lattice structure and along grain boundaries. The high-temperature strength and reasonable nuclear properties of niobium have prompted its use as a reactor material in contact with uranium fuel. Hence, diffusion data for the U-Nb system are of considerable importance. In the previous diffusion study1 on the U-Nb system using pure element couples, reliable data were obtained only in the range of 0 to 10 at. pct Nb due to the large variance of the diffusion coefficient with composition. Also, a large Kirkendall effect and considerable porosity in the uranium-rich areas of the specimen were reported, which suggests that the true diffusion coefficients are somewhat larger. The purpose of the present study was to obtain reliable diffusion coefficients at all compositions using incremental diffusion couples with intervals of 10 at. pct. In view of the abnormal self-diffusion be- havior of y uranium2-4 and some other bcc transition elements,&apos;-&apos; it was felt that a comparison of the interdiffusion coefficients in the bcc U-Nb system with those of Reynolds et al.9 for the fcc gold-nickel system might shed some light on the diffusion mechanism involved. Both systems have similar phase diagrams, in that complete solid solubility exists above a miscibility gap. EXPERIMENTAL PROCEDURE The uranium used in this investigation was obtained through the courtesy of Argonne National Laboratory. An analysis of this material detected only Si-30, A1-7, C-6, N < 10 and 0-18 ppm. The niobium was electron-beam melted material obtained from Stauffer-Temescal. The gaseous impurities were less than 50 ppm, and the spec troc hemical analysis showed Ta-500 and W-200 ppm. U-Nb alloys were prepared at composition intervals of 10 at. pct by melting the appropriate amounts of the pure elements in an arc furnace. The buttons were inverted and remelted 6 times to assure complete mixing. The buttons were then wrapped in molybdenum foil, canned in Zircaloy-2 or stainless steel, and hot rolled 30 pct reduction in thickness at temperatures between 850" and 1100°C. Alloys with 10, 20, 30, 40, and 90 at. pct Nb rolled quite easily under these conditions, but the 50, 60, 70, and 80 pct alloys remained brittle. After melting and rolling (when possible), the alloys were annealed for 24 hr at a temperature within 100°C of their melting point in a dynamic vacuum of better than 4 x 10-8 mm Hg. These treatments produced alloys which were homogeneous on a 1 p scale within the detectability limits of the electron probe. During fabrication, the alloys picked up as much as 100 ppm Mo and 100 ppm Zr. Other elements checked for but not found were Co, Cr, Fe, Mn, Ni, and Ti. The grain size of the annealed samples ranged from 3 mm for the uranium-rich alloys to 0.3 mm for the niobium-rich alloys. This permitted measurements of the concentration gradients in the diffusion samples without crossing more than one or two grains, thereby eliminating any grain boundary effects. The specimens were bonded by theU&apos;picture frame" technique as reported by Kittel.10 Specimens of composition b)U + (100 - x)Nb were sandwiched between two specimens of composition (x + 10)U + (90 - x)Nb after they were ground flat and parallel

Jan 1, 1963

By J. E. Walstrom

While intensive research continues to promote a more complete understanding of the potential and resistivity measurements that comprise the electric log, it is believed that consideration should also be given to translating these numerous and often widely separated findings into a coordinated and readable body of fundamental facts designed specifically for the petroleum engineer and geologist. Although provision is made through publication for a ready exchange of new theoretical concepts. it is also desirable to provide reviews and appraisals of the more established techniques and methods from the operating standpoint so that an economic and practical application may be realized concurrently with the theoretical progress. With these basic premises as a guide the author reviews the presnt state of electric log interpretation. The paper is directed not so much to the logging or research specialist as to the petroleum engineer and geologist to whom the electric log is only one of the many tools which he employs. Frequently, these persons do not have the time to follow in detail the many specialized contributions that appear and, as a consequence. are not in a position to place these contributions in proper relation to each other, or to the art as a whole. The paper reviews the basic steps in making quantitative determinations from the electric log of the amount of oil or gas present in subsurface formations and also discusses the degree of reliability of these determinations under various conditions. The paper also indicates the trend of future developments in electric logging systems and methods of interpretation. INTRODUCTION The electric log has been used about 20 years as a means for studying the formations penetrated by a well bore. The first half of this period is characterized by the development of suitable logging techniques and equipment. Although progress in this direction is continuing at a satisfactory rate, the last ten years are characterized more by an increasing interest in methods of electric log interpretation. During this period, a large number of fundamental papers have been published, expounding various logging techniques and particular phases of the interpretation problem. Many of these papers represent important contributions, and a few are classic. This paper is an effort to outline as concisely as possible and in simple terms the main course of progress in electric log interpretation. More specifically, it is the purpose of the paper to review the necessary elements and basic steps used in making quantitative determinations of water saturation from the electric log; and to point out the degree of reliability of these determinations under different conditions. It is strongly advised that the operating staffs of the drilling and exploration departments of oil companies cooperate wholeheartedly with both the electric logging service companies and research organizations in the testing and development of new logging systems and interpretation methods. One purpose of the paper is. however, to indicate the degree of caution which must be exercised in placing confidence in new techniques and interpretation methods that have not been thoroughly tested in the field. It is entirely possible to be cooperative in trying new methods and yet reluctant to believe in the results until the methods are firmly established. It is important to define the meaning of quantitative electric log interpretation. In the most general sense, an interpretation of the log has been made when the electrical characteristics of the formations, as portrayed on the log, have been translated into terms describing the formation geometry, rock type, or any other physical characteristics of the formations. The determination that the top of a sand is at a certain depth is an interpretation of the log. Structural determinations made by correlating electric logs from a given area are also interpretations of the logs. The term quantitative interpretation, however, will be used in this paper in the restricted sense to indicate the determination of the water saturation of a formation. This determination defines the fluid content of an oil and gas productive formation only if the porosity is known, and it assumes that the remainder of the pore space contains hydrocarbons. This assumption is believed to be true for most oil and gas productive formations. The quantitative electric log interpretation may he said to be a determination of the fluid content only to the extent which the water saturation, under the conditions given above. defines it. THE BASIC STEPS The fundamental steps in calculating water saturation from the electric log are: 1. Determination of the true resistivity of the formations from the apparent resistivities as recorded on the electric log.

Jan 1, 1952

By D. B. Robinson, C. A. Macrygeorgos, G. W. Govier

Experimental data have been obtained on the volurrletric behavior of ternary mixtures of methane, hydrogen sulfide and carbon dioxide at temperalures of 40°, 100" and 160°F up to pressures of 3,000 psia. The results indicate that the compressibility factors for this system do not agree with compressibility factors for sweet natural gases at the same pseudo-reduced conditions. The deviation increases as the temperature and methane content decrease. Discrepancies of up to 35 per cent were observed. A careful analysis has been made of the existing pUrblished data on compressibility factors for binary systems containing light hydrocnrbons and hydrogen sulfide or carbon dioxide. It has been found that the deviation of actual from predicted compressibility factors for methane-acid gas mixtures is a function of the methane content and the pseudo-critical properties,.v of the mixture. The ratio between actual compressibility factors for methane-acid gas mixtures and compressibility factors for sweet natrlral gases at the same pseudo-reduced conditions has been currelated over a range of pP,, from 0 to at least 7 arid a range of pT, from about 1.15 to at 1east 2 0 with an error not exceeding 3 per cent and over most of the range within I per cent. The validity of the correlation for mixtures containing appreciable hearvier hydrocorbons has not been fully established, but it is shown to be preferable than the use of a corretation based only on hydrocarbons. INTRODUCTION Although a relatively accurate method for predicting compressibility factors of pure materials is provided by charts based on reduced properties and the assumption that the compressibility factor is a unique function of T P and z the determination of the correct values of compressibility factors for gas mixtures is somewhat difficult. Two general methods of dealing with gaseous mixtures have been proposed. The first assumes a direct or modified additivity of certain properties of the mixture in terms of the properties of the individual components. Examples of this method are based on the familiar laws of Dalton and Amagat. The second method averages the constants of an equation of state applicable to the pure components. Both of these methods are of limited value in engineering calculations because the first usually provides reliable answers only over narrow ranges of pressure and temperature and the second is cumbersome to handle. In petroleum engineering practice accurate estimations of the volumetric behavior of natural gases arc frequently required. To fulfill this need, several generalized compressibility charts have been developed.&apos; &apos; Of these, the one prepared by Standing, el al is widely used at present. In the construction of charts of this type a third method for dealing with mixtures has been followed. It is based on correlation of pseudo-critical properties as outlined by Kay and calculated from the critical properties of the individual components in a mixture. Although these charts provide relatively accurate information on the compressibility of dry or wet sweet natural gases, they are less reliable when used for gases containing high concentrations of hydrogen sulfide or carbon dioxide or both. Thus, an experimental program, although time consuming, is the best means now available for the determination of the volumetric behavior of sour or acid gas mixtures. An increased interest in the behavior of these gas mixtures, particularly in connection with some of the fields in Western Canada where the acid gas concentration of the reservoirs may be as high as 55 per cent and where hydrogen sulfide alone may be as high as 36 per cent, provided the incentive for this study. It was the purpose of the investigation to determine the volumetric behavior of selected mixtures of methane, hydrogen sulfide and carbon dioxide over a range of temperature from 40" to 160°F and at pressures up to 3,000 psi. EXPERIMENTAL METHOD The apparatus used in this investigation was basically the same as that described by Lorenzo.&apos;" The amount of each pure component used in preparing the gas mixtures was measured over mercury in a glass-windowed pressure vessel. The pure components were then transferred individually in the desired amounts to a second glass-windowed pressure vessel where the volumetric behavior of the mixture was determined. Volume was varied by mercury injection or withdrawal. The capacity of the cell was about 125 cc. Temperatures in the cells were measured with copper-constantan thermocouples and a Leeds Northrup semi-