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By Mikhail Mikhaylenko

Natural and technogenic sources of rare earth elements (REE) and other rare and scattered metals are remarkable for their chemical diversity. The pregnant solutions going to processing for the valuable metals have very complex compositions. Both targeted elements and competing impurities are present in the solutions in different chemical forms. Thus processing of such materials demands application of different technological tools addressing numerous specific tasks on the way to the final product. Screening work was undertaken to identify the best resins among developmental and commercial products addressing typical cases in the hydrometallurgy of scandium and REE. The cases outline typical sources of scandium and REE, such as streams of TiO2 production, extracted phosphoric acid, barren uranium solutions and others. Specially designed ion exchange resins can be effective tools.

By J. S. Osoba, J. W. Graham, P. H. Monaghan

Of the many factors which affect the productivity of hydraudically fractured wells, the wettability of the propping sand has received little attention in the pas/. This paper shows that the wettability of the propping sand is an important factor which shorcltl not he overlooked. An analysis of relative permeability data shows that fractures packed with water-wet sand should be more permeable to oil than are fracturer packed with oil-wet sand. Laboratory results verify this conclusion. Cnlculations show that higher permeability to oil in the fracture should provide higher well productivity. A method is presented which ensures that the propping sand in an induced fracture is water-we1 even though oil is used as the fracturing fluid. The rnethod has been used in more than 150 field jobs: the field resrrlts are discussed briefly. The fluidized nature of water-wet sand in oil has giver1 unexpected benefits. This characteristic of water-wet sand and how it has been used advantageously in field operations are discussed. INTRODUCTION Hydraulic fracturing of subsurface strata to increase the productivity of oil and gas wells has been practiced for about 10 years. Today, fracturing is used more often than any other method of well stimulation. Basically, the process consists of breaking down (fracturing) a subsurface formation with pressure applied by means of a carrier fluid, usually oil or water, and propping the induced fractures apart by means of an agent, usually sand. suspended in the carrier fluid. Currently about 68 per cent of all fracturing is done with a simple mixture of refined oil or lease crude oil and sand'. The research of other investigators has suggested that dry sand is rendered oil-wet when it is contracted with certain types of crude or refined oils.' Hence, it may be expected that some fracturing operations employing an oil as the carrier for sand leave fractures packed with oil-wet sand. Conversely, those operations which employ water as the carrier for the sand probably leave the fractures packed with water-wet sand. Since the permeability of a sand-packed fracture to a mixture of oil and water is dependent upon the wettability of the fracturing (frac) sand, research was undertaken to determine to what extent the wettability condition (water-wet or oil-wet) controls fracture permeability which, in turn, affects well productivity. Additional research was directed toward the development of a method for obtaining the desired fracture wettability. In this report both theoretical and experimental evidence is presented to show the desirability of employing water-wet sand in fracturing operations. A method to obtain water-wet sand is discussed, and field results are reviewed briefly. DEPENDENCE OF WELL PRODUCTIVITY ON FRACTURE WETTABILITY To determine the dependence of well productivity on the wettability of the frac sand, it is necessary to know, first, the effect of fracture wettability on fracture permeability and, second, the effect of fracture permeability on well productivity. The relationship of these variables is considered separately in the order indicated. Effect of Wettability on Permeability Fig. 1 shows relative permeability relations for 20-30 mesh Ottawa sand. Inspection of these curves reveals that the relative permeability to oil when a small amount of water accompanies the flow is considerably higher when water rather than oil is the wetting phase. For

By A. Eilers

A MARKED peculiarity of most of the smelting-works of the Far West is the looseness with which accounts of the operations are kept. Indeed, probably over half of the works do not keep any detailed accounts at all, the yearly gross statement of profit or loss being considered sufficient for all purposes. The reasons for this must apparently be sought in the as yet unsettled state of all business relations, and in the deplorable fact that only in isolated cases educated metallurgists are in charge of the smelting-works. Continual and regular assays of the ores, by-products, and slags, are almost unknown, so that it is impracticable to ascertain, even approximately, the losses in the smelting processes. Of cases where regular accounts are kept of the quantities of ore smelted, of the composition of charges, and of the fuel consumed, I know only two or three. Under these circumstances it is extremely difficult to collect figures which cover the operations for a considerable length of time, and which are so valuable for the metallurgist, who wishes to get an insight into the economy of smelting operations, as shown by practice. Figures obtained by personal observation, which can of course cover only the brief space of the visit of the travelling metallurgist, must, therefore, be made to replace the more valuable data. The writer has had occasion, during the last and the preceding summer, to visit the larger number of the Western lead-smelting works, and offers, in the following pages, such data relating to the economy of lead-smelting in the blast furnace at various works, as he has been able to obtain. The only object in doing so is to place these figures on record, so that they may be from time to time supplemented with other data, which are now wanting. I. EUREKA CONSOLIDATED COMPANY'S SMELTING-WORKS. These works smelt the ores from the mines of the same company on Ruby Hill, Eureka, Nevada. The supply is almost unlimited,

By K. L. Gabby

Selective removal of mercury from cyanide leaching solutions while retaining silver has been a long-standing problem, due to the chemical similarity of mercury and silver. In order to be practical, a mercury removal process needs to be both highly selective and use inexpensive materials. This paper reports the use of zinc sulfide (ZnS) as a precipitant for mercury. The mercury cyanide complex (Hg(CN)4 2-) undergoes a replacement reaction with the zinc sulfide, forming insoluble HgS, while the silver cyanide complex (Ag(CN)2 -) remains in solution. Under appropriate conditions, the separation of mercury from silver is nearly quantitative, with close to 100% removal of mercury, while nearly none of the silver is precipitated.

By T. K. Perkins, L. R. Kern

A study of fluid mechanics, rupture of brittle materials and the theory of elastic deformation of rocks shows that, for a given formation, crack width is essentially controlled by fluid pressure drop in the fracture. Operating conditions which cause high pressure drop along the crack (such as high injection rate and viscous fluids) will result in relatively wide cracks. Conversely, operating conditions which cause low pressure drop (low injection rates and thin fluids) will result in relatively narrow cracks. Charts and equations have been derived which permit the estimation of fracture widths for a variety of flow conditions and for both horizontal and vertical fractures. INTRODUCTION There has been considerable speculation concerning the geometry of hydraulically created fractures in the earth's crust. One of the questions of practical importance is the width of fractures under dynamic conditions, i.e., while the fracture is being created and extended. Such width information could be used, for instance, to help estimate the area of a fracture generated under various conditions. Also, there has been a recent trend toward the use of large propping partiles.13, 15 Therefore is is desirable to know what factors can be varied in order to assure entry of the large particles into the fracture. There has been some work on fracture widths reported in the literature. In particular, there have been several Russian publications dealing with this sub-jeCt.1.31,3 These papers have dealt principally with the elastic theory and the application of this theory to hydraulic fractures. These studies have not led to an engineering method for estimating fracture widths under dynamic conditions. A recent paper3 has reviewed and summarized the Russian concepts. An earlier paper- from our laboratories also discussed the application of the elastic theory to hydraulic fractures. This first approach, based largely on photoelastic studies, has proved to be too simplified to accurately describe the fracturing process. However, these early thoughts have served as a guide during the development of more exact concepts. We would like to present in this paper our current concepts regarding fracture widths and some estimates of hydraulic fracture widths for several conditions. We believe that it is now possible to predict with fair accuracy the factors influencing fracture widths. Furthermore, the method of prediction has been reduced to a simple and convenient graphical or numerical calculation. CRACKS IN A BRITTLE, ELASTIC MATERIAL Many investigators2, 4, 30 have shown that competent rocks behave elastically over some range of stresses. Of course, if the tensile stress imposed upon a rock exceeds some limiting value, then the rock will fail in tension. In similar manner, there are some limiting shear stresses that can be imposed upon rocks. Hubbert and Willis11 have discussed the shear conditions which will lead to failure. Under moderate stress conditions (such as those likely to be encountered when hydraulically fracturing) and when stresses are rapidly applied, relatively, most rocks will fail in a brittle manner. Hence, for this discussion of hydraulic fractures in the earth's crust, we assume the rocks behave as brittle, elastic materials. Let us develop the discussion in the following way. (The following thoughts are applicable only to brittle materials.) 1. First we consider a brittle, elastic system. An energy balance will show the minimum pressure necessary to fracture rock, and from this pressure we calculate the minimum crack width resulting from extension of a hydraulic fracture. 2. Then we will show that, under ordinary fracturing conditions, fracture widths are appreciably greater than the minimum widths of extending fractures. In fact, we will find that crack width is controlled by fluid pressure drop in the fracture. 3. We will discuss pressure drops in fractures and resulting crack widths for various operating conditions and both vertical and horizontal fractures. 4. Finally, we will discuss the significance of these concepts, their relationship to fracturing pressures, etc. First, consider minimum fracture extension pressures. We can shed some light on this question by considering the theory proposed by Griffith7, 8 Yo explain the rupture of brittle, elastic materials. Griffith recognized that solid materials exhibit a surface energy8 (similar to surface tension in a liquid). The fundamental concept of the Griffith theory is that, when cracks spread without the application of external work (in the interior of an elastic medium which is stressed

By Oswald J. Heinrich

In conclusion of a series of deep exploration-borings with the diamond drill, I beg to submit the following statements, supplementary to those in my former papers on this subject: Since my communications read at the St. Louis Meeting, in May last, I have finished two more borings, one terminating at the depth of 922 feet 7 inches, the other at the depth of 715 feet 6 inches. The results in regard to time and expenditure have been highly favorable and fully confirmatory of my opinion stated in previous

By Deventer Johanna van

Ore bodies around the world are declining in grade, whilst increasing in complexity. The level of impurities relative to the valuable metal is steadily increasing, posing new challenges to existing operations. Ion exchange is widely used in the hydrometallurgical industry for both primary recovery of metals and the removal of impurities. The superior selectivity of ion exchange resins makes them exceptionally suitable for the removal of target impurities to very low levels, thereby saving operating costs, increasing the value of the final product and significantly improving revenue. The ion exchange process in these applications is very simple, using standard ion exchange equipment and acid regeneration. The process can be fully automated, requiring minimal operator interference and supervision Examples of impurities that are successfully removed via ion exchange include iron, antimony and bismuth from copper electrolyte. In the copper electrolysis process, antimony, bismuth and arsenic tend to form slimes which are dispersed in the electrolyte. These slimes contaminate the cathode and/or decrease the quality of the copper deposition. A special chelating resin was developed to remove antimony and bismuth, while at the same time ensuring minimal chloride leakage to the sulphate matrix. The work is described in more detail in this paper. Ion exchange is also used to remove copper, zinc and nickel from cobalt electrolyte. This paper addresses a few of these examples in more detail.

By J. W. Walker, G. J. Heuer, E. W. Hough

An improved apparatus is described for the deterrni-nation of interfacial tension* by the pendant drop method in the pressure range from 15 to 15000 psi and the temperature range from 100º td 280°F. The chief characteristics of this apparatus are reliability and ease of operation. Temperature control was accomplished by means of an electrically heated jacket which could he completely removed while cleaning the apptrratus. The cell was designed so that the camera could he placed about I in, from the window without overheating the carnera lens. Separate "0" rings employed to seal each window and corresponding window backup plate gave very reliable window operation at 10,000 psi. An extra pistorr-cylinder combination was added so that a high compression ratio could he attained when gas was employed as one phase in the pendant drop cell. Other essential parts of the system were similar to an apparatus already described.' The interfacial tension for carbon dioxide and water varies from about 69 dynes/cm at 15 psi to about 19 dynes/cm at 1,250 psi for 100°F. For pressure.r between t,500 and 3,500 psi, the interfacial tension is between 32 and 24 dynes/cm at this temperature. The interfacial tension at 280°F varies from about 50 dynes/cm at 200 psi to about 17 dynes /cm at 10,000 psi. The maximum surface excess for carbon dioxide, assuming the surface excess of water to be zero, occurs at about 1,500 psi jor the 100°F isotherni and Itas a value of about -79 X 1014 mol/sq cm. At 160°F this maximum IS shifted to about 2,000 psi and has a value of about 10 X 1014 111ol/.sq cm. Other maxima, us well as several minima, are present at these and other temperatures. Judging from the data on the solubility of water in carbon dioxide at elevtrted pressures2,3, it appears that the principal maxinza natned are in regions of increasing solubility of the water in the carbon dioxide rich phase. INTRODUCTION AND APPARATUS A pendant drop interfacial tension apparatus which would accommodate an opaque liquid in a gas phase was constructed several ycars ago' for industrial purposes. This apparatus was used as a starting point for the present development. The objective of the present development was to enhance reliability and convenience of operation. Other articles'" have described pendant drop apparatus which could not accommodate a gaseous phase adjacent to the windows. A schematic diagram of the apparatus is shown in Fig. 1. The water used followed the path; A, intro-

By E. A. Barrett, L. L. Rethi, B. Fotta

Employment and accident trends of independent contractors working at coal and noncoal mines in the United States are reported. Data include employee hours and accidents, both fatal and nonfatal, from 1985 through 1994. Also noted are increases or decreases in certain accident classifications and accident rates, particularly those which have shown significant change during the ten-year period.

This volume, which was advertised in the December, 1968, issue of the Journal at a pre-publication price of £4, is edited by W. Ryan of Warren Spring Laboratory and published by the Institute of Mining and Metallurgy, London. It is an up-to-date review of the operations of some 50 or so companies whose activities embrace the extraction and refinement of metals in the United Kingdom. Thirty-four metals are discussed, ranging from aluminium to zirconium and also there are chapters on ferro-alloys, non-ferrous alloys, high purity metals and metalloids, the platinum group metals and the rare earths. The sources of the various metals are given, followed generally by a brief description of the primary recovery process. Thereafter the operations of specific companies that deal in a particular metal are described in some detail. Certain metals such as barium, bismuth, gallium, thallium and zirconium are perforce covered very briefly as their commercial application is limited but in other cases, especially aluminium, copper lead and zinc, fairly detailed descriptions and illustrations are provided. This publication should be of considerable value to students as it presents modern procedures with regard to the refining and uses of the particular metals under review. This information may not be available from text books which in any case tend towards obsolescence. The book should also prove a valuable addition to the bookshelves of practising metallurgists providing, as it does, a schedule of most of the metallurgical companies operating in the United Kingdom. The quality of the paper and binding, the clarity of printing and illustrations and the arrangement of the subject matter are excellent and are subjects for which the editor and publishers are to be commended. R.J.A.

By Jeremy Butkovich

Dynamic soil-structure interaction (DSSI) analyses are becoming more common in bridge designs, especially in seismically active areas. Because of its proximity to two active fault zones, the Evergreen Point west approach bridge replacement will be base isolated, and will be designed using DSSI. The project team completed two independent bridge designs to satisfy peer review requirements. The designs required substantial characterization of the soil dynamic behavior using both laboratory and in-situ testing. The analyses made use of earthquake time histories spectrally matched to conditional mean spectra. This led to reduced, and more realistic seismic demands on the structure, compared to conventional uniform hazard spectrum matching. The bridge analyses suggest that the preliminary bridge design is relatively conservative. This will allow the design team to potentially reduce shaft/column diameters and reinforcement. The design team estimates that the dynamic analysis design could represent a net savings of around $60 to $90 million compared to a conventional design.

By Stephen C. Tadolini, Thomas M. Barczak, Peter (Yunqing) Zhang

A cooperative study was conducted with Emerald Coal Resources, L.P., an affiliate of Foundation Coal Corporation, and the National Institute for Occupational Safety and Health (NIOSH) to evaluate the effectiveness of (partially) pre-driven longwall recovery rooms supported with pumpable roof supports. This paper evaluates the load transfer mechanics associated with the advancement of the longwall face into the pre-driven recovery room and the widening of the room to recover the longwall shields. The results show that the yielding of the panel fender produced uncontrollable convergence that caused yielding of the shields and stiff pumpable roof supports when the face was approximately 10 ft from the recovery room. The shields continued to yield until the face advanced into the recovery room. Convergence in the pre-driven recovery room typically reached 6-8 in once the pumpable supports yielded and shed load through a declining residual load capacity prior to being cut out by the longwall shearer. Roof deformations occurred beyond the 32-ft horizon with total deformation ranging from 2 to 4 in, indicating that standing support was necessary to help control the span as the longwall face advanced into the pre-driven recovery room. Stability improved as the pumpable supports were cut out, thereby reducing the span between the shields and the outby pillars. In the end, the shields were successfully recovered under stable ground conditions. However, a disconcerting discovery was the load shedding of the outby pillars as the recovery room was mined into. It is postulated that this may be due to the progression of the rear “abutment” moving toward the recovery room as the panel fender and standing support in the recovery room yield and shed load. This behavior was not expected with a relatively narrow room that is fully supported with standing support. If this mechanism is indeed occurring, the width of the room and performance of the standing support becomes even more critical. Premature failure of the support can lead to excessive convergence on the shield line that cannot be controlled even with modern shields, resulting in roof instabilities that can lead to catastrophic results.

By Eric Eisold

The Wachovia Headquarters and Arts and Cultural Campus project in Charlotte, NC includes a 1.5 million square foot, 48-story office tower, two museums, an Afro-American cultural center and a 1,200 seat theater for the performing arts. Public access to the Cultural Campus is through two pedestrian tunnels constructed under city streets connecting to parking garages. The 5.7 m wide by 4.7 m high mined tunnels were procured through a design-build contract. The tunnels were designed as initial/final shotcrete linings with a sprayed water barrier sandwiched between layers of shotcrete. In addition, the mix design was supplemented with a cementitious admixture to develop internal water resistant properties in the shotcrete.

By Haijian Fan

Currently, deep foundation designs for the service limit state are deterministic in nature. The settlements and lateral deflections of deep foundations are calculated by means of numerical techniques whereby the foundation-soil interactions are characterized by discrete load transfer curves such as t-z or p-y curves. The noted deficiency of the deterministic approach is that the uncertainties arising from various sources, such as soil properties and model errors are not considered. To address this deficiency, a performance-based reliability design methodology is developed using Monte Carlo statistical methods. The performance based design criteria are defined in terms of the specified allowable displacement. The input to the numerical solution techniques, including the soil strength parameters, unit weight of the soil are relevant to the generation of the load transfer curves are treated as random field. The well established random field generator algorithm, local averaging subdivision, is used to generate random samples of input, where the mean values, variances, the probability distribution, and correlation structures are required statistical parameters for these random variables. The objective of the performance based reliability design is to determine the optimized foundation dimensions so that the probability of failure is less than the target probability of failure. The probability of failure by the Monte Carlo approach is simply the ratio of the number of unsatisfactory performance to the sample size. A numerical example for laterally loaded drilled shaft is given to illustrate the application of the methodology. The incorporation of the correlation length is shown to be critical for properly accounting for the site soil spatial variability.

When most people think of coal mining, they envision men in soot-covered clothes and hard hats digging at deposits in deep underground caverns. These mental images commonly include coal cars rumbling on rails as they emerge from the earth, filled to the brim with rocky ore. The world of modern, longwall coal mining is a far different place. Yes, it?s underground, the miners still wear hard hats and the environment is filled with soot. However, today?s mining operations are carefully monitored and the entire process is highly automated. Five kilometers (3 miles) underground, a sophisticated, high-powered mining machine moves steadily through a 2-m (6-ft) high tunnel at an average speed of 3.2 km/h (2 mph), carving out coal, then conveying it to a crusher and carrying it to the surface. Instead of digging out the ore, a longwall mining system slices it from the exposed tunnel face, using giant rotating shears. The shorn coal tumbles onto a conveyer below the shears and is conveyed to the stageloader, where it is crushed and dumped onto the main conveyer belt that eventually hauls it out of the mine. Integral to the longwall shear and conveyor is a moving metal roof that protects it from the thousand plus feet of ground above. The ceiling panels automatically advance above the shears, powered by hydraulic roof supports that stand on the other side of the tunnel, moving in a slow, sideways lock-step with the shears. This complex and massive machine makes longwall mining the most ef?cient and productive method for excavating coal. In fact, it produces 2.7 kt to 22.6 kt (3,000 to 25,000 st) of ore per shift, versus 544 to 907 st (600 to 1,000 st) for the conventional room-and-pillar mining. Using that method, miners develop one section of a mine at a time after carving out load-bearing columns of coal to support the roof above their heads. Longwall mining also is considered safer than the room-and-pillar method, largely because the process is mostly automated, requiring fewer workers. Still, longwall mining has its drawbacks: The equipment is expensive and the mining conditions are harsh. An entire longwall system can cost between $50 million and $100 million, while the electrical controls used to operate it can cost an additional $1 million to $2 million. These investments grind away all day, every day, in hot tunnels filled with coal dust.

By V. C. Robinson

INTRODUCTION Most presidential addresses are in the nature of a review of some specific topic and this will be no different. In thinking about the subjects which might be suitable for this address I decided that as next month will see my retirement from the gold mining industry I might review the four decades since I started in the industry in 1929. These four decades have been more than usually in',~resting and exciting. They have covered a period when the price of gold increased from the old figure of 84/- an ounce to the price of $35 an ounce today, taking in on the way at least two periods of premium sales from which the producer benefitted. The industry in these four decades has survived the most totally destructive war in history and has seen fundamental changes in the political, economic and governmental life of South Africa. There have been great technological changes and improvements, some of which I shall refer to later, and in addition there have been profound changes in the relations between employer and employee in the industry which have affected not only the economy of the industry but the traditional thinking of both management and labour. I believe that the address presented to this Institute on the occasion of its 75th Anniversary by Mr Goode covered more than adequately the history of the Institute and the part it has played in the mining industry of South Africa. It would be merely repetitive, therefore, to discuss the affairs of the Institute of Mining and Metallurgy. Having said this, however, it is also necessary to point out that the history of the Institute is, and always will be, an important record of the history of mining in South Africa. There are many facets, however, on which we ought to look back and to re-examine. One of the most rewarding, but at the same time one of the dullest, places to look for historical facts is in the annual reports of the Chamber of Mines. I suppose that some of the dullest of these have been the reports for which paragraphs have been prepared by me personally. The notes which follow do not claim to be anything like a full record of this exciting period. RISE AND FALL OF THE GOLD MINING INDUSTRY In talking about the mining industry of South Africa it is inevitable that one talks, particularly in the historical sense, about the gold mining industry - an industry of fundamental importance which has made South Africa what it is and which has been dying since the early part of this century. In Table I is shown the progress of the gold mining industry measured by its output of ounces of fine gold from the beginning of operations until the end of 1969, and if you are interested in the productivity of the men who work this industry the table, composed entirely from figures set out in the Chamber's annual reports, also shows the production of gold expressed as fine ounces per European and fine ounces per Bantu worker over a long period. If you are still minded to think of this industry as dying then the last column in the table shows how uranium has played such a vital part in the prosperity of the country.

By Jr. Schnakenberg

The National Institute for Occupational Safety and Health (NIOSH) has been working with diesel emissions control technology and the underground mining industry for a number of years. Underground isolated zone studies provided the emissions reduction performance of all of the alternative technologies currently available. A NIOSH/MSHA guide is available which provides mines with information and a process for selecting diesel particulate filters (DPF). Recent NIOSH experience suggests that more attention may be needed in managing the issues associated with diesel emissions and their control. The author argues that a holistic approach is needed which involves several key mine operations departments or disciplines by positing that workplace air can be considered as the product of a complex manufacturing process and examining how that process could be managed.

By H. J. Ramey

As fluids move through a wellbore, there is transfer of heat between fluids and the earth due to the diflerence between fluid and geothermal temperatures. This type of heat transmission is involved in drilling and in all producing operations. In certain cases, quantitative knowledge of wellbore heat transmission is very important. This paper presents an approximate solution to the wellbore heat-transmission problem involved in injection of hot or cold fluids. The solution permits estimation of the temperature of fluids, tubing and casing as a function of depth and time. The result is expressed in simple algebraic form suitable for slide-rule calculation. The solution assumes that heat transfer in the wellbore is steady-state, while heat transfer to the earth will be unsteady radial conduction. Allowance is made for heat resistances in the wellbore. The method used may be applied to derivation of other heat problems such as flow through multiple strings in a wellbore. Comparisons of computed and field results are presented to establish the usefulness of the solution. INTRODUCTION During the past few years, considerable interest has been generated in hot-fluid-injection oil-recovery methods. These methods depend upon application of heat to a reservoir by means of a heat-transfer medium heated at the surface. Clearly, heat losses between the surface and the injection interval could be extremely important to this process. Not quite so obvious is the fact that every injection and production operation is accompanied by transmission of heal between wellbore fluids and the earth. Previously, the interpretation of temperature logs',' has been the main purpose of wellbore heat studies. The only papers dealing specifically with long-time injection operations are those of Moss and White3 and Lesem, et al.' The purpose of the present study is to investigate wellbore heat transmission to provide engineering methods useful in both production and injection operations, and basic techniques useful in all wellbore heat-transmission problems. The approach is similar to that of Moss and White:' DEVELOPMENT The transient heat-transmission problem under consideration is as follows. Let us consider the injection of a fluid down the tubing in a well which is cased to the top of the injection interval. Assuming fluid is injected at known rates and surface temperatures, determine the temperature of the injected fluid as a function of depth anti time. Consideration of the heat transferred from the injected fluid to the formation leads to the following equations. For liquid, Eqs. 1, 1A and 2 are developed in the Appendix. These equations were developed under the assumption that physical and thermal properties of the earth and wellbore fluids do not vary with temperature, that heat will transfer radially in the earth and that heat transmission in the wellbore is rapid compared to heat flow in the formation and. thus, can be represented by steady-state solutions. Special cases of this development have been presented by Nowakl and Moss and White.3 Both references are recommended for excellent background material. Nowak' presents very useful information concerning the effect of a shut-in period on subsequent temperatures. Since one purpose of this paper is to present methods which may be used to derive approximate solutions for heat-transmission problems associated to those specifically considered here, a brief discussion of associated heat problems is also presented in the Appendix. Analysis of the derivation presented in the Appendix will indicate that many terms can be re-defined to modify the solution for application to other problems. Before Eqs. 1, 1A and 2 can be used, it is necessary to consider the significance of the over-all heat-transfer coefficient U and the time function f(t). Thorough discussions of the concept of the over-all heat-transfer coefficient may be found in many references on heat transmission. See McAdams5 or Jakob," for example. Briefly, the over-all coefficient U considers the net- resistance to heat flow offered by fluid inside the tubing, the tubing wall, fluids or solids in the annulus, and the casing wall. The effect of radiant heat transfer from the tubing to the casing and resistance to heat flow caused by scale or wax on the tubing or casing may also be included in the over-all coefficient. According to McAdams, on page 136 of Ref. 5>

By Kenneth N. Han

The effect of anions such as sulfate, chloride and nitrate on the solubility of rare earth element (REE)-bearing phosphates and fluoro-carbonates was examined using relevant thermodynamic data. The study found that these anions have significant influences on the overall dissolution of REEs from various sources in the aqueous media.