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By D. S. Fuerstenau, S. Chander

The results of a preliminary investigation undertaken to explore the possibility of treating potential in sulfide mineral flotation systems as an external variable are reported in this note. Two different methods were used to assess floatability. One involved measurement of contact angles at a mineral electrode in reagent solutions, and the other involved direct measurement of flotation recoveries in a Hallimond tube flotation cell that had been modified such that mineral particles were in electrical contact with a gold electrode. Fairly good correlation between the contact angles and flotation recoveries has been obtained.

Jan 1, 1976

By M. B. Yung

The Fu Chuan district lies near the eastern boundary of Kwang Si province in Southern China and is connected with the coast by the West river and its branches.

Jan 1, 1915

By Fredrick C. Kruger

Risk capital for mining ventures becomes harder to get each year as the costs for exploration, construction and money continue to skyrocket in today's inflationary economy. Because of this and because mining prospects must compete for the same dollar as many other needs of a diversified company, then the success or failure of any new proposal depends on how well its return on investment compares with all other capital requests. Mr. Kruger presents case histories showing what it costs to explore for new mines, how many of these prospects reward their promoters with success and how well some of the more famous mines have paid off.

Jan 9, 1969

Continuing a tradition of excellence established in 1937 when a group of editors under the chairmanship of Samuel H. Dolbear produced the first edition, the fourth edition of Industrial Minerals and Rocks just published by SME-AIME with the support of the Seeley W. Mudd Memorial Fund offers a treasure of information for geologists, mining engineers, marketing people, executives, chemists, chemical engineers, educators, engineering students, government officials - and, indeed, anyone whose work is directly or indirectly related to industrial minerals. This fourth edition is the end result of several years of effort by 86 authors and 11 editors, under the guidance of Editor-in-Chief Stanley J. Lefond.

Jan 12, 1975

By Benjamin C. Craft

Operations on the Louisiana Gulf Coast during 1936 resulted in the discovery of five new fields and the proving of flank production or new sands on 12 of the older fields. This district gained the rank as the outstanding deep-drilling region of the world. At the close of the year. 10 wells had been drilled beyond 10.000 ft. One of the most important

Jan 1, 1937

By Ralph H. Sweetser

To control the slag in an iron blast furnace is to control the quality of the pig iron produced (and to a certain extent the tonnage), and to control the whole operation of the furnace itself, including a large part of the cost of production. The character of the slag is the determining factor in the character of the pig iron as to the controllable limits of sulfur, silicon, and, to a certain extent, the manganese; it has an influence on the proportions of combined and graphitic carbons.

Jan 1, 1935

I AM sure you know that it is necessary to draw the gold into wire in order to make gold cloth, gold embroidery, or gold filigree work. Just as it is beaten to form leaf for ornamenting pictures, so also can gold be drawn easily. The same is done with silver and tin, and I believe it could also be done with iron, copper, and brass. Although brass is not so

Jan 1, 1942

By M. A. Mahtab

When characterizing orientations of rock joints in an engineering site with respect to mean values of the existing clusters or joint sets, a need may arise for a similarity test that allows grouping of observations from several adjacent sampling stations. Subjective judgment, though based on experience, may not produce realistic groupings in the data. A similarity test is developed in this paper for objective grouping of samples of joint orientations in engineering sites. The test is applied to the data from a large, geologically complex site of a potential open pit mine.

Jan 1, 1984

By Ben B. Sweet

The ongoing controversy over mining and agricultural use of ground water in Arizona underscores the importance of this commodity to both industries. Although the principles presented in this article are fundamental, a method of systematic data collection and interpretation is provided for evaluating a water well by a set of uniform standards common to all areas where ground water is a primary source of supply.

Jan 8, 1978

Ocean engineers and technologists will assemble in Houston, Texas, during May 3-6, 1976, for the Eighth Offshore Technology Conference (OTC) . More than 50,000 members of industry, government, and academia from 94 nations will participate in what is generally acknowledged as the offshore industry's show-of-shows. A well-diversified 280-paper technical program has been divided into 42 general sessions that range from seafloor surveying and offshore mining to navigation systems and environmental issues. In addition, the largest technical- educational exhibition in the conference's eight-year history will augment the OTC '76 program.

Jan 4, 1976

By Wayne C. Hazen, James K. Kindig

As the complexity of hydrometallurgical systems increases, it offers new opportunity for applications of solvent extraction. However, the high capital cost of mixer-settlers for large flow rates is a drawback to wide application in base metal recovery. This paper presents information on the use of cyclone separators in place of settlers with attendant significant reduction in capital cost. Various flowsheet possibilities for this development are discussed.

Jan 1, 1972

By Louis P. Gignac

INTRODUCTION The selection of trackless equipment for underground mining can be a complex engineering problem due to the wide range of equipment sizes and operating modes. Computer simulation is particularly useful in estimating the performance of different systems for specific rock- handling problems. A hybrid simulator, incorporating some of the features of deterministic and stochastic simulation, was developed in order to handle not only queuing delays at loading and dumping points, but a1 so traffic interferences. Any number of vehicles can operate in any one of four basic modes (LHD, LAF, FEL, HFC) in parallel or in series. If the units use common roadways, loading and dumping points, certain operating delays will occur and be registered by the simulator and thus give a better evaluation of the marginal productivity of each additional unit. Based on a typical layout of drawpoints and ore passes for the sub-level stoping method, productivity and operating costs of different rock-handling systems will be examined. 1 . COMPUTER SIMULATION Numerous applications of computer simulations are reported in the 1iterature for various mining problems. Depending on the complexity of the system to be studied, simulation models were conceived with different degrees of sophistication. Three different types of simulators are generally recognized: stochastic, deterministic, and hybrid. Stochastic or Monte Carl o simulation randomly generates items, transactions, or events from some population defined by a frequency distribution and produces some expected future situations. Because this type of simulation is governed by the input of probability distributions, it requires a detailed knowledge of the system to be simulated; it implies expensive and time-consuming studies and reports to gene- rate this input information. A major short- coming of stochastic techniques is in new equipment evaluation, where the lack of data is unavoidable, and in new system design where the conditions are outside the range of the known historical behavior of the equipment. However, probabilistic simulation is almost essential for the study of cyclic queues and traffic problems. Deterministic simulation studies a system by generating performances on the basis of the mechanical capabilities of the vehicles and the physical limitations of the mining scheme. It is based on the engineering principle that the engine converts its energy into a rimpull at the wheels, which is in turn opposed by the rolling resistance and the grade of the ground; the machine is accelerated or decelerated until the tractive and resistive forces are in equilibrium, at which point it moves at constant speed. The information required by this technique, such as rimpull charts and equipment weight, is readily available from equipment suppliers. However, equipment performance at the mining site is also dictated by human and environmental conditions and changes with time and usage. For this reason, deterministic simulation generally overestimates the system capabilities; these must then be adjusted by efficiency factors based on observation and experience. Recently, hybrid simulation models, using both stochastic and deterministic techniques, have been built with some of the events generated stochasticly and others being deterministic. This compromising approach originated at the Pennsylvania State University. O'Nei1 (1966) designed a simulator for truck-and- shovel operations that allows for transportation from multiple faces to mu1tiple destinations. Each truck performs according to its mechanical capabilities while its loading and dumping time and its load fluctuate according to specific probability distributions. A major advance in the simulation of mining systems is due to Sanford's model (1969) of underground coal mining operations. The originality of the model is in the use of an Executive System Control which sets up the initial system, de- fines the operation conditions , and instructs continuously four sub-assemblies representing shuttle cars, trains, continuous miners , and conveyors, which in turn generate a feed-back of their movement to the Executive Control System for further instructions. The model has enough flexibility to simulate simultaneous and sequential jobs that characterize any dynamic system. Sanford's early work evolved slowly to what is known today as the Under- ground Materials Handling Simulator for coal mining (Manula, 1974).

Jan 1, 1981

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By Paul B. Crawford, Melvin B. Burton

A procedure is given which describes how the gelatin model may be-used to study the effect of mobility ratio on areas swept before and after breakthrough in fluid injection programs. Differences in mobility ratio are achieved through the proper selection of electrolytes for the invading and displaced fluids. The progress of the front is followed visually and photographed or traced onto plates (it desirrd positions before and after breakthrough. Example applications to standard flooding pattrrrls, vertically and horizontally fractured reservoirs and the in-situ combustion recovery process ore presentrtl. INTRODUCTION In water flooding, gas cycling and other fluid injection programs, the sweep efficiencies and swept areas after breakthrough are known to depend on the mobility ratio. Previous investigators have described the application of the X-ray technique, stepwise use of the poten-tiometric model and numerical procedures for studying these problems.1,3,4,6 Others have described the application of the electrolytic and gelatin models for studying sweep efficiencies at a mobility ratio near one.2,5,7,8,9 It is a purpose of this paper to describe a procedure for using the gelatin model to study swept areas at mobility ratios other than one. PROCEDURE The technique developed for gelatin model studies is composed of four phases: the construction of the model, the selection and preparation of electrolytes, the running procedure, and the recording of the swept areas. Each phase is discussed independently in order that the over-all procedure will not be confused. Construction of the Model Since some of the advantages of the gelatin model are its economy, and speed, it is desirable to have as small a model as is possihle without creating error through the inability to follow visually the progress of the colored front. For this work, it was found that a distance of 4 to 6 cm between salt bridges is convenient to use. Since the size is relatively small, it follows that the gelatin layer must be thin. For this study, 1/8 in. was used as the gelatin thickness in each case. The model was constructed on a flat 1/2-in. plastic (Lucite) base with boundaries constructed from 1/8-in. plastic strips. The well pattern to be studied was outlined with the 1/8-in. plastic strips on the base with narrow apertures (- - 2 mm) in the boundary to represent the wells. Behind each well opening, a rectangular area of some 8 to 12 sq cm was outlined by additional plastic strips. The plastic strips were fastened to the base by any suitable non-conducting cement so that the boundary system was liquid tight. The electrodes were constructed from sheet copper in a fashion that would allow easy removal. In this work, it was found that by simply forming a large U-shaped clip from a strip of the copper that would slip over the boundary was satisfactory and easily removed. The electrodes should be as wide as one of the sides of the rectangular area behind the well opening. If a fractured pattern is studied, fractures inside the well pattern may be represented by strips of copper of the desired shape mounted in some easily removable fashion. The reason that apertures (or salt bridges) were used for wells instead of metallic electrodes is that the plating of the electroactive ion at the cathode and the introduction of an electroactive ion at the anode has a detrimental effect on the swept area outline if these operations \rere permitted to be carried on within the well pattern itself. The anode may be used within the well pattern

Jan 1, 1957

By J. D. Testerman

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

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By John G. Hall

The pumping operations at the Chief mine have been unique in the respect that for many years the entire flow of water into the mine has been disposed of by pumping into natural underground "caverns" or "sinks." Volumes up to 4000 gpm have been pumped into these caverns with no apparent tendency for the caverns to fill with water, and it has never been proven that any of the water returns to the mine workings. Major pumping operations have been carried on during two periods, the first from 1918 to 1927, and the second from 1942 to the present time. Early Pumping Operations CHIEF MINE The Chief Consolidated Mining Co. was organized in 1909, and for the following nine years ore was developed and mined from the 600 level down to the 1800 level, all above the permanent water table, the 1820 level. The ore occurs as extremely-irregular pipes of replacement ore in limestone, and to date a total of approximately 2 1/2 million tons of ore has been produced. The ore was highly oxidized down to the permanent water level, and some highly-oxidized ore runs occur beneath the permanent water table. In 1916, with extensive mining being done on the 1800 level, 20 ft above the water table, there were indications that a zone of secondary enrichment might exist below the water, and in order to follow the ore runs to greater depth, it was realized that arrangements would have to be Made to pump water to the surface. The original pumping installation was designed to pump 350 gpm in five stages against a 1900-ft head to the surface. By January 1919, the water had been lowered to the 1900 level and an excellent grade of silver-lead ore was being produced from the zone of secondary enrichment. At this point. the flow of water equalled the capacity of the pumps, and pumps of an additional 1000 gpln were installed to supplement the original system. By January 1920, the water had been lowered approximately 100 ft, and the total flow of water was 1000 gpm. The water was being pumped from many different places in the mine where ore was being followed downward, with 27 different pumps operating below the 1800 level, mainly Cameron air-driven sinker pumps. These first sinking pumps were cumbersome and inefficient, and each of the larger pumps weighed approximately three tons and required tremeridous volumes of compressed air. During this period, an exploration drift being extended north and west from the Chief shaft on the 1600 level encountered a large natural cavern some 2000 ft from the shaft. This cavern in places measured 60 ft in diameter. Sometime later the disposing of water into this cavern was suggested, and as an experiment to determine the results of such an operation, an attempt was Made to fill the cavern by pumping in a small volume of water, but the water disappeared as fast as it was discharged into the cavern. It was decided then to try the cavern as a drainage outlet for the entire volume of water being pumped to the surface, and the water apparently did not return to the mine workings. Subsequently water up to 3000 gpm was pumped into this cavern. An attempt was made to determine whether any water was being returned from the cavern to the lower workings, and 100 lb of sodium fluorescein salt was added to the water discharged into the cavern, but no trace of it was found in the drainage water in the mine. Results of another such test will be described later.

Jan 1, 1950

By Edward B. Walker, Michel Grosmangin

The geological and economic conditions peculiar to the Greater Oficina area are presented to demonstrate the necessity of a low-cost, well-site method of distinguishing gas-bearing formations. The method of gas detection with the neutron log is briefly discussed and its limitations are explained. A new method is described which consists in running a second neutron log with a larger source-to-detector spacing. Field data indicate that under favorable conditions the larger spacing response is proportionately more influenced by the virgin gas zone than is the shorter spacing response. One important condition is that the gas sands be invaded, with a diameter of invasion equal to about two to three times the hole diameter. The calibration of the longer spacing log is made so that the two logs read the same deflection in shale and in a known water or oil sand. Under such conditions, gas is indicated by a positive separation, i.e., the curve for the longer device is displaced to the right of the curve for the shorter device. Because of the non-linearity of the long spacing response, low porosity formations also show positive separations. In sands with large porosity variations, the gas sands can no longer he located visually. They can be detected on a plot of shorter spacing vs longer spac-ing deflections. INTRODUCTION In the Greater Oficina area of Eastern Venezuela, the rapid and accurate detection of gas from well logs is of primary importance because of a combination of economic, geologic, and operational conditions. Briefly, these conditions are: economic—there is no market for gas at the present time; geologic—a single well may contain as many as 30 or more oil or gas sands for which intervals -to be tested must be selected; opera-tional—first, once opened to the casing through perforations, gas sands are extremely difficult and expensive to squeeze off, and second, gas detection must be rapid because the geologist must decide immediately, at the well, which sand to perforate. During the early period of exploitation in Greater Ofi-cina, when clay base muds were used, sidewall samples, together with electric logs, gave fairly good distinction between oil and gas sands. When exploitation became concentrated on deep fields of poorer sidewall sample recovery, and after the advent of oil emulsion muds, now the standard drilling fluid in Greater Oficina, the regular neutron log became the most reliable indicator of gas. In 1953, R. Norelius devised the dual-spacing neutron technique for gas detection. The dual-spacing neutron log has proved to be highly successful in detecting gas and has been adopted as a regular survey by all of the oil companies of the area. Several hundred dual-spacing neutron logs have been run in Eastern Venezuela and several tests per well are available for positive evaluation of the logs. The findings outlined below are based upon this extensive field experience. GEOLOGICAL CONDITIONS OF THE GREATER OFICINA AREA The Greater Oficina area lies on the south flank of the Eastern Venezuela Basin (Fig. 1). Nearly all accumulations of oil and gas in the area are trapped, in whole or in part, against normal faults. All known oil and gas reservoirs in Greater Oficina occur in the Ofi-cina formation (Miocene-Oligocene) or in the "U" sands. The U sands are the lithologic equivalent of the Merecure group (Otigocene-Eocene), which contains oil in many fields north of Greater Oficina. Most of the petroleum produced in Eastern Venezuela is from the Oficina formation.

Jan 1, 1958

By J. M. Markowitz

The movement of hydrogen in two-phase Zircaloy-2 under the influence of a thermal gradient was studied in specimens of cylindrical geometry. A gross displacement of hydrogen toward the cooler regions of the specimen was observed with consequent copious precipitation of 6-ztrconium (ZrH) there. The kinetics of the diffusion are analyzed and discussed. X HE temperature-gradient redistribution of hydrogen in a-Zircaloy-2 has been treated both theoretically and experimentally Hydrogen moves toward the cold side of the temperature gradient until a steady state has been established; tendency for further hydrogen movement because of temperature differences is nullified by the tendency to move in the reverse direction because of the concentration gradient. The steady state condition is described by the equation in which iV is the concentration of hydrogen at a point in the specimen corresponding to absolute temperature T, R is the gas constant,k is a constant of integration, and Q is a parameter called the heat of transport, characteristic Of the particular system. The value of Q has been determined for hydrogen in Zircaloy-2 by several investigators, using Eq. [11. There is considerable variation in the results, the cause of which has not been resolved; reported values lie in the range 3 to 6 kcal per mole. The physical situation for two-phase thermal migration is much more complex. The -phase boundary for the solubility of hydrogen in Zircaloy-2 ranges from a concentration of 25 ppm at 200°C to a maximum of about 600 ppm at 550°C.4a Thus, if the concentration of hydrogen in Zircaloy-2 is sufficiently great (>600 ppm), the specimen will be entirely two-phase, consisting of a matrix of a-Zircaloy-2 surrounding particles of zirconium hydride. At time zero, with a temperature gradient imposed, the relative amounts of hydride and a-phase in each infinite-simally thin isothermal section of the specimen can be determined from the phase diagram by the lever rule. Moreover, the concentration of hydrogen in the matrix phase varies from point to point, following the a solubility line. Over most of this temperature range (<450°C) 6 phase, Fig. 3, has a constant concentration.5 The diffusion rate toward the cold side should be governed by 1) the slope of the a solubility line and 2) the temperature gradient, The extra complication of two-phase thermal diffusion lies in the fact that migration of hydrogen would leave the a-phase concentration gradient unaffected, since it is fixed at any temperature only by the solubility; gross concentration changes would reflect only the relative amounts of matrix and hydride, which could vary continuously at every point. Migration of hydrogen out of a region would lead to dissolution of hydride, and

Jan 1, 1962

By W. R. Foster, J. M. McMillen, A. S. Odeh

The complete equations of average linear momentum balance for a single-phase fluid in an incompreisible, homogeneous, porous medium are derived. The derivation begins with Euler&apos;s equation of motion for a continuum and uses an integral transform recently developed by Slattery. 7 For steady flow of a compressible, Newtonian fluid, the usual equations of motion result. For transient flow, the space-time description of the pressure is determined in the lowest approximation by the telegrapher&apos;s equation. From the analysis a new phenomenological coefficient results which connects the viscous traction to the deriv ative of the linear momentum density. The magnitude of this coefficient determines the velocity of sound through the pore structure in this approximation to the pressure field. INTRODUCTION The modification of Darcy&apos;s law of momentum balance for steady, single-phase flow through porous media has been discussed for many years. The first modification was suggested by Forcheimerl who added terms of higher order in the velocity. These can be expected to appear because the underlying microscopic equations of momentum balance are themselves nonlinear in the point velocity field. The Reynolds tensor pvv, which represents the convective flux of momentum density, appears in the momentum balance equation. Only in rectilinear flow (parallel stream lines) does the divergence of this tensor vanish. Since the steady flow stream lines in most porous media are not parallel, nonlinear dependence of the pressure gradient on the velocity should naturally appear. This nonlinearity has nothing to do with turbulence in the ordinary sense of random fluctuations in the pressure and velocity fields. It arises simply because the stream lines converge and diverge, even for steady flows. Klinkenberg2 demonstrated that the permeability coefficient in Darcy&apos;s law depends on the absolute pressure or, alternatively, on the density field. However, because he neglected inertial terms of the Forcheimer type, his correction coefficient could not be represented by a constant but tended toward a constant as the velocity decreased. Forcheimer&apos;s and Klinkenberg&apos;s modifications can be combined in a rigorous way to account for both inertia and slip during steady flow. This will be shown in a future paper. The transient change of pressure in porous media has been described by the diffusion equation.3 This form results from eliminating the velocity and density fields from a combination of the equations of motion in the form of Darcy&apos;s law, the continuity equation and an equation of state. Fatt4 suggested that the cause of deviations from the prediction of the diffusion equation for pressure transients lies not in the choice of Darcy&apos;s law as the equation of motion but on the existence of dead-end pores which might invalidate the averaged equation of continuity. On the other hand, Oroveanu and Pascal5 noted chat the time derivative of the momentum density must be included in the equations of motion since this measures the local rate of change of momentum density. Their differential equation for pressure is the telegrapher&apos;s equation (neglecting gravity). However, their form of this equation predicts that the speed of pressure propagation through the pore structure is the same as that through the bulk fluid. M. K. Hubbert6 attempted a derivation of Darcy&apos;s law by volume averaging the Navier-Stokes equations. Since these equations represent momentum balance at a point within an open set of points containing the fluid itself, Hubbert&apos;s volume averaging cannot lead to tenns involving transfer of momentum between the fluid and the walls of the pores. Once these viscous tractions are lost by choosing a control volume containing only fluid, they cannot