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By Luther W. Bahney

(San Francisco Meeting, October, 1911.) LIME is the alkali that is almost universally added to the solutions in the cyanide process of gold- and silver-extraction for maintaining the so-called, protective" alkalinity. It is produced by the burning of limestone. The value of lime for this purpose depends upon the percentage of calcium oxide contained, which is determined by three factors : 1, purity of the limestone used; 2, degree of the burning-temperature and the period of burning; and 3, length of time of storage of burned material and the condition stored, and whether it has been damp or wet during the storage. These three factors render uncertain the quality of lime bought in the open market. In the United States, lime bought from reliable manufacturers, who thoroughly burn a pure limestone and deliver at once to the consumer from the kilns, may be of a fairly-high and uniform composition ; but in Mexico and Central America, where it is purchased from many small producers, who often start with a poor grade of limestone and burn it in small crude kilns with as little fuel as possible, the quality of the product is quite variable. In consideration of the foregoing, it is apparent at once that there is a great need for a rapid technical method for the valuation of the lime to be used in a cyanide-plant. The determination of calcium by the gravimetric method, with the necessity of determining also the proportion of carbon dioxide, silica, and iron, requires too much time, and is usually out of the question for an isolated plant unequipped with a skilled chemist and, the necessary apparatus. The calculating of all the calcium so found to calcium oxide, although sometimes done, is manifestly very inaccurate.

Nov 1, 1911

By Granville S. Borden

TAXES in general are onerous and are not a pleas- ant subject for discourse. There are, however, some very cogent reasons why we should dedicate a part of our thoughts and services to the solution of our taxation problems: The happiness of every individual in the United States depends on the maintenance of a stable government. The collection of taxes is an indispensable function of a stable government, and the power to collect taxes depends in part on the question whether taxes are fair and equitable. As representatives of the mining industry it is our duty to .protect it from tax burdens that are discriminatory or- unjust, As citizens we find that taxation is incessantly endeavouring to unravel the knots in our purse-strings. Many members of the Institute may be consulted .by clients on taxation problems, especially the phases which re- late to depletion and valuation. It is the hope of the writer that the discussion of some of the current depletion and valuation problems will stimulate interest in the problems, and as a consequence of this new interest facts will be ventilated, opinions rendered and services performed, which will be a means of solving the problems to the satisfaction of all parties interested.

Jan 1, 1929

By William F. Boericke

RESEARCH in the modern refractories laboratory has two practical ends in view-to develop refractory materials for the metallurgist that will meet particular operating difficulties more effectively and to ?manufacture these refractories at a cost sufficiently low to make their use economical to the metallurgist. At the research laboratories of E. J: Lavino and Co., at Plymouth Meeting, Pa., the technical staff, under Dr. Gilbert E. Seil, is giving principal attention. to an. exhaustive investigation of the following factors in refractories:

Jan 1, 1931

By K. Adam

Grinding in steel mills adversely affects the flotation of pyrrhotite. The electrochemical nature of inter action between pyrrhotite and active metals was investigated by contacting pyrrhotite with platinum at different applied potentials. Flotation tests, scanning electron microscopy, Auger electron spectroscopy, and X-ray photoelectron spectroscopy were wed to examine the surface properties of pyrrhotite. The formation of hydroxide or oxide and sulfate species of iron through the oxygen reduction reaction at the cathodically polarized surface of pyrrhotite was shown to be the mechanism responsible for the reduced floatability of pyrrhotite.

Jan 1, 1985

By AIME

The Taconites Are Ready, the editorial appearing on P. 933 of the September issue, has provoked comment from several informed engineers to the effect that the indicated profit margin was considerably exaggerated. The cost figures in the editorial, taken from the Congressional Record, were characterized as inaccurate by some correspondents. The theme of the story was, however, substantiated in the announcement (P. 1023, October) that Republic and Armco had joined forces in a $160 million project for taconite development. Chief among the dissenters was E. W. Davis, , Director of the Mines Experiment Station at the University of Minnesota. Mr. Davis has worked up the following set of cost figures:

Jan 1, 1950

By Brehon B. Somervell

SOMEONE has called this war a war of gadgets. Someone else says it is an engineers' war. It is a war of production, transportation; a war in the sky; a war on wheels; a civilians' war. Let us not quarrel about nomenclature. Call it what you want. If four motored bombers and thirty-ton tanks are gadgets, then it is a gadget war. Engineers, scientists, shop laborers, air-raid wardens all have their highly important jobs to do. The fact remains that this war, like all others, is a soldiers' war. The basic strategy employed today is the same strategy that Philip of Macedon used on the Plains of Thessaly twenty centuries ago. His phalanx was a striking force armed with every known weapon. It was armored with breastplate and casque. It depended for success on superior man power and mobility, upon superior weapons and supply, and upon superior discipline. It executed commands faster than its enemies; it had more catapults and spears, more men in the back areas bringing up supplies. It was a new idea. It used what today we call the scissors movement to cut up its foes. It took sharp advantage of surprise. It introduced terror as a weapon-terror inspired by a vast, moving, shouting army with banners. It laid waste the cities by fire. The Greeks had a word for it but that word wasn't "blitzkrieg."

Jan 1, 1942

Charles H. Morgan, Worcester, Mass. (communication to the Secretary): In connection with Mr. Douglas's mention of the continuous charcoal kiln used at Kopparberg, some further data concerning this important invention may be of interest. Before giving these, however, I will say a word or two concerning other features of Swedish practice. In 1894 I spent two days at Soderfers with Mr. Tom Bergendal, the manager of the works, and was specially interested in the gas-producers and wood-drying kiln, illustrated in the paper contributed to our Transactions by Mr. Odelstjerna in that year.* The wood-drying kiln is, however, quite different in design and construction from Ljungberg's charcoal kiln. In the summer of 1894 it was discovered that by placing the gas-producer as close as possible to the open-hearth furnace, and working the producer hot, ordinary weather-dried wood, still containing a considerable percentage of moisture, could be used to advantage in the melting-furnace. Hence, the dryingkiln was needed for wet wood only. One of the iron-works of the Udeholm Go. was the first to adopt the Lundin saw-dust gas-producer and condenser, enabling them to make gas from saw-dust containing 45 per cent. of moisture, and convey the gas from the condenser through wooden pipes to the Siemens steel-melting furnace.† This sawdust gas gave very satisfactory results in iron-works; but the proprietors experienced much trouble by reason of the pollution of rivers by the tar-water from the condenser. On my visit, in 1894,I found that the Udeholm Co. had put in for their steel-melting furnaces the same wood-gas producers

Jan 1, 1899

By P. J. Clifford, A. B. Brown

The development of computerised mine planning has been hindered by the cost of processing the large data bases associated with mineral deposits and the inherent inconvenience of performing an interactive process on a time-shared computer. A dedicated computer is ideally suited for the purpose but reasonably priced micro/mini-computers have not had the capacity to store the volume of data or the processing capability required. Hardware development has cleared the way for the development of truly interactive mine planning software, covering the complete range of activities associated with mine planning, from geological assessment to short-term scheduling of operations, incorporating them into a single system using a common database. The integrated system, comprising software and dedicated hardware, adds previously unattainable speed, flexibility and clarity to the planning process because it has been tailored exclusively for that purpose.

Jan 1, 1983

By Frederic L. Kadey

Perlite, as a volcanic glass, has been recognized since the Third Century, B.C. (Langford, 1978). The precise details of discovery often become lost in antiquity, and the variations among the stories pertaining to the more recent discovery of perlite as a material of commerce are no exception. Credit in the United States is given to a dentist who, while experimenting with tooth enamels about 1941, discovered that perlite-the rock-intumesced when subjected to heat. At about the same time it is reported that the chief geologist of Silver and Barytes Ores Mining Co. attempted to put out a picnic bonfire on the shores of Milos Island, Greece by throwing beach sand on it. The ensuing pyrotechnic display immediately conjured up in that man's mind the possibility of a new use for the volcanic rock that constituted most of the island. Very little was done with this discovery either here or abroad until after World War II. Today the name perlite is applied to both the hydrated volcanic glass, generally of rhyolitic composition, and to the lightweight aggregate that is produced from the expansion of the glass after it has been crushed and sized. Petrologically, it is defined as a glassy rhyolite that has a pearly luster and concentric, onionskin parting. Occurrences of perlite are restricted to several Tertiary to Quaternary age rhyolitic belts that trend in a generally north-south direction around the world. Commercially suitable deposits generally occur as domes of several hundred feet in height, although glassy zones in welded ash-flow tuffs and others associated with dikes and sills also have been reported. Mining is by ripping and blasting from open pits. Because of weight considerations, perlite usually is shipped to the local market area for subsequent expanding. In the United States, New Mexico leads in production with Arizona, California, Nevada, Idaho, and Colorado following in approximately that order. The principal use for expanded perlite is as a lightweight insulating aggregate in cryogenics, in plaster, concrete, and in loose fill insulation. Expanded perlite is also used in horticultural applications, and after subsequent milling and classification, as a filter aid. The United States is the world's largest producer and consumer of perlite. Table 1 shows the world production of perlite and Table 2 shows the perlite mined, processed, expanded, and sold or used by producers in the United States. Geology Composition and Morphology Any discussion of perlite must take into consideration its dual nomenclature, for it is known by the same name as both the naturally occurring rock and, after processing and expansion, as the lightweight aggregate of commercial significance. In its naturally occurring form, perlite is a rhyolitic glass that contains from 2 to 5% combined water. While perlite also can occur as andesitic or dacitic glass, these latter types are of negligible commercial significance. Table 3 lists the chemical composition of a few typical perlites (Anderson, et al., 1956; Langford, 1979). What sets perlite of commercial significance apart from other volcanic glasses is the fact that under the proper conditions of preparation-crushing and sizing-it will, when rapidly introduced into a flame of sufficient temperature, expand or "pop." All of the elements of composition contribute to the expansibility of the rock. The role of the combined water, however, is the most significant because it is believed not only to produce a fluxing effect in the softening of the highly siliceous glass prior to expansion, but it is also responsible for the explosive force of expansion through volatilization during heating. The current theory of the origin of the water in perlite is now less con-

Jan 1, 1983

By C. R. Kyle, R. L. Perrine

A transparent model of a reservoir has been used to study some characteristics of instability in miscible displacement. The linear model dimensions are 1/4 in. x 91/2 in. x 10 ft. The model is packed with spherical glass beads. Thee groups of experiments have been performed. The objectives were to measure, respectively, the rate of growth of the transition zone, flow velocity variations in the transition zone, and the effect of a graded viscosity zone on stability. All experiments were compared, where possible, with theory. The transition zone grew almost linearly with distance traveled, regardless of flow rate, where adverse viscosity ratios were used. At very adverse viscosity ratios and large distances traveled, some reduction below linear growth was noted. This could be attributed to the effects of mixing. General similarity in flow pattern was commonly shown in different tests, although exceptions occurred at the higher viscosity ratios. Injection of tracer spots permitted direct experimental measurement of velocity variations. Statistical methods were used to compare observed velocity variations with recently published theories. Surprisingly good agreement with some theoretical predictions was obtained. In the experiments using an initially graded viscosity zone, macroscopic stability was reached before predicted by theory. Under conditions theoretically considered to be slightly unstable, any fingering tendency was too slight to become observable within a 10-ft long system. The general correlation of all experiments with published theory was good, and suggests that theoretical predictions can be extended to reservoir problems. INTRODUCTION Early laboratory studies of miscible displacement demonstrated the high recovery efficiency possible with this method. Linear laboratory models showed that, under some circumstances, all in-place hydrocarbons could be recovered using as little solvent as 5 per cent of the pore volume. These results led to a series of pilot field projects. Under realistic conditions, however, other laboratory studies showed that a small solvent bank may not recover much more oil than a conventional gas drive. The cause of this lack of efficiency is unstable viscous fingering. The size of the solvent bank required to give optimum recovery is, therefore, a question of great economic significance. The object of the experiments described in this paper was the quantitative measurement of unstable flow parameters, the verification of present theories on the miscible displacement process, and correlation of these theories with ex peri mental observation. Of the theories which have been advanced, those by Dougherty, Koval and Perrine show promise of predicting reservoir performance with reasonable accuracy.l-7 The present experiments were correlated, where possible, with the theories of Koval and Perrine. Dougherty's theory was not used because of the additional computational difficulty it presented and the belief that no further information would result. EXPERIMENTAL EQUIPMENT A transparent reservoir model, consisting of a vertical reinforced plexiglass column, was used for the experiments. The column was packed with glass beads, which served as the porous medium. To induce a known velocity disturbance in the flow, a double cosine wave restriction in the transverse cross-section was placed at the top of the column. To mark the flow field and provide a means of measuring the local fluid velocity, a dye-spot injection system was provided. The column was 10 ft high by 1/2 in. wide by 1/4 in. deep. The cosine restriction was placed 16 in. from the top of the column. The glass beads were smooth and spherical and had a mean diameter of 0.0102 cm. Liquids entered the top of the column through a manifold allowing three points of entry (left, center, and right, or any combination of these). A positive-displacement pump with variable-speed drive was used to control liquid flow rates. The pump transferred viscous oil from a reservoir to an accumulator, which displaced the test liquid into

Jan 1, 1966

By Augustus Locke

MY conclusions apply to the engineer in California ore hunting; and, because the product has been overwhelmingly gold, that means gold-ore hunting. But, I wish to think of ore hunting, not as employment for engineers, but as engineering. I wish, moreover, to think of it as productive of ore in significant quantity. The small mine, even if good, means little. Only new districts, or large extensions of old districts can engage our attention here. The conclusions are summarized as follows: (1) The bright color of California mining history comes from the suddenness and intensity of its outburst of gold. Had the mining been averaged from the start, it would soon have become dimmed among greater industries. For fifty years, California has proceeded as an agricultural, timber and oil, but not a mining region. 1

Jan 1, 1931

By AIME AIME

THE difficult problem of visitors is being met by the Hudson Coal Co. at Scranton in an ingenious fashion. The Company had long made it a point to have dealers selling its coal visit the mines, whenever possible. "The excellent reaction obtained from these dealer visits brought up the question of whether it would not be possible to open one or more mines to the public, and give the consumer an opportunity of seeing for himself how anthracite is mined and prepared. Ac-

Jan 1, 1929

By George C. Bateman

WE in Canada want to see industry get back to a normal economic basis as soon as possible but wartime controls cannot be dispensed with immediately the war is over. Perhaps never again will we be entirely free from some of the types of controls such as those set up during the war. Certainly the taking over and disposal of surplus materials contemplates the continuation of some form of control for many years to come. However, to the extent that it is possible, the Allied nations are exponents of free enterprise.

Jan 1, 1944

By E. H. Rose

From the more distant members and some not so distant, the plaint is often heard that they cannot justify the expense and time required to attend the AIME Annual Meeting. Almost invariably, the reason given takes this form: "I just don't see that I would get enough out of it." Often the would-be clincher is added: "Besides, the meat of it all comes out in print anyway." Not long ago, a group of us who have seldom missed a meeting in recent years fell to discussing this phenomenon, and found ourselves in emphatic agreement that anyone holding such a belief indicates by his first remark that he does not know how to attend a convention, and by his second, proves it. He is, by and large, the man who has never been there, and of him, there are many.

Jan 1, 1949

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970

By R. D. Carter

Nurnerical .solutions are presented to some problems of unsteady-state radial flow of gas in which Darcy's law holds. These solutions are intended to aid in explaining the observed behavior of gas wells during drawdown tests. The variation of viscosity and Z-factor with pressure is accounted for in the solutions. Results are presented for three types of problems: (I) unfractured wells producing at a constant rate, (2) fractured wells producing at a constant rate and (3) unfractured wells producing through a critical flow prover. In the critical-pow-prover solutions, a correction of the calculated well-bore pressure to account for non-Darcy flow is made. A good correlation is shown between the solutions to the problem of Type 1 and the corresponding diffusivity-equation solution. Using this correlation, the diffusivity solution may be used to obtain gas-well solutions. The solutions to the problems of Type 2 illustrate the difference in drawdown-curve behavior to be expected between fractured and unfractured gas wells. Methods for estimatting fracture radius and flow capacity are presented and verified from solutions of Type 2. The solutions to the problems of Type 3 illustrate the differences to be expected between critical-flow-prover drawdown tests and constant-rate tests. An equation is presented for correcting critical-flow-prover data to constant-rate conditions. A description of the methods used in obtaining the solulions appears in the Appendix. INTRODUCTION It is necessary for many engineering purposes, such as predicting future deliverability performance, to be able to relate bottom-hole flowing pressure, formation pressure and flow rate for conditions of stabilized flow in gas wells. This information is customarily given as a plot of on logarithmic co-ordinates. It is desirable to be able to predict stabilized performance curves for gas wells based on data obtained from drawdown tests of short duration. Tests of long duration may be wasteful of gas, and low-permeability wells do not stabilize in a short-duration test. Although it is now commonly recognized that non-Darcy flow plays a significant part in gas-well behavior, it is believed that an understanding of transient behavior of systems obeying Darcy's law is still important in the interpretation of short-term test data, and the prediction of stabilized performance curves therefrom. In this connection, an equation for correcting Darcy flow It seems likely that solutions of the type presented herein, combined with the non-Darcy flow correction of the type of Eq. 1 and the usual laminar-flow skin factor, could provide a model which would adequately explain transient gas-well behavior for times after the non-Darcy flow region (which should be confined to a small area surrounding the well) has been established. The solutions presented in this paper are for three types of problems: (1) unfractured wells producing at a constant rate, (2) fractured wells producing at a constant rate and (3) unfractured wells producing through a critical flow prover. In the problems of Types I and 2, no corrections for non-Darcy flow were made in the results presented, since it was reasoned that the constant-rate boundary condition would facilitate such a correction if it was desired later. For the problems of Type 3, however, a condition of varying flow rate required that a non-Darcy flow correction of the type of Eq. 1 be included. This was done. Based on the numerical results presented, a number of approximations and a correlation are presented which may be useful in analyzing gas-well test data. It is assumed that the system can be described as a finite cylindrical gas reservoir produced by a single cylindrical well located at the center of the reservoir. Flow is strictly radial.

By V. A. Josendal, J. W. Wilson, B. B. Sandiford

Two radioactive tracers have been tested as a means of determining core saturation in multiphase flow studies. Cesium chloride was tried as a water-phase tracer, but complications in its use in low permeability cores resulted from sorption of cesium by the core or water-wet pads. IodoI3'ben-zene proved very satisfactory as an oil-phase tracer. The synthesis of iodobenzene from the sodium iodide as received from Oak Ridge is simple and direct. The tracer is insoluble in water and there was no evidence of sorption by any of the core materials used. use of the method to determine saturation profiles during capillary and dynamic desaturations and relative permeability measurements on oil-water and oil-gas systems is described. Comparisons of the dynamic and capillary methods of relative permeability determination were made using the tracer to check core saturation and saturation distribution. Other experiments are also described in which mobility of the oil phase at various saturations was measured by displacing labeled oil by flowing inactive oil. Similar experiments were made using water labeled with cesium 134. INTRODUCTION To be fundamentally sound. any laboratory method of determining relative permeability must meet, among others, the following requirements: (1) the core saturation between the pressure taps must be uniform, and (2) there must be uniform pressure difference between the phases in the region between the pressure taps. In practice it may eventually be shown that appreciable departure from either or both of these conditions may be permitted without introducing sensible error. but the magnitude of such error remains to be established. There is need then for methods of saturation determina- tion which will determine the saturation profile in a core as well as the overall average saturation given by the gravimetric or material balance methods usually employed. Methods which have received consideration include resistivity, X-ray absorption, gamma ray absorption, neutron diffraction, and radioactive tracers. The resistivity method has use in the determination of profile, but needs checking by independent means.' The X-ray method has been used successfully, but requires elaborate equipment and calibration.23 4 At present gamma ray absorption is practical only for very large cores. The neutron methodo does not appear adaptable to measurement of saturation variations in short cores since it is a scattering method. Russell, Morgan and Muskat' employed radiovanadium in a study of the mobility of interstitial water. Coomber and Tiratsook used radioiodine as an oil-phase tracer and measured profiles in unconsolidated sand packs. ADVANTAGES OF RADIOACTIVITY METHOD A thorough discussion of the theory of radioactive tracers and the technique of using them to study the movement of fluids in sands is given by Coomber and Tiratsoos and need not be detailed here. The method requires less equipment than the X-ray method; the counting problem is similar, but the generation and regulation of the radiation, which is a major problem in the X-ray method, is not required in the radioactivity method. In the X-ray method it is customary to add up to 20 per cent of absorber, usually an iodine compound, to the phase to be labeled. while in the radioactivity method a mere trace is sufficient. A possible disadvantage of the radioactivity method is that a disproportionate amount of the activity comes from the portion of the core nearest the counter, whereas the X-ray gives a true average saturation in the region traversed by the beam. 011 the other hand, this characteristic of the radioactivity method renders it peculiarly adaptable to study of certain types of radial variations in saturation. As with the X-ray method, a tracer may be added to either the oil or water-phase. An oil-phase tracer is more generally useful. however. since it permits work on oil and gas in the

Jan 1, 1952

By T. D. Murphy, G. V. Henderson

The element silicon, with its usual partner, oxygen, plays the same role relative to inorganic materials as carbon and hydrogen play with respect to living organisms. The crystallographic structure of silicon dioxide (SiO2) consists of one atom of silicon well-nigh inseparably bonded to four contiguous atoms of oxygen, a gas of but slightly more than half its atomic weight, forming a three-dimensional network of SiO4 tetrahedra (Dietz, 1968). This wispy arrangement is the fabric of the mineral quartz which is one of the harder, more abrasive, and chemically stable raw materials to be found in Mother Nature's cupboard. Most of us are vaguely familiar with the observation that nearly 60% of the lithosphere to an approximate depth of 10 miles is composed of these two elements, which proportion actually rises to about 75% if the atmosphere, hydrosphere, and biosphere are included (Parker, 1967). Elemental silicon is a brittle steel-gray metalloid with a density of 2.42 and does not occur in nature. In its limited commercial form, which is still brittle and metallic in appearance, its density drops to 2.33. It combines with oxygen to form the gaseous oxide SiO, or the solid dioxide Si02 (analogous to its congener carbon in CO and CO2); a tetrachloride SiCI4 (analogous to CC14); or, combining with oxygen and one or more metal ions, forms the largest rock-making family of all, the silicates. Further, next to the feldspars, quartz is the most abundant known mineral and, in some form or another, accounts for roughly 12% of surficial terrestrial rock. It is this so-called "free silica" to which your attention is chiefly directed in this chapter. In any such consideration of silica, its several crystalline phases with their attendant differing physical properties appear worthy of delineation. Alpha quartz is the only one of this interesting polymorphic family that is thermodynamically stable at normal pressures and temperatures up to about 573°C. The low phases of tridymite and cristobalite can exist in the so-called metastable state below 117° to 200ºC but seldom occur in nature in these two different crystal forms (Sosman, 1965). Opaline silica, now considered by most researchers to be a variety of cristobalite, occurs in abundance and is the only exception. The three remaining polymorphs, keatite, coesite, and stishovite, also are metastable under ambient conditions. Keatite, however, is not known to occur naturally and has only been synthesized in the laboratory. The other two have been identified in submicron sizes and in microscopic amounts, occurring naturally as a result of high order shock-wave pressures generating quite elevated temperatures --such as might accompany the impact of a large meteorite on a hard sandstone terrain (Chao et al., 1962). An intriguing characteristic of these silica minerals, and one which has very practical applications, is their extremely variable densities. The classic 2.65 specific gravity of alpha quartz drops to 2.20 in tridymite, cristobalite, and lechatelierite (natural silica glass), as well as in many man-made glasses of commerce which are merely noncrystalline or amorphous solids in the form of super-cooled liquids which can no longer change their shapes (Pauling, 1950). It rises again to 2.50 and 2.93 for keatite and coesite, respectively, and finally becomes a reported 4.35 for stishovite-nearly a 50% range in density for the known physical combinations that silica naturally assumes (Frondel, 1962; Konnert et al., 1973; Pecora, 1960). Pursuing its esthetic aspects, briefly, silica is well-represented among gem stones which, to qualify as such, must have the attributes of beauty, durability, and rarity (Jahns, 1983). As quartzose gems usually have but one or, at

Jan 1, 1983

By M. R. Tek, F. F. Craig, J. O. Wilkes, C. S. Goddin

The waterflood performance of a water-wet, stratified system with crossflow is computed by a finite difference procedure. The effects of five dimensionless parameters on tile oil displacement efficiency, water saturation con-tour.7 and crossflow rates are evaluated in the absence of gravity forces. Crossflow due to viscous and capillary forces is shown to exert a significant effect on oil recovery in a field-scale model of a two-layered. water-wet sandstone reservoir. The crossflow is at a maximum in the vicinity of the front advancing in the more permeable layer. Under favorable mobility ratio conditions, the comparted oil recovery with crossflow always is interrnerliate between that predicted for a uniform reservoir and that for a layered reservoir with no crossflow. INTRODUCTION The important erects of reservoir heterogeneity on waterflood performance are commanding increased attention in the technical literature. Much of this attention is centered on two categories of layered reservoirs: those in which layers are non-communicating and those in which crossflow of fluids occurs between the layers. In the first category, the reservoir is assumed to consist of discrete layers, each uniform within itself and differing from the others only in such properties as thickness, porosity and absolute permeability. The performance within each layer is calculated by one-dimensional flow theory, and the performance of the total reservoir is obtained by summing individual layer performances. Capillary and gravity effects usually are not considered. Representative publications dealing with thi5 type of reservoir are those of Stiles,' Dykstra and Parsons,' Hiatt,3 Warren and Cosgrove' and Higgins and Leighton." Prediction of performance for reservoirs in the second category is considerably more difficult since viscous, capillary and gravitational forces all play important roles in causing crossflow between layers. A number of authors have investigated the simpler problem of two-dimensional displacement flow in a stratified system with a mobility ratio of unity and negligible capillary and gravity effects.'; Others have considered two-dimensional, non-steady-state flow of a single, slightly compressible fluid in a stratified reservoir. A limited number of laboratory oil displacement tests in layered models with crossflow have been reported. Miscible floods (with resultant zero capillary forces) in layered five-spot models were conducted by Dyes and Braun," who studied the effect of mobility ratio with zero gravity forces, and by Craig et al. 12 who studied the effect of gravity forces at constant mobility ratio. Waterfloods in layered five-spot models (with cross-tlow due to capillary, viscous and gravity forces) were conducted by Gaucher and Lindley,"' who showed the effect of gravity forces in causing underrunning of the injected water and by Carpenter, Bail and Bobek, 14 who demonstrated the reliability of Rapoport's" dimension-less parameters for scaling layered systems. Waterfloods in rectangular layered models were conducted by Richardson and Perkins."' who investigated the effect of velocity at constant mobility ratio and with zero gravity forces, and by Hutchinson," who studied the effects of varying mobility, layer permeability and layer thickness ratios. The differential equations which rigorously describe waterflooding in a heterogenous porous medium are non-linear and do not facilitate analytical solution. By using finite difference approximations it is possible to obtain a solution to any desired degree of accuracy. Such a solution, using an alternating direction implicit procedure (ADJP), is described by Douglas, Peaceman and Rachford.18 In the present study, a computer program using ADJP explores systematically the effects of important parameters on waterflood performance of a two-dimensional, two-layered, field-scale model of a water-wet sandstone system. Particular attention is given to evaluation of the water saturation contours and crossflow rates at the interface between layers to gain improved understanding of the crossflow mechanism. PROCEDURE BASIC: FLOW EQUATIONS The basic flow equations for two-dimensional, two-phase, immiscible, incon~pressible flow in a porous medium are:

Jan 1, 1967

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.