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Jan 1, 1902

By F. E. Calkins

THE following presentation of the more important accumulated facts and probabilities involved in copper ore deposition is based on my experience in examination work and study of the extensive litera-ture of the subject; to make personal mention of all sources of information would require the naming of a small army of able geologists and other investigators who have contributed to, building up the science. I have tried to present the salient features of the subject in logical order and condensed form, and to point out the relative importance of processes involved. Doubt-less many geologists could suggest some changes and many additions. ORIGINAL SOURCE The original source of all copper was in the earth's interior; it has been brought to the outer part of the earth, within reach of man, in three ways: (1) By intrusions and flows of basic igneous rocks containing copper in minute quantities, presumably as silicate or sulfide. No orebodies have been formed by this method. (2) As segregations within intrusive igneous rocks, the copper minerals having solidified at the same time as the rock itself. The few deposits known to have been formed in this manner have been of little or no importance. The oft quoted Sudbury nickel-copper deposits are now known to belong to the class following. (3) By gaseous or liquid aqueous emanations from ,large deep-seated masses of intrusive molten rock. These emanations, or mineral solutions, ascended through zones of connected openings in the earth's crust and dropped their load at points far above their source. Deposits formed in this manner were the primary source of nearly all, if not all, of the world's copper production.

Jan 10, 1923

By Thomas H. Leggett

A number of papers on the use of electricity in mining operations have been presented at the Institute meetings recently, but only a very few of them have given particulars and details of the

Jan 1, 1895

By James A. Soles

Concrete is a complex, multicomponent mass whose stability is dependent on three principal variables: quality of the mix, its composition, and environment of the site. The aggregate is only one component, but its constituent minerals may react in unfavorable regimes and, given sufficient time, destroy the concrete. Therefore, besides ensuring that a concrete will meet the strength requirements of a structure, the concrete engineer must be confident that the mortar and aggregates will resist destructive processes. This paper reviews the principal causes and effects of aggregate instability, notes reactions of certain phases, and suggests precautionary measures that can be taken to extend the useful life of concrete structures.

Jan 1, 1984

T. W. ROBINSON, Pueblo, Colo.: Mr. Potter's review is a striking testimony to the important part played by science in this branch of practice. But, the question arises, In which department has science effected most ? The available raw material, the size of furnaces, the general design and equipment of the plant, and the daily management, are particulars, each of which contributes to the general result, while the effect of each merges into that of the others. The following notes concerning the operations of the furnace-plant of the Colorado Fuel and Iron Company (formerly the Colorado Coal and Iron Company), at Pueblo, may throw some light upon the question of their relative importance. This company operates three stacks, and when the plant first came under my observation, about nine months ago, the furnaces were constructed, equipped,and run as stated below: Raw Materials.—The main sources of ore-supply were, as they still are, the Orient and Calumet mines of the company. The Brecce and Morning Glory ores, mentioned below, were formerly brought from Leadville, but are practically now no longer used. The Orient ore is a porous brown hematite, easily reducible in the furnace. The Calumet is a magnetite, very refractory in character, requiring preliminary roasting. Both are fairly uniform in composition. The Breece and Morning Glory are red hematites, resembling in appearance the soft ores of the Vermilion range, Lake Superior. The coke here used is made of coal from the company's mines in southern Colorado, and is distinct from that produced by the company in the western part of the State. The structure is similar to that of Alabama coke. The limestone employed is a calcite. The analyses are given in Table I. I would note, parenthetically, that I know of no section of the country presenting harder conditions for furnace-practice than these materials impose. Results cannot be measured by the more

Jan 1, 1894

By Walter Harvey Weed

THE enrichment of mineral-veins as a result of the migration of material from an upper oxidized or disintegrated part of a vein to a lower level, where it is redeposited, is now, I believe, quite generally accepted as one explanation of the occurrence of bonanzas in gold- and silver-veins, as well as that of bodies of high-grade ores in cupriferous deposits.* Vogt has called attention to the fact that there are numerous examples of such rich shoots which are " of exclusively primary character, and dependent upon the laws which governed the original ore-deposition." To this I would add that there are also other examples which are neither of primary origin nor clue to descending waters, but result from a reopening of the veins and their penetration by ascending heated waters whose metallic contents are deposited by reaction with the primary pyrite (and possibly other minerals), forming "secondary" enrichments. My studies of the copper-veins of Butte, Montana, show: That the veins there are of several ages and systems; that the older primary quartz-pyrite veins were reopened by later movements, correlated with a period of volcanic activity; and that they were penetrated by hot alkaline waters carrying copper and arsenic in solution, which were deposited presumably by reaction with the pyrite of the original vein. The enormous development of the Butte deposits, attendant upon the extraction of nearly 10,000 tons of ore a day, has revealed many facts concerning the nature and distribution of the ores. Enargite, the copper sulpharsenate, formerly a relatively rare mineral, is now found to be the chief ore of some veins,

Jan 1, 1913

By E. T. Dumble

In continuation of the geological work begun in Sonora, Mexico, a partial account of which has already been given in the Transactions of the Institute,* a similar reconnaissance was made of Cochise county, Arizona, and a part of the Whetstone mountains. The investigation resulted in the identification of beds of similar age and character to those of the Sonora region, and in the discovery of interesting deposits, which, so far as I call ascertain from the literature at my command, have not been described heretofore. Route.—Starting from Nogales, we followed the railroad to Crittenden, and then drove to the southeastern slope of the Whetstones. After a brief examination of some reported coalbeds we continued our route, following the wagon-road between the Whetstones and the Mustang mountains to Huachuca, and eastward to Tombstone. Crossing the Dragoon mountains at South Pass, we traveled south and west by way of Turquoise and Antelope Spring into the road from Tombstone to Bisbee. Our route over the Mule mountains lay through Mule Pass and Bisbee, where we stopped a day or two. Thence, crossing Sulphur Spring valley, we drove around the southern end of the Swisshelms, and N. through the valley between these mountains and the Chiricahuas, to White river. From that point our way led through Rucker canon into the San Simon valley, then northward along the eastern face of the Chiricahuas, and by way of Fort Bowie to Willcox, Arizona, from which place we returned to Nogales. It was greatly regretted that the extremely wet weather prevented us from including in our examination the Huachuca

Jan 1, 1902

By D. T. Peters, J. C. Bisseliches, J. W. Spretnak

The pain boundary relaxation phenomenon in high-purity copper, 0FHC copper, and a precipitation-hardenable alloy o-fCu-2 uit pct Co has been studied by internal ,friction and elastic aftereffect techniques. The data were analyzed by assuming the broad distribution of relaxation times observed obeys a lognormal distribution law which enables calculation of the relaxation strength. Grain size had no effect on relaxation strength, although the peak width increased with increasing grain size and decreasing temperature. A double grain boundary peak was produced in high-purity copper by annealing to produce secondary recrystallization. The activation energy measured for 99.999 pct Cu is 37.5 * 3 kcal per mol and 46.5 kcal per mole for OFHC copper. A small peak in the Cu-Co alloy at about 220°C at 1 cps was deduced to be the grain boundary peak. Its height increased and its activation energy decreased with increasing aging time. Except for erratic peak positions the observations were consistent with the theory of pain boundary sliding. BEFORE the mechanism of the grain boundary internal friction peak in metals can be satisfactorily explained, the detailed characteristics of the relaxation process must be documented. Of interest are the effect of grain size on relaxation strength, the high-temperature background, and peak width and position. The effect on the grain boundary peak of a precipitate at grain boundaries and of the change in distribution of the particles with aging time must also be explained by any existing or forthcoming theory. The model which has received the most attention was proposed by KG' and zener2 and proposes that the anelastic strain results from sliding of adjacent crystals at grain boundaries. The sliding is limited by the interlocking of grain corners. It follows, according to this model, that the relaxation strength is independent of and the relaxation time is proportional to the grain size. The proportionality between grain size, D, and relaxation time, t, has been confirmed by K&' and Bisseliches . In this case, the internal-friction peaks of various specimens can be superimposed by plotting Q-' as a function of the parameter vD exp H/RT where v is the frequency and H the activation energy. However, the data of Starr et 01.' and Leak6 fit better to a parameter containing D to an exponent near two. A meaningful relationship is not always deducible from the shift of peak temperature with grain size. KG7 demonstrated that a twofold variation in grain size obtained by varying the amount of cold work followed by identical recrystallization anneals will cause a peak shift that is too large to be accounted for even by an exponent of two. Since the decreased grain boundary area existing with a larger grain size is exactly compensated for by an increased sliding distance, the relaxation strength should not decrease with increasing grain size. The height of the internal-friction peak has generally been observed to be rather insensitive to grain size as long as the average grain diameter does not approach the specimen diameter. Exceptions have been reported by Koster, Bangert, and Lang8 for copper, and by Leak6 for iron. The observations for copper could well have been confused by the presence df 0.3 pct0. The possibility that the peaks may simply be increasing in width with increasing grain size and that the relaxation strength, which is proportional to the area under the peak, may remain constant was not examined. his point has been checked in this investigation using high-purity copper. Atomic mechanisms to account for damping by sliding at grain boundaries have been proposed by KG7 and Mott. KG predicts the activation energy to be identical to that for self-diffusion. Mott's "island" model suggests the activation energy is nL where n is the number of atoms in an island and L is the latent heat of fusion per atom. Other authors have felt that a value equal to the activa-

Jan 1, 1964

By H. A. Bedworth

ALLOYS of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry1 proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche3 and Corson.4 The constitution of the system has also been recently investigated by Matuyama,5 and in the laboratories of the American Brass Co. by Smith.6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of, the constitution of copper-silicon alloys, the solubility reaches its maximum value, 6.7 per cent. silicon, between 721° and 782° C. At 852° C. the solubility is 5.25 per cent., while at 400° C. it is only 4.1 percent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent. silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By J. C. Bartlett

As American students of mining, philosophy, philology, music, history, or art have found it necessary or highly advantageous to supplement their course of study at home by a residence of some years at a foreign university, so, ever since mining has been practiced in this country in any other than a rude and wasteful manner, many American students of mining have sought in London or Paris, but chiefly in the Academy of Freiberg, Clausthal, or Berlin, such infor-

Jan 1, 1877

The classification here used is one of convenience only; it is not intended to include all known types of ore deposits. The characteristic features of the several well-marked types of primary mineralizations are described without reference to the ultimate source of their metals. The minerals of many deposits of obscure origin were probably introduced through fissures that are now healed, or are due to the migration of metals from such deposits. [ ] It is not within the scope of this book to enter into a general discussion of the genesis of ore deposits but, in view of the progress being made in our comprehension of the conditions under which ore deposits were formed, mention should be made of recent work. J. E. Spurr's two volumes, "The Ore Magmas," are recommended as crystallizing the views of those who are inclined to ascribe the origin of most ore deposits to a differential precipitation from magmatic rock masses and to the migration and precipitation of the viscous, liquid or gaseous exhalations from those masses. He has especially emphasized the role

Jan 1, 1932

By D. J. Carney, R. R. Burt, E. J. Whittenberger

Hardenability (multiplying) factors for carbon, mongonese, silicon, chromium, nickel, and molybdenum have been developed for hypereutectoid low-alloy steels in which bainite is the first subcritical transformation product. These factors permit the calculation of 95, 80, and 50 pct martensite hardenability from chemical composition when steels with spheroidized structures are quenched from 1475°, 1525°, and 1575°F. The strong contributions to hardenability of the less expensive elements, silicon and manganese, suggest their use to obtain additional hardenability in hypereutectoid low-alloy steels. DURING the past decade a number of investigators'"11 have carefully developed information which permits calculation of the hardenability of medium -carbon low-alloy steels from chemical composition and grain size. These data have been especially valuable in developing less costly low-alloy steel compositions with equivalent or Improved

Jan 1, 1957

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By G. W. Garside

In order to render my descriptions more intelligible, I have compiled a general map of this section of Alaska, showing accurately the relative positions of the most important districts where valuable deposits of minerals have been discovered (page 819). Upon inspection of this map, it will be observed that the chief metalliferous belt in this mineral field is in close proximity to the mainland shore, the trend of which it follows for more than a hundred miles in a northwest and southeast course, while the mineral croppings on the adjoining islands are much shorter in extent, and more irregular with respect to their strike and continuity. This principal metalliferous zone, which I will call the main-land system of lodes, contains gold, silver and lead, besides traces of copper, zinc and iron, gold being found extensively in a free state and also associated with sulphur, and with many of the sulphides of iron, lead and other substances. On the line of this belt, as shown on the map, there are a number of distinct mineral districts. Beginning at the southerly extremity, they are named as follows: Sumdum, Snettishham, Grindstone Creek, Sheep Creek, Gold Creek, Lemon Creek, Montana Creek and Berners Bay districts, each deriving its name from the hay or creek on which it is situated. Harris mining district, as legally organized under the local customs, rules and regulations adopted by the miners of Juneau, embraces, within its exterior boundaries, Grindstone, Sheep, Gold and Lemon Creeks, and all of Douglas Island. The limits of this immense metalliferous horizon are becoming definitely known through the exposures made by prospectors. The belt, as now recognized, varies in width from one to several miles, the lateral measurement being greatest at Juneau in Harris district, where the famous Treadwell mine, with its slate foot-wall, marks the westerly boundary of the zone, while the eastern side of Silver Bow Basin, with a granite hanging-wall, defines its easterly border.

Jan 1, 1893

By George Dyott

THERE are many who may consider a paper on aerial transport and its possibilities in connection with mining operations somewhat premature. Nevertheless, as there is considerable interest manifested in the subject at the present time and the amount of information available is both scanty and misleading, the result of investigations in some of the remote mining districts of Peru will not only be of interest, but will help crystallize, in the minds of many, a more correct conception of just what an airplane is capable of doing. By way of introduction, I will deal briefly with the types and varieties of airplanes now in use, and the developments of the past few years, pointing out -how the war has encouraged machines. of startling performance rather than those of commercial utility. I will then take up aerial transport in general, showing how airplanes may be employed to advantage and the particular kind of work for which they are best suited. This will cover a preliminary discussion on cost, which is one of the most important phases of the subject. In passing on from a general survey of the situation, I will deal with actual observations and investigations made in Peru. This part of the paper will be divided into two sections: the first, covering the mountainous districts of the Andes (Tamboras, Pataz, Soledad, etc.); the second, the alluvial deposits in the rivers, Chinchipe, Santiago, and Napo. In each case the question of atmospheric conditions, altitude, landing grounds, motors, cost, etc. will be discussed. While it is my intention to deal chiefly with mining in the sections mentioned, the same line of argument will be applicable to any other districts in the world. In conclusion, I will touch on the possibilities of using lighter-than-air craft of the Zeppelin type, followed by a summary of the most salient points brought out in the paper.

Jan 2, 1919

Jan 1, 1953

By J. H. Waxweiler, L. C. Ikenberry, R. J. Bendure

Carbon which is present as insoluble carbides in austenitic stainless steels can be measured quantitatively by dissolving the steel in iodine-methanol and analyzing the residue for carbon. Severe sen-sitization was observed in Type 302 due to precipitation of only 0.003 pet carbon. Both cold work and the presence of delta ferrite caused a marked acceleration in rate of carbide precipitation. Carbide precipitation rates in 17-7 PH were stzulied for the austenite conditioning and also the aging heat treatment. CARBON and its compounds exercise a major influence on the properties of stainless steels and their response to thermal treatment. Sensitization in 18-8 type stainless steels has been the subject of numerous investigations throughout the years. Bain, Aborn, and utherford," and Binder, Brown, Frankss all studied the effects of heating austenitic stainless steels in the temperature range of 1000° to 1500°F. The primary purpose of most of these studies was the investigation of susceptibility to in-tergranular attack in acids due to these sensitizing heat treatments. Intergranular precipitation of carbides was always associated with intergranular attack but it was recognized2 that severe attack could occur with but minute quantities of precipitated carbide. Mahla and ielsen utilized the electron microscope to make a significant contribution in illustrating the appearance and method of growth of chromium carbides during sensitizing heat treatments. However, as they stated, their studies of residues could not be used to obtain a quantitative measurement of the amount of carbon which was actually precipitated. The aim of the present investigation was to devise a relatively fast, simple method for the quantitative measurement of carbides in stainless steel. EXPERIMENTAL WORK The initial investigations were made to determine the best means of separating carbides from the matrix. A number of dissolving media were tried using both chemical and electrolytic attack. Qualitative examination of the extracted residues by X-ray diffraction indicated that solution in iodine-methanol would furnish a good means of separation. Consequently, further work was pursued along this line. The method is quite simple. The sample in the form of millings or nibblings is dissolved in iodine-methanol solution at room temperature (6-g iodine, 25-ml methanol per g of sample). The insoluble residue containing the carbides is separated by suction filtration through an ultra-fine glass filter disc. This is a very fine filter medium that will retain particles as small as 0.1 to 0.2 p in diameter. After washing with methanol and drying, the filter disc and residue are placed in a conventional combustion carbon-tube furnace and the carbon determined gravimetrically. Using this technique it was found that reproducible insoluble carbon values were obtained. However, since such small amounts of insoluble carbon were obtained on Type 302 after sensitizatipn at 1250°F and 1500°F, the values were confirmed by a second method. In the second method the sample was dissolved with copper potassium chloride and filtered through a millipore paper. This treatment dissolves the matrix but leaves undissolved practically all of the carbon irrespective of how it is present in the steel. The amount of insoluble carbon present as chromium carbide is determined by calculation from the analysis of the residue for chromium and iron. The derivation of the formula used for this calculation is discussed later. The values obtained by the indirect copper-potassium-chloride method were in agreement with those obtained by the iodine-methano1 method. See Table I. It should be pointed out that the sensitivity of the direct combustion method is not too high when the amount of carbide present is small. This is due primarily to inherent blanks and to analytical errors such as weighing. For this reason it cannot be stated with any degree of certainty that there is a significant difference between values of 0.002 and 0.005 pct. Having confirmed that the iodine-methanol extraction gave a quantitative measurement of the precipitated carbides in Type 302, exploratory tests were conducted on Armco 17-7 PH stainless steel. Samples from commercial Heat 54807 were solution annealed at 2000°F, water quenched and heated at 1250" and 1500°F, and water quenched. The analysis of Heat 54808 is as follows:

Jan 1, 1962

By L. A. Rapoport, W. J. Leas, C. W. Carpenter

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By W. A. Oates, J. A. Lambert, P. T. GaIIagher

Monte Carlo methods have been used to compute the arrangements of interstitial atoms dissolved in tetrahedral sites in bcc lattices. It is assumed that the presence of an interstitial atom "blocks " a certain number of neighboring sites and prevents their occupancy. Sites "blocked" by more than one filled site are allowed for. The computed values of. the mean occupation number (defined as the ratio of the total number of sites blocked to the number of solute atoms are used to calculate the configurational entropies of the solutions. These entropies are compared with those resulting from previous theoretical studies of this problem and also with available experin~ental data for the p Zr-H, Nb-H, V-H, and Ta-H systems. Evidence is also given that the "blocking" explanation of low limiting compositions in these systems, rather than this being due to initial limitations on the number of sites available, is probably correct. THE ideal partial configurational entropy of mixing of an interstitial solute in a metal is given by: where p is the number of interstitial sites per metal atom and Xi is the atomic fraction of the interstitial. For the bcc lattice. which we shall be concerned with in this paper, the interstitial positions are shown in Fig. 1. It can be seen that for the tetrahedral sites, p=6. whereas for the octahedral sites, p = 3. Different emphasis has been placed on the relative importance of energy and entropy effects in determining deviations from ideality in interstitial solid solutions. In some cases the same system, e.g., Fe-C, has been described by the contradictory regular and athermal solution models indicating that the enthalpy and entropy functions, derived from equilibrium data, are frequently not accu.rate enough to differentiate between these treatments. However, for certain metal-hydrogen solutions the equilibrium data is available over sufficiently wide ranges of temperature and composition to permit a reasonably accurate determination of the compositional variation of the heats and entropies. Hoch&apos; has attempted to interpret the results of interstitial solid solutions in terms of a regular solution model. In the case of the Ta-H system where 13 = 6, this model entails fitting the experimental relative partial entropies of solution, asH, to the equation: where ASgs is the relative partial excess entropy of solution of hydrogen. Hoch found that the results of Mallett and Koeh1 could be fitted to this equation with an approximately constant value of AF up to XH = 0.25. However, it is apparent from the solubility isotherms in this system which become asymptotic to the composition TaH that, since (Xh /6 - ~Xh ) becomes infinite only at TaH6, it is necessary that AS<&apos; tends to infinity at TaH. In other words, the low saturation composition of TaH, instead of the anticipated TaH,, eliminates the possibility of applying regular solution theory to such systems. Rather large negative excess configurational entropies must exist at higher hydrogen concentrations in order to explain the lower saturation values. To account for these low limiting compositions and excess entropies two distinctly different approaches have been followed. Rees and many others1-l2 have assumed that not all interstitial sites are crystallographically equivalent with respect to the interstitial addition; that is, in Eq. [I] p is less than the value anticipated from geometrical considerations. To describe, say, a bcc metal-hydrogen system with a limiting composition of MH by this approach one would consider that p = 1 in the first instance instead of p = 6.&apos;j3 In some cases, nonintegral values of B have been taken in order to improve the fit with the experimental data over limited ranges of composition. The other approach which has been used to explain the low saturation compositions is to assume that, although all sites are available for occupancy, strong repulsive interactions exist between the neighboring interstitial atoms, and hence occupancy of any site excludes or blocks a certain number of neighboring sites from being occupied. Earliest treatments of this concept considered the exclusion of an integral number, of nearest-neighbor sites from being occupied at all concentrations. In this case, the partial configurational entropy is given by: These early treatments failed to allow for the overlap of the blocked sites which will arise at all but the very lowest concentrations. More recently attempts have been made to calculate the effect of this decrease in the number of blocked sites on the configurational entropy. Using the quasichemical treatment of interstitial solid solutions as given by Lacher and assuming that an infinite repulsive interaction energy existed between the solute atoms. atom obtained an approximate configurational entropy applicable to the blocking with overlap case:

Jan 1, 1970