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By B. A. Eaton

The subject of many discussions and technical papers in the last 20 years has been the prediction of the well-bore pressure gradients that are required to induce or extend fractures in subsurface formations. The subject merits this attention because of the frequently recurring problems that arise from an inability to predict fracture pressure gradients. Encountered in several common types of operations in the oil industry are problems associated with the prediction of formation fracture pressure gradients. When wells are being drilled in both new and old fields, lost circulation is often a very troublesome and expensive problem. Complete loss of circulation has been disastrous in some cases. Many times, such disasters could have been avoided if techniques for calculating fracture pressure gradient had been employed in the well plans, and if casing strings had been set, and mud weight plans had been followed accordingly. In areas of abnormally pressured formations, the prediction of fracture gradients during the well-planning stage is extremely important. In fact, it is as important as the prediction of formation pressure gradients, which has received a great deal of attention in recent years. There are several published methods used to determine fracture pressure gradients. However, none of these methods appears to be general enough to be used with much reliability in all areas. In 1957, Hub-bert and Willis published a classical paper that included the development of an equation used to predict the fracture extension pressure gradient in areas of incipient normal fau1ting.l Overburden stress gradient, formation pore pressure gradient and Poisson's ratio of rocks were the independent variables that were shown to control fracture pressure gradient, the dependent variable. In 1967, Matthews and Kelly published another fracture pressure gradient equation that is different from that of Hubbert and Willis in that a variable "matrix stress coefficient" concept was utilized.3 Later the same year, Costley wrote about a similar idea.5 Goldsmith and Wilson used a least-squares curve-fitting technique and field data from the Gulf Coast area to correlate fracture pressure gradient with formation pore pressure gradient and formation depth.' They noted that the fracture pressure gradient increased with increasing depth while the pore pressure gradient remained constant. In each of these cases, the problem for which a solution was sought was to determine the bottom-hole pressure gradient required to initiate or extend a fracture. Results of the previous work show that fracture pressure gradient is a function primarily of overburden stress gradient, pore pressure gradient, and the ratio of horizontal to vertical stress. There is argument for a fourth variable in that in many cases breakdown fracture pressure gradient is greater than the fracture extension pressure gradient. However, if the fracturing fluid is able to penetrate the formation through the pores or existing cracks, there is very little

Jan 1, 1970

By Wm. Reuben Webster

BRASS is an alloy of copper and zinc. The brasses (using this term to denote all useful proportions of the two constituents) are the most valuable and widely employed of all [ ] nonferrous alloys, because of their high resistance to ordinary corrosive agencies and the very wide range of properties that may be imparted to them by variations in the proportions of the constituents and by variations in mechanical treatment and heat-treatment. Fig. I shows the normal physical properties, as determined by standard tensile tests, of the series when in the annealed condition. Fig. 2 shows the effect of varying amounts of cold-working on an almost pure brass containing 70 per cent copper and 30 per cent zinc. Fig. 3 shows the effect of annealing at various temperatures on the same alloy. This effect is somewhat modi [ ] fled by the degree of cold-working to which a brass has been subjected, as shown by Fig. 4. A fourth test, which is empirical, has been found useful because of its simplicity -the hot hammer test. Samples Y2 in. in diameter and ¾ in. long are placed in a suitable furnace. These are withdrawn one at a time at successively higher tempera¬tures and are subjected to the blow of a drop hammer weighing 50 lb. with a drop of 4 ft. The percentages of' reduction in length of the cylinders are plotted against temperatures and give a comparative measure of plasticity at different temperatures. The results of this test on several

Jan 1, 1942

By Charles Will Wright

The present struggle for economic and industrial supremacy by the Communist world is against the United States, its main target, and the other Free World nations. The basis of industrial power is minerals, so the Communist nations are building up mineral production within their borders, often regardless of costs, and are acquiring quantities of mineral products from Free World countries for future use. They are contracting for additional supplies and advancing funds for the development of these quantities. A number of the less developed mineral producing countries of the Free World are being infiltrated by Communists and Communistic influence. This situation is well known, but as yet little has been done to oppose these activities or to awaken the public to their seriousness. The Communist countries are still far behind the Free World Nations in production of many essential minerals. But, shortages are being made up from Free World nations in exchange for petroleum, manganese ore, chromite and other products. Restrictions on shipments of strategic materials to Communist countries have not been maintained.

Jan 1, 1964

By H. Becke, D. Stolnitz, D. Flatley, W. Kern

Extensive solid solubilities of CdTe (zincblende-type struckre) and InTe (B37 type) in each of the rock salt-type compounds, PbTe and SnTe, have been observed. Partial phase diagrams have been determined by thermal analysis and X-ray metallography. The limiting mol fraction. X,, of the solute in the rock salt-type a phase and the corresponding eutectic temperatures, T,, are: (PbTe)l-x(CdTe)x: X,- 0.2, T, =866°C; (PbTe),-,(lnTe),: X, - 0.35, T, = 646"C; (SnTe),-,(CdTe),:X,- 0.11, T, = 784 "C; (SnTe),-,(lnTe),: X,-0.53, T, = 630°C. The lattice parameters of the a phase decrease linearly with X, even in (PbTe),-,(CdTe),, where a, (CdTe) = 6.481A > %(PbTe) = 6.459A. This is taken as proof that the cadmium atom enters an octahedral interstice of the tellurium atom sublattice; i.e., the formation of the a phase entails the direct replacement of lead by cadmium. The a, us X curve extrapolates to 6.16A at X = 1, in agreement with the value predicted for an ionic crystal of CdTe; it is also consistent with the reported lattice parameter It is well-established that the compositions of intrinsic semiconducting and semimetallic compounds conform to normal valence rules.1"5 The apparent exceptions can be explained by taking account of anion-anion covalences, as in CdSb, or of multiple cation valences, as in In Te.'This empirical generalization is the basis of the chemical approach to semiconductors2 by which the properties of an intrinsic semiconductor are rationalized in terms of the ionic-covalent bonds necessary to saturate the valence-electron complement of the anion sublattice. A fundamental shortcoming of this approach is its disregard of long-range crystal interactions. It cannot, accordingly, deal with the phenomenon of charge conduction except through the use of ad hoc postulates. As an example, a crystal of CdTe would, in the valence-bond picture: be described in terms of electron pairs, each with the same discrete energy, localized between every cadmium and tellurium atom. This is, of course, contrary to the Pauli of the high-pressure rock-salt form of CdTe, corrected for decompression from 36 kbar. The free energy of formation of the a phase of pure CdTe at room temperature is calculated from the phase diagram to be +10 kcal per g-atom, in accmd with the value calculated from the transformation pressure. The standard enthalpy is +13 kcal per g-atom, and the standard entropy is +9 eu. The latter value implies the formation of extra classical particles, such as vacancies, interstitials, or nondegenerate charge carriers, but these alternatives are not consistent with the semiconducting properties and the densities of the a phase. The extrapolated values of the lattice parameters of (PbTe),-,(lnTe), and Spectively, for the rock salt-type modification of InTe. The corresponding interatomic separation is intermediate between monovalent and trivalent indium. The qualitative implications of the results are considered from the viewpoints of both valence-band theory and energy-band theory. principle, and is corrected by methods of molecular-orbital theory in which bonds are replaced by bands of molecular orbitals whose energies, E, depend upon a crystal-momentum vector, k.7 Each band is derived from a linear combination of atomic orbitals with two electrons required to saturate each molecular orbital in the band. In a crystal of N atoms containing z atoms in its primitive unit cell, there are 2 N/z states per band which lie in a region of k space bound by the Brillouin zone. In an intrinsic semiconductor, the bands can be grouped into valence bands which are normally filled and conduction bands which are normally empty. If the highest valence band and the lowest conduction band overlap anywhere within the Brillouin zone, the material is rendered semimetallic. The quantity defines the effective mass, m*, of an electron in a conduction band (or of a hole, i.e., an electron deficiency, in the valence band) and leads directly to the concept of charge mobility through the relation \x = et/m*, where e is the electron charge and t is the lattice relaxation time.

Jan 1, 1964

By Norbert R. Morgenstern

INTRODUCTION An understanding of the role of water in controlling the stability of rock masses is central for a rational approach to the subject. The presence of water can hinder mining opera- tions in two ways: 1. excessive discharge 2. excessive pressure It should be noted that if the rock mass is very tight, excessive pressures can exist without large discharges. Alternatively, if abundant water is available and the rock mass is open, then substantial discharges can occur under quite small pressures. The problems associated with excessive discharge are usually well understood by the mining engineer. Vehicle mobility is inhibited, some areas are flooded and hence become inaccessible; at best, a costly nuisance exists. The methods of solving these problems are also well-known to mining engineers. They generally involve tapping the source of the excessive discharge and channeling it away in such a manner that any hindrance to the mining operation is minimized. The effects of water pressure on the stability of rock masses are less obvious and the following will be devoted solely to this aspect of the problem. The manner in which water pressures enter into the consideration of stability is made clear by an understanding of the concept of effective stress. THE CONCEPT OF EFFECTIVE STRESS The simplest mechanical model for the problem of rock slope stability consists of a rough, rigid block sliding down an inclined plane under the influence of gravity. This is illustrated in [Fig. 1]. The down-slope component of the weight of the block tends to produce movement which is resisted by the shearing force generated by friction along the base of the block. The shear stress per unit area inducing movement is

Jan 1, 1971

By J. D. Rice, S. C. Pitzer, C. E. Thomas

Interpretation of pressure build-up data obtained in the conventional manner has often been difficult because of the deviation from theoretical behavior. Major causes of this deviation have been attributed to damage and afterflow, and to fluid redistribution in the wellbore which, in extreme cases, can result in a pressure hump in the early portion of the build-up curve. Theoretical investigations show that bottom-hole pressure is definitely influenced by phase redistribution in the tubing column during surface shut-in tests, and that the magnitude of the effect is sensitive to the producing gas-oil ratio and stabilized rate of flow in the well. For field experiments a wire-line tubing packer, which can be run in the tubing against a stabilized flow rate, was developed for bottom-hole shut-in tests. By use of this bottom-hole .shut-in method, pressure humps previously observed in surface shut-in tests were completely eliminated and the effects of afterflow minimized. Analog and digital computer studies have been made to obtain theoretical curves for comparison with field curves, and remarkable agreement between the results of bottom-hole shut-in tests and theoretical curves has been obtained. INTRODUCTION Pressure build-up data from shut-in wells have been used by the petroleum industry to determine the permeability of the formation, to estimate wellbore damage, to evaluate the static reservoir pressure and to speculate reservoir volume. Calculation of these factors is based on methods of analysis developed for theoretical systems whose build-up curves have a charac- teristic shape when the wells are shut-in at the sand faCe.1,2,3,5,8,10 However, field curves obtained by conventional surface shut-in methods do not always exhibit this characteristic. Such factors as stratification, rock heterogeneities and irregular reservoir geometry can cause the character of a build-up curve to deviate from that predicted by theory for a simple system. In addition, all field build-up data are affected by the methods utilized in obtaining the measurements. Conventional surface shut-in techniques allow two effects to occur which contribute directly to the manner in which pressure builds up at the sand face. The first, afterflow, has been recognized for some time and methods are available for estimating the magnitude of its effect and for correcting its influence.' The second, phase segregation in the tubing column after shut-in, has been reported only recently and appears to exert a considerable influence on the character of field build-up curves.!' In extreme cases, phase segregation can produce "pressure humps" in the early portion of the build-up curve. Such curves have been considered anomalous and have defied analysis. It is the purpose of this paper to discuss the effect of phase segregation in the tubing string during build-up and to present a bottom-hole shut-in technique for obtaining field build-up data which minimizes the influence of afterflow and eliminates phase segregation effects. It will be shown that reliable reservoir information can be calculated from build-up measurements obtained using this method, even though conventional surface shut-in tests on the same wells yield anomalous data. DISCUSSION OF PHASE REDISTRIBUTION EFFECTS Some of the effects of phase redistribution on pressure build-up curves have been described previously by Matthews and Stegemeier" who have presented evidence that phase segregation is responsible for the pres-

By AIME AIME

ROBERT F. MEHL was born in Lancaster, Pa., March 30, 1898 and graduated from Franklin and Marshall College in 1919. He then went to Princeton and was granted his doctor's degree in physical chemistry in 1924. Two years as head of the department of chemistry at Juniata College, followed by a like period as National Research fellow at Harvard, working with T. W. Richards and Albert Sauveuir, satisfied Bob's immediate affections for college and university life and prepared him to turn temporarily to other fields.

Jan 1, 1938

OPEN-HEARTH refractories are not merely an accessory to the furnace. They are the furnace, to all intents and purposes. The steel work of the main structure is merely an open frame which helps to support the refractories ; and the regenerators, a necessary part of the furnace system, consist almost entirely of refractories. Not only do refractories constitute the essential part of the furnace, but they also carry the liquid steel all the way to the point where it begins to solidify. On leaving the furnace the liquid passes through a refractory runner into a refractory-lined ladle, then through a refractory nozzle closed by a refractory stopper on the end of a rod protected by refractory sleeve bricks. The liquid is sometimes sent through an additional refractory- lined tundish, a supplementary ladle, or a refractory runner for bottom pouring, until it finally enters the iron mold in which it solidifies. Even in the mold, refractory materials are sometimes used to provide a nonconducting "hot top." This series, from runner and ladle to hot top, inclusive, is often referred to collectively as the "pouring-pit refractories." REFRACTORY RAW MATERIALS The raw materials available are best classified into basic and acid types. The principal basic raw materials are magnesite, dolomite, and chrome ore. The principal acid materials are silica in various natural forms, and fireclay. Magnesite. Austria was the principal source of magnesite (MgCO3) until recent years, when the Province of Quebec, in Canada, and the states of Nevada and Washington became important sources for the American steel industry. More recently these natural sources have been supplemented by the so-called "sea-water magnesite"-which is the name somewhat incorrectly given to magnesium hydroxide obtained as one of the products

Jan 1, 1964

By EDWARAD A. SIVEDENBORMG

REPORTS have been made at different times on the progress of water encroachment in the Frontier sands in the Salt. Creek oil field, Natrona county, Wyoming. All previous reports have, -however, been largely based on the position of water in the sands as determined by various physical tests. Subsequent information has been secured through a preliminary investigation of the porosity, grain size and degree of saturation of the Frontier sands. Also, a closer differentiation has been made between the waters encountered incident to the production of oil by means of chemical analysis. In view of the more recent developments there has been a need of a water encroachment map of the first Wall Creek based on a field survey and additional information acquired since the water encroachment map of the sand of 1926, by J. S. Ross and E. W. Henderson, petroleum engineers of the U. S. Geological Survey. The present report is confined to a study of the first Wall Creek sand and was written in connection with the preparation of the map, showing water encroachment in this sand. The first Wall Creek sand was the discovery sand in the field, the first well having been drilled in 1908. Its thickness averages 120 ft. and, varies between 90 and 160 ft. The sand is in the Colorado group of the Upper Cretaceous series and is further considered as a part of the Frontier formation found in other parts of Wyoming.

Jan 1, 1930

To Install Waste Heat Boiler at White Pine White Pine Copper Co.'s smelter 18 miles southwest of Ontonagon, Mich., will have a six story high boiler utilizing what otherwise would be waste heat from a copper reverberatory furnace. Designed and under construction by the Babcock & Wilcox Co., the boiler will supply steam to a turbo-generator furnishing power for the projected development. The boiler will be in line with and following the reverberatory furnace. Using waste heat from the furnace in place of fuel for steam generation, about 50 pct of heat in the fuel originally supplied to the furnace will be recovered by the waste heat boiler. Exploration conducted over the past 15 years at White Pine, wholly owned subsidiary of Copper Range Co., has disclosed reserves of 309 million tons averaging 21.3 lb of copper per ton. Ore mineral is chiefly chalcocite (Cu2s).

Jan 5, 1953

By Wm. Reuben Webster

BRASS is an alloy of copper and zinc. The brasses (using this term to denote all useful proportions of the two constituents) are the most valuable and widely employed of all [ ] nonferrous alloys, because of their high resistance to ordinary corrosive agencies and the very wide range of properties that may be imparted to them by variations in the proportions of the constituents and by variations in mechanical treatment and heat-treatment. Fig. I shows the normal physical properties, as determined by standard tensile tests, of the series when in the annealed condition. Fig. 2 shows the effect of varying amounts of cold-working on an almost pure brass containing 70 per cent copper and 30 per cent zinc. Fig. 3 shows the effect of annealing at various temperatures on the same alloy. This effect is somewhat modi- [ ] fied by the degree of cold-working to which a brass has been subjected, as shown by Fig. 4. A fourth test, which is empirical, has been found useful because of its simplicity the hot hammer test. Samples 1/2 in. in diameter and 3/4 in. long are placed in a suitable furnace. These are withdrawn one at a time at successively higher temperatures and are subjected to the blow of a drop hammer weighing 50 lb. with a drop of 4 ft. The percentages of reduction in length of the cylinders are plotted against temperatures and give a comparative measure of plasticity at different temperatures. The results of this test on several

Jan 1, 1942

OPEN-HEARTH refractories are not merely an accessory to the furnace. They are the furnace, to all intents and purposes. The steel work of the main structure is merely an open frame which helps to support the refractories; and the regenerators, a necessary part of the furnace system, consist almost entirely of refractories. Not only do refractories constitute the essential part of the furnace, but they also carry the liquid steel all the way 'to the point where it begins to solidify. On leaving the furnace the liquid passes through a refractory runner into a refractory-lined ladle, then through a refractory nozzle closed by a refractory stopper on the end of a rod protected by refractory sleeve bricks. The liquid is sometimes sent through an additional refractory- lined tundish, a supplementary ladle, or a refractory runner for bottom pouring, until it finally enters the iron mold in which it solidifies. Even in the mold, refractory materials are sometimes used to provide a nonconducting "hot top." This series, from runner and ladle to hot top, inclusive, is often referred to collectively as the "pouring-pit refractories." REFRACTORY RAW MATERIALS The raw materials available are best classified into basic and acid types. The principal basic raw materials are magnesite, dolomite, and chrome ore. The principal acid materials are silica in various natural forms, and fireclay. Magnesite. Austria was the principal source of magnesite (MgC03) until recent years, when the Province of Quebec, in Canada, and the states of Nevada and Washington became important sources for the American steel industry. More recently these natural sources have been supplemented by the so-called "sea-water magnesite"-which is the name somewhat incorrectly given to magnesium hydroxide obtained as one of the products

Jan 1, 1951

By Russell G. Haworth

Three companies, United States Potash Company, Potash Company of America, and International Minerals and Chemical Corporation, are now operating potash mines and reGneries in the Carlsbad, New Mexico, area. The three mines are located approximately twenty miles east of Car1sbad. The deposits have been found ideal for mechanized mining methods. This summary has been compiled from information made available by the three operating companies. Prospecting Since outcrops of potash are nonexistent, prospecting is accomplished by drilling and coring of the salt section to establish the grade, thickness, and outline of the potash beds contained in the salt deposits. Information regarding the nature of the formations in the cover of 400 to 600 ft thick over the salt and potash beds is also obtained from drill cuttings in the same operation. By proper interpretation of assembled data the best location for shafts may be determined. The overburden varies in character but consists in general of interbedded shales, sand, gravels, limestones, and anhydrite beds. Water, in unpleasant quantities, especially in the sands and limestones, often completes the geologic section. Some of the shaftas in the area have been sunk without undue difficulties, others have been delayed by flows of water. Most of the shafts are concreted from the surface to the salt section. Each of the three mines in the Carlsbad area has one shaft for hoisting ore and one for hoisting men and supplies. Mining Methods Information acquired from initial drilling and prospecting affected the choice of mining methods. Since the tabular, slightly rolling deposits were similar to coal seams, the room-and-pillar system used in coal mining was adopted by all the companies. Pillars have not been removed in any of the mines on a large scale. One company has conducted experimental robbing of pillars in one restricted area. Where it is known that overlying strata contain water in large amounts, it is not considered practical to risk flooding of the mines by removing pillars without fill. Some thought is now being directed toward development of economical methods of filling for pillar recovery. The problem is not identical at the three mines and local conditions will govern the methods employed for eventual pillar recovery. The important point is that, with large reserves, it has not been necessary to resort to mining of pillars for adequate production. The ore deposits are laterally extensive but are irregular in shape and lie at a depth of 700 to 1100 ft below the surface. The major operations of all mines are on the same bed strati-graphically, except for the langbeinite level at International Minerals and Chemical Corporation. The deposits are apparently not connected and in many parts of the deposits being mined, "salt horses" or barren zones occur. From 400 to 700 ft of salt with minor beds of polyhalite and anhydrite lie immediately above the ore horizon. The ore differs from the salt only in the potassium chloride content and color due to small amounts of iron associated with the sylvite, giving the ore a somewhat mottled red and white cast. Thickness of the ore varies from 5 to 14 ft. Rooms and break-throughs in the mines vary from 24 to 40 ft in width, the overlying salt forming an excellent roof and providing safe mining conditions. Almost no timber is used in any of the mines for roof support. Drilling is normally the first step in mining the face of a room. Electric motor driven auger drills are used in the area. Jack hammers were used to some extent when the mines were first opened but the ore is easily drilled if bits are sharp and the coal type

Jan 1, 1950

By S. J. Aresco, A. A. Orning

This paper presents a scheme for determination of precision for the various steps in coal sampling, sample preparation, and analysis. It also gives resulting data on 100 American coals from various coal fields covering all ranks from lignite to low-volatile bituminous. The variances of the various steps of the process are studied as a function of the coal preparation, the top size of coal as sampled, and the ash content. To understand the variables that control the overall precision of coal sampling, sample reduction and analysis, there is need for measurement of the variances due to successive steps of the process. The purpose of the present paper is to study these variances as a function of the coal preparation, the top size of the coal as sampled, and the ash content. The sampling data included are from 100 individual preparation plants from various coal fields in the United States and cover all ranks of coal from lignite to low-volatile bituminous; various types of preparation; deep, strip and auger mines; and, in many instances, mixtures from two or more coal beds or types of mines. The collection of data is continuing, but sufficient work has been done to draw some important conclusions. Since the work was done in conjunction with the Bureau of Mines sampling of coal, the time that could be spent at any one preparation plant was limited. This, in turn, limited the number of samples that could be taken for each coal. For this reason, the results from various plants were pooled in blocks. Two major blocking categories were "raw" and "washed!' The raw coals had no preparation other than crushing and/or screening. The washed coals were prepared further by some combination of wet or dry mechanical cleaning. The categories were further divided ac-

Jan 1, 1965

By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,

By P. E. Baker

An experimental study of heat flow in steam flooding was carried out with steam displacing water in a plane-radial fluid-flow model. Temperature distributions in the model reservoir, overburden, and substratum were measured at frequent intervals during flooding by means of a fixed array of thermocouples. Heat losses to overburden and substratum and the division of heat between the steam and hot-water zones in the reservoir were calculated from the temperature data by performing numerical integrations over the appropriate volumes. Temperature profiles and heat distribution results are presented. Some results were (1) the fraction of injected heat that is lost to overburden and substratum, when expressed as a function of time, did not depend on injection rate; (2) a significant portion of the injected heat was contained in the hot-water zone ahead of and underlying the steam front in the reservoir. The division of heat between the steam and hot-water zones did depend on injection rate; and (3) considerable gravity override was observed. The experimental results are compared with those of several published theoretical studies of heat transfer in hot-fluid injection; approximate agreement on heat losses is found with some of the most idealized theories. A valid comparison cannot be made in regard to steam us hot-water zone; basic interpretation of the hot-water zone, in terms of a vertical steam front, is clouded by gravity override in the experiments. INTRODUCTION The experimental study reported here primarily concerns two problems of heat transfer in steam flooding that have economic and engineering importance. These are (1) the fraction of injected heat lost to the overburden and substratum, and (2) the division of the remaining heat between a zone containing steam and a zone of hot water at lower-than-boiling temperature. The volume of the steamed region, which has a direct effect on oil recovery, can be calculated readily from these results. Several valuable theoretical studies have been published on this problem, but no experimental tests of the theories have previously appeared. Tests were needed because the effects of the necessary simplifications in the theories could not be determined otherwise. The basic, untested theoretical problem is the effect of "decoupling" heat and mass transfer, and the resulting inability to include the effects of heat transfer and condensation on fluid flow. The theoretical problem solved so far has been a heat transfer problem in which fluid is present as a heat carrier and flows in a stipulated manner, either linear or plane-radial. The simplifications that have sometimes been made in regard to thermal conductivity by, for example, Marx and Langenheim,l Lauwerier2 and Thomas3 apparently do not have an important effect on heat loss calculations, although the results of the different methods disagree to a certain extent, as shown by Spillette4 and by Ramey.5 A recent paper by the author6 compared the results of experiments in hot-water flooding with several theoretical results and showed a rather poor agreement. It will be seen that the experimental heat loss results for steam flooding, however, show acceptable agreement. These comparisons are discussed in a later section. EXPERIMENTAL APPARATUS AND PROCEDURE The system studied was one in which a sand pack, initially water saturated and at a uniform temperature, was flooded with steam at a constant rate and temperature. The temperature distribution in the "reservoir" and adjacent "strata" was measured with an array of thermocouples, and heat losses were determined from these measurements. The sand pack contained no oil because the only concern of the experiments was heat flow, and it was important to have the flow pattern as simple

Jan 1, 1970

By W. R. Ingalls

Jan 1, 1922

By W. R. Ingalls

Jan 1, 1922

By Henry Howe

THIS paper is a discussion of the extremely valuable one of Mathewson and Phillips, The Recrystallization of Cold-Worked Alpha Brass on Annealing,1 which not only gives us a wealth of important data reached with great intelligence, but also shows both uncommon powers of imagination and a perfectly fair spirit. Let me try to analyze some of their results, and to enunciate some of the laws to which these results point. For brevity I refer to them as "The Authors." The page numbers in parentheses refer to their paper. 1. The Visible Aspects of Recrystallization.-Plastic deformation in a single direction, as in cold-rolling, draws the grains out in that direction, that is, inequiaxes them, without destroying their apparent individuality. Each grain seems to endure the drawing out without changing either its volume or its orientation materially, for the etching tint of each grain seems to be as uniform after as before the drawing out, save for the "etch bands,"2 shown in Figs. A to D of the Authors' Plate I. As the drawn-out metal is heated progressively, on reaching a certain "disintegration temperature" these old grains seem to break up, probably into submicroscopic fragments, and this apparent disintegration is followed by a coalescence of these fragments, so that their number decreases and their size increases, till they may become very much coarser than before the drawing out. Ruder3 coarsened the grains of silicon steel in this way till single grains reached an area of 50 cm. (7.75 sq. in.). The deformation itself probably breaks each grain up into many very small fragments, but the fact that each grain continues to have a uniform etching tint different from that of its neighbors indicates that these fragments retain the initial common orientation of the grain. The apparent disintegration which we observe, then, is rather an abandonment of community of orientation for individuality of orientation, by the fragments formed earlier during the deformation. Hence we

Jan 10, 1916

By Charles Will Wright

Brief descriptions of the occurrence of the various deposits of strategic minerals then known in South America are published in "The Mineral Deposits of South America," by B. L. Miller and J. T. Singewald, 1919; in "Ores and Industry in South America," by H. F. Bain and T. T. Read, 1934; and in many publications on the individual countries. To give a gen.era1 idea of the situation today and possibilities for future output of strategic minerals in several of the countries, the following notes are offered. All tonnages are in metric units.

Jan 1, 1940