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By F. Keller

SOME PHRASEMAKER has aptly said that nature made aluminum light but research made it strong. Research has been a vital element in the past progress of the aluminum industry and its future growth likewise depends upon the application of the results of research. The role of aluminum products in World War II is well known and this metal will certainly be increasingly important in the postwar world. Some of the principal developments in the war years were in the field of high-strength aluminum alloys. New and stronger alloys were developed which enabled designers to get increased speed and performance in our fighter planes and bombers. The aircraft industry will continue to use these new materials for peacetime passenger and cargo airplanes. High-strength alloys will also find structural applications in trucks, buses, trains, ships, and bridges.

Jan 1, 1946

By Jerome Strauss

IN his review of developments in 1943, Gilbert Seil, Chairman of this Committee on Reduction of the Ferroalloy Ores, tabulated the consumption of the alloying metals in relation to the steel production of that year. In the year just closed the approximate tonnage was of the same order, differing only to a minor degree or suffering some correction with more precise figuses available, as indicated in the following estimates: Consumption Metals in Tons Steel 92,000,000* Manganese 700,000 Silicon 200,000 Chromium 200,000 Nickel 75,000 Molybdenum 20,000 Tungsten 8,000 Vanadium 1,700 Titanium 1.600 Boron 10 `Production figure. The technologic studies instituted during 1942 and carried forward with such great vigor during 1943 continued into 1944 although in some instances were brought to a close either by completion of the specific development

Jan 1, 1945

By J. R. Linney

THE Eastern magnetite industry has not failed in its contribution to the war program during the past year. Man-power shortage was the critical problem in maintaining production and for the last half of the year, owing to lack of man power, it was necessary for some mines to change from seven to six days per week schedule. At Cornwall, Pa., the mine operated by the Bethlehem Steel Co. produced approximately 2,000,000 tons of crude ore and 1,200,000 tons of iron ore concentrates, a decrease of about 10 per-cent compared with the previous year. Railroad haulage in the open-pit at this mine was discontinued, being replaced by Mack trucks of approximately 30 tons' capacity. At the Mt. Hope mine in New Jersey, the Warren Foundry and Pipe Corp. produced about 195,000 long tons of crude ore obtaining 70.000 long tons of lump ore and 35,800 long tons of concentrates. An additional 24,500 long tons of concentrates was produced from a stock pile of 47.000 long tons of crude ore accumulated during the latter half of 1943, following the fire in their old dry mill. All of this material was handled through their Brown

Jan 1, 1945

By N. N. Breyer, W. R. Warke, S. Dinda

A model for the low-temperature peak, LTP, in fcc metals is presented. In high stacking fault energy metals, e.g., aluminum and nickel, it is proposed that a reversible dislocation glide and climb process might give rise to the observed high relaxation strengths and activation energies equivalent to volume self-diffusion values. In low stacking fault energy metals such as copper, gold, and silver, dislocation climb is energetically unfavorable at T < 0.5 Tm and the relaxation process is therefore mainly one of reversible glide. This model is used to explain the effect of a change in grain size and impurities on the LTP. THE low-temperature grain boundary damping peak, LTP, in spectroscopically pure aluminum,&apos; copper,17&apos; gold,2 nickel,3 and silver4 has recently been the subject of a detailed investigation by our laboratory. The main results are summarized in Table I. An empirical relationship was found between the peak relaxation strength, AE, and the width of the dissociated dislocation, do,* given by: do = µa2/24p? (Ref. 5) [I] where p is the shear modulus, y is the stacking fault energy,6-8 and a is the lattice parameter, Table 11. 4E is plotted against do in Fig. 1. Two regions are apparent: region (a)! which contains all but one of the metals, where AE decreases linearly with increasing do, i.e,, AE 1/do; and region (b), where ?E is approximately independent of do. A similar trend is observed when the ratio Qp/QL is plotted as a function of do, Fig. 2. (Qp and Ql are the activation energies for the peak and for lattice diffusion, respectively). In the past, when Qp and QL were found to be comparable, the relaxation peak was explained in terms of grain boundary sliding.10 The equivalence of Q, and Qb. the activation energy for grain boundary diffusion, prompted the suggestion that it was a consequence of reversible grain boundary migration on an atomic scale." A new model for the LTP, which is based on the experimental relationships in Figs. 1 and 2, is presented. In region (a) it is suggested that stress relaxation occurs through the reversible glide and climb of grain boundary dislocations; in region (b) only reversible glide can take place. The resultant effect on the grain boundary might be sliding or "a bowing out", but, since the total distance moved will be 50A, the atomic movements are considered of primary im- portance. It must be emphasized that this is only a qualitative model, but at the moment it appears the most likely way to explain the widely varying, but re-

Jan 1, 1969

By C. R. Van Hise

[Concluding Contribution of Prof. Van Hise to the Discussion of his Paper, and Others on the Same General Subject, presented at the Washington Meeting, February, 1900 (see Trans., xxx., 27, 177, 323, 424, 5 S); also of the contributions of Vogt, De Launay, Beck, Lindgren, hemp, Rickard, Bain, Keyes, Collins and Adams, presented at the Richmond Meeting, February, 1901, and printed in the present volume.] IN June, 1900, shortly after my paper was published in the Transactions, I made a briefer statement* before the Western Society of Engineers covering the same `round, which, in certain respects, is somewhat of an improvement. For instance, instead of using the terms descending and ascending with reference to the waters resulting in the two concentrations, my modified statement is as follows " The first concentration of many ore-deposits is the work of a relatively deep water-circulation, while the reconcentration is the result of reactions upon an earlier concentration through the agency of a relatively shallow water-circulation. Commonly the deep water circulation is lacking in free oxygen, and contains reducing agents, and the shallow water contains free oxygen. The deep water is therefore a reducing, and the shallow water an oxidizing agent."† Of the papers upon ore-deposits which, in vol. xxx. of the Transactions, follow my own, or which were presented at the Richmond meeting, a considerable number are wholly confirmatory of the conclusions which I have presented. Among these are the Washington paper of Emmons upon the Secondary Enrichment of Ore-Deposits‡ and his discussion at Richmond of other papers,§ that of Weed upon the Enrichment of Gold and Silver Veins,[ ]the discussion of Emmons&apos;, and at Richmond of Weed&apos;s paper by Collinst and Prof. De Launay,† the paper of Lindgren on Metasomatic Processes in Fissure Veins,¶ that of-Rickard upon the Formation of Bonanzas in the Upper Portions of Gold Veins,** and the remarks of Bain upon the Mississippi Valley lead- and zinc-deposits.†† It is therefore un-

Jan 1, 1902

By William Colby

INCREASING governmental control of human activities seems inevitable. Within the present generation railroad rates and the public sale of water, gas and electricity have been subjected to rigid regulation. The field of control is slowly but surely being enlarged, and it is the object of this paper to outline in brief space this tendency toward increased governmental regulation, as far as mineral resources are concerned. Our, dual form of government complicates the problem. We must deal not only with the powers of the Federal Government, but also with those of the individual States. In order to approach this question intelligently we must have some conception of the powers and jurisdiction of the States and the United States, respectively, over mineral lands and mineral production. Starting with the Federal Government we find it never owned any public domain within the States that formed a part of the thirteen original colonies and, for historical reasons, the same is true of Tennessee and Texas. The Mid-Western States were erected out of the public domain which was acquired by the United States through cession from the original States or by purchase from foreign nations. Congress early in the last century adopted a policy of leasing public lands containing lead deposits in a portion of this Mid-Western territory, but later abandoned that policy and disposed of such public, lands, mineral and non-mineral, outright so that they long since have practically all passed into private ownership and become subject to the general jurisdiction of the respective State governments. In the great public domain lying west of the Mississippi River, and in portions of some of the Southern States, the Federal Government adopted a new mineral land policy following the discovery of gold in California. (Acts of Congress of 1866, 1870, and 1872.) The mineral lands within these States, instead of being disposed of on the game basis as agricultural lands, as occurred in the Mid-Western States, were segregated from agricultural lands and sold under special laws intended to encourage mining, giving the miner the free right to locate and work these mineral lands without paying any royalty to the Federal Government. A miner could also obtain at slight expense a complete

Jan 1, 1930

By K. J. McGrew, J. W. Murphy

Introduction Maximization of profit consistent with environmental protection is the principal goal of new applications development for any conventional or in situ mining technique. Efficient evaluation of all the parameters that contribute to mining costs and production hinges on proper design and evaluation of testing programs and data. The program discussed uses several field and laboratory procedures to estimate ore deposit characteristics and optimize lixiviant compositions. Ore characteristics and lixiviant compositions are then used in a long path leaching test (stream tube test). Stream tube test data are analyzed by mathematical models with computer assistance to predict such wellfield rate parameters as target metal production, lixiviant consumption, and restoration. When these predicted rates are combined with market values for target metals, capital expenditures, prices of lixiviant chemicals, and other economic variables (labor costs, power rates, and licensing fees), an assessment of the relative feasibility of various proposed mining plans is possible. The flowsheet in Fig. 1 illustrates this process. [ ] Field and Laboratory Procedures In general terms, the procedures followed in the evaluation of an in situ leaching application aim at accomplishing: •rapid leaching and maximum recovery of the target metal in a marketable form, •low consumption of lixiviant chemicals, •unquestionably satisfactory restoration of the mined aquifer, and •minimization of capital and operating costs for the above through development of an optimum mine plan. Keeping these goals in mind, the following minimum test program is generally recommended. Geology •Estimate of ore reserves and their variability. •Average disequilibrium value for uranium deposits. •Ore thickness, depth to ore, water level, degree of confinement, and consolidation. •Characterization of quality and quantity of other ore deposit constituents (e.g. sulfide minerals, ion exchange parameters). Hydrology •Single well pump and injectivity test. •Downhole vertical permeability test to compare flow rates of barren and mineralized formations. •Groundwater quality as it may affect licensing, hydro metallurgy, and restoration. Hydrometallurgy • Flask or autoclave tests for optimization of lixiviant parameters and determination of specific reaction rate constants. • Flask or autoclave tests for assessing amenability of lixiviant solutions with ore, consumption of lixiviant, stability of metal in solution contacting ore, and environmentally important species mobilized. • A long-path leach test for modeling the behavior of the lixiviant solution flowing through a long mineralized streamline (stream tube testing). •Metal recovery tests from lixiviant solutions (ion exchange, electrowinning, etc.). •Lixiviant regeneration tests. •Environmental restoration tests.

Jan 1, 1985

By Albert Sauveur

THE following experiments were conducted in order to study the influence of the rate of cooling through and below solidification on the dendritic structure (macrostructure) and microstructure of some hypoeutectoid steel. The steel selected was of commercial grade and had the following composition: C, 0.40 per cent.; Mn, 0.85; Si, 0.70; P, 0.099; S, 0.043. After melting in vacuum in an Arsem furnace, the various samples were allowed to solidify and to cool to room temperature as indicated in Fig. 1. Samples were thus obtained representing all possible combinations of slow and fast cooling through the various ranges of temperatures indicated, namely: (1), zone of solidification or primary crystallization, (2) zone of granulation, and (3) zone of secondary crystallization. The location of the different temperature zones in the iron-carbon equilibrium diagram is shown in Fig. 2. The authors adopted. Belaiew&apos;s notations. The designations of the various samples readily indicate their treatment, as will be apparent from Table 1.

Jan 1, 1930

By Allen D. Garrison

THE chemistry of clays and shales has been assuming increasing importance in the petroleum industry, and two factors have greatly influenced this trend. The first has been the growing evidence that the marine shales are source beds, and that the petroleum compounds have migrated to the sand reservoirs overlying or underlying these shales: the second has been the demand for drilling fluids better adapted to penetrate these marine shales without difficulty and expense. ORIGIN AND GENERAL COMPOSITON OF CLAYS AND SHALES Clays, shales and surface soils are all closely related materials. They are mixtures of finely divided compounds formed during the weathering of the solid crust of the earth. Their nature is essentially colloidal; that is, their behavior is determined by the state of division of the materials and the surface reactions of the smallest grains. Many of their chemical changes affect only the exposed areas and do not involve the interior of the grains of matter. The extent of these reactions is more nearly proportional to the area of the substances than to their mass, therefore it is possible for a small amount of a material in an extremely fine state of division to completely dominate the character of the mixture. More than 83 per cent of the crust of the earth is composed of three elements-oxygen, silicon and aluminum. Consequently, the corrosion products of the crust are predominantly aluminosilicates, or compounds of aluminum, silicon and oxygen. If we add the compounds of six elements-iron, calcium, sodium, potassium, magnesium and hydrogen-more than 98 per cent of the crust has been accounted for. These six elements, together with the first three, also appear in soils, clays and shales. But direct chemical analysis is of little value in describing the nature of such materials. Many chemical individuals may be present in variable amounts, and the extreme subdivision of any one of the individuals may contribute qualities that dominate the mixture.

Jan 1, 1939

By Persifor Frazer

IN his “Final Report," Vol. II, part second, p. 763, Prof. Rogers sums up the metalliferous veins of the mesozoic sandstone by remarking that these are not associated with dykes or trap-rock, but are independent metalliferous injections. But singularly enough, in enumerating the different kinds of ores, no mention is made of

Jan 1, 1877

By Jackson M. Langton

Substantial evidence supports the theory that high-angle faults and overthrusts in the Morenci-Metcalf region were initially caused by a Late Precambrian-Early Paleozoic stress field. These faults were reactivated in Late Paleozoic-Early Mesozoic time which completed the structural framework prior to the Laramide Orogeny. Excluding an interruption by diabase dikes and sills, Paleocene-Eocene magmas invaded the pre-existing structures and became progressively more sialic in composition and nearer to the surface with each subsequent injection. The last sialic intrusion was highly explosive, rendering the country rocks more permeable for hypogene and supergene activity. Widespread dilation, instigated by uplift and subsequent magma intrusion, caused extension to the northwest and southeast. A major locus of hypo gene alteration and mineralization appears to be centered around the south and southeast periphery of the youngest granite porphyry stock. A potassic, sulfide-deficient core is telescoped by a pyritic, phyllic zone which in turn is enveloped by widespread propylitic alteration.

Jan 1, 1974

By Milton E. Wadsworth, J. Brent Hiskey

Galvanic interaction between particulate chalcopyrite (CuFeS2) and copper results in the rapid conversion of chalcopyrite to chalcocite. The effects of temperature, surface area, concentration of sulfuric acid and agitation were systematically evaluated. The kinetics were found to be controlled by a steady-state current flow controlled by the effective anodic and cathodic surface areas involved in the galvanic couple. The experimental activation energy was 11.5 and stoichiometric data and reaction products have been characterized. The overall kinetic system has been evaluated based upon an electrochemical model.

Jan 1, 1974

By F. P. Haver, M. M. Wong

The Federal Bureau of Mines has developed a leach= electrolysis method for recovering lead from galena (PbS). Flotation concentrate is leached with ferric chloride (FeCl3) solution to obtain lead chloride (PbC12) and elemental sulfur, PbS + 2FeC13 -+ PbC12 + 2FeC12 + Sº. Over 99% of the P~S in the condentrate is converted to PbC12. The leach solution, composed of brine (NaC1) and FeC13, dissolves the PbC12 as it is formed, leaving a residue of elemental sulfur plus gangue. Very pure PbC12 (>99.9%).is crystallized from the leach filtrate on cool- ing and is subsequently electrolyzed in a fused-salt bath to obtain molten lead metal (>99.9% Pb). Spent leach solution (FeC12) is regenerated for further use by reaction with the chlorine obtained in the electrolysis of lead chloride, and other values, such as Ag, Cu, Zn, and Sº, are recovered by additional treatments of the leach solution and leach residue. This paper discusses results and conditions of the leaching and electrolysis operations.

Jan 1, 1976

By Walter C. Holmes

IN the recently published book entitled "Man in a Chemical World," by A. Cressy Morrison, the several pages discussing explosives were included in the chapter on "Serving Industry." Such a classification is entirely correct, as blasting explosives function only as a tool for accomplishing certain useful work, a tool which is completely destroyed in one use. Explosives are so important to industry and to modern society, in fact, that it seems impossible to imagine the existence of civilized nations without access to commercial explosives as ready servants. Two main types of explosives are now in use, the low-velocity or deflagrating type, such as black powder, which is adapted for use in coal mining and other applications where a slow, heaving effect is desired, and high explosives of the dynamite type,

Jan 1, 1938

By C. R. Hocott

THE viscosity of the oil in the reservoir is one of the properties that influence its movement through the sand to producing wells. Measurements of viscosity, therefore, are pertinent to problems associated with well behavior and with the estimation of recoveries, and afford an indirect means for partial evaluation of various methods of controlling reservoir behavior. The effect of dissolved gases on the viscosity of crude oil has been determined,1,2 but no data have been published on the viscosity of repre-sentative samples of reservoir oils. This paper describes a simple instrument that has been used to determine the viscosities of a number of subsurface oil samples at the temperatures and pressures existing in the reservoirs, and presents the results of the determinations for typical fields.

Jan 1, 1940

By Persifor Frazer

In his " Final Report," Vol. 11, part second, p. 763, Prof. Rogers sums up the metalliferous veins of the mesozoic sandstone by remarking that these are not associated with dykes or trap-rock, but are independent metalliferous injections. But singularly enough, in enumerating the different kinds of ores, no mention is made of

By P. J. G. duToit

The continually growing shortage of skilled underground miners, the escalating costs of labor, supplies and equipment, and the indisputable example of "what can be done" by our friends in the space-travel field, seem to be catalysts that are accelerating improvements in underground mining technology. The search for an economic, automated continuous excavation method that would produce rock at the mining face in sizes suitable for automated transportation directly into the rod-, ball-, or autogenous grinding mills is continuing. New mining methods and techniques were devised and many improvements on old methods and techniques came forth at an increasing pace that reflected a widely spreading policy among mining men to shun the shackles of conservatism and to forge ahead and venture into newer ideas.

Jan 2, 1967

By Edward H. Robie

MANY engineers currently are working harder than usual, in part because of the demands being made upon them for increased production in the war effort, and in part because engineers are in short supply so that there is more to do for those who are available. In some instances the question has come up as to what additional payment, if any, should properly be made for overtime work, and to what extent is such payment legally permitted under the rules of the Salary Stabilization Board. Most engineers employed in an executive, administrative, or outside salesman capacity are not paid for overtime. They are paid for doing a job instead of for the hours they put in, and are free to do all the unpaid home work they feel they should do after dinner, as well as to do a bit of thinking and worrying during wakeful hours in bed. But engineers employed in a strictly professional capacity normally have standard office hours. Some employers pay for overtime and some don&apos;t. Their practice as it existed on Jan. 25, 1951 may be continued. In the absence of such practice at that time, the Salary Stabilization Board says that the engineer may now receive additional compensation up to his straight-time rate for an extended work week. No formal approval of the Board is required. "A professional engineer," in the mind of the Board, "is a person employed in a professional capacity, who, by reason of his special knowledge of the mathematical and physical sciences and the principles and methods of engineering analysis and design, acquired by professional education and practical experience, is qualified to practice engineering." Inducted Engineers A letter from a young man just inducted into the service and fearful that his engineering training is not going to be utilized reached us last week from Fort Riley, Kan. The AIME, cooperating with the other Founder Societies, is doing what it can, through the Engineering Manpower Commission, to see that engineers are not being wasted in the military establishment. So we passed this young man&apos;s letter along to T. A. Marshall Jr., executive secretary of that Commission. Mr. Marshall tells us that the normal procedure now being followed by the Army in handling Selective Service inductees is to have them first complete 16 weeks of basic training before assignment to specialized categories. During that time they are classified. If one has an engineering degree he should be classified as scientific and engineering personnel at the end of the basic training period. He should then be transferred to a technical detachment and assigned an MOS (Military Occupational Specialties) reflecting his education. If a young man is looking for a commission, it might be added that the current policy in the Army is to transfer to OCS (Officer Candidate School) applicants for commissions in the infantry only. The local unit commander can give information on this point, based upon the aptitude shown in tests. In view of the current shortage of engineers, it is believed that a young man should seriously consider remaining in enlisted status unless he can obtain a commission in a branch of the service that can make full use of his technical skills. His work may thus be more to his liking even if his uniform is not. New York or Atlantic City? In which place is it preferable to hold the annual meeting of a professional society like the AIME-New York or Atlantic City? That is, a winter meeting. The American Society of Mechanical Engineers has held its recent meetings at Atlantic City, with increasing attendance and satisfaction. The American Institute of Chemical Engineers chose Atlantic City for its recent December annual meeting. Only twice has the AIME ever met in this famous seashore resort: in 1898 and 1904. Chief advantages of going to Atlantic City over New York are that technical sessions are better attended, there being little else to do there in Winter; the cost to members is less, and hotel facilities are better adapted to a large meeting. As to cost, take a banquet, for instance. The Chalfonte-Haddon Hall, which caters especially to winter conventions, charges about $7 for a banquet dinner of standard quality. A similar dinner at the Statler in New York would cost about $8.50, and about $10.50 at the Waldorf-Astoria. (The charge for tickets is somewhat greater than this because of the cost of music, programs, flowers, and other incidentals.) Rooms, too, are somewhat less at Atlantic City, two in a room being accommodated for about $7 per day each, compared with $7 to $10 at a headquarters hotel in New York. On the other hand, AIME headquarters is put to some extra expense for staff travel, food and lodging, and members living in New York and environs are forced to pay a hotel bill. New York, of course, has more varied amusements to offer, plenty of big stores, and the glamour of a big city. The choice may be discussed at the forthcoming meeting in New York. In the meantime if any reader cares to express an opinion one way or the other we shall be glad to hear it. College Scholarships Most parents of children in the later stages of high school find it necessary to give some consideration to the cost of a college education. Although salaries have increased substantially it seems that the cost of the necessities of life, such as food, housing, and maintaining the family automobile, have gone up even more, so the problem of financing the children&apos;s education is as acute as ever. Many overlook the possibility of scholarships, or feel that only a student at or near the top of his class has a chance to get one. As a matter of fact, close to 150,000 scholarships and more than 15,000 fellowships, worth some $42,000,000, are available in 1200 American colleges and universities. Those who are interested should send 55¢ to the Superintendent of Documents, Government Printing Office, Washington 25, D. C. for a 248-page publication just issued by the U. S. Office of Education, entitled "Scholarships and Fellowships Available at Institutions of Higher Education."

Jan 1, 1952

THIS chapter and Chapter 19 deal with the heat quantities involved in open-hearth steelmaking, including the thermal efficiency of the furnace as a generator of high-temperature heat, the heat storage in the steel and slag produced and in the furnace walls, and the heats of the various chemical reactions involved in combustion, in the formation of slag, and the refining of steel. The fundamental laws to be considered are the first two laws of thermodynamics as applied to problems involving sensible and potential (or latent) heat only: 1. Heat input equals heat outflow plus storage. 2. Heat may be transferred only from a hotter body to a colder one. The first of these laws relates to the various heat quantities or the heat balance of the process. No one has as yet made an open-hearth heat balance that came out almost exactly balanced. The cause probably lies in the difficulties of accurate temperature and flow-rate measurements at the high temperatures involved and the inherent complexities in flow distribution and air leakage present in any real open-hearth furnace system. Some idea of the magnitude of the heat quantities involved can be obtained by a brief, crude outline of the heat balance of a 90-ton heat of steel. We will assume a 60 to 70 per cent hot- metal charge in a fairly fast working and only moderately efficient furnace, burning fuel oil, with a fuel consumption of around 4 million Btu per net ton of ingots produced. The time from start of charge to tap is 9 hr. During this period, the oil burned represents 360 million Btu and the sensible heat in the preheated air at the port ends is 117 million Btu, so that the total heat input at the ports is 477 million Btu. Heat stored in the steel and slag at the end of the heat, plus the various amounts absorbed by certain bath reactions, amounts to a total of 195 million Btu, but 120 million of this is supplied by the heat in the hot metal and by various heat-evolving reactions in the bath,

Jan 1, 1951

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation&apos; can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation&apos; in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of