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By S. H. Ward

Since the advent of the first airborne electromagnetic system, it has been evident that such systems were inherently limited to shallow depths of exploration of the orderof 100 to 200 feet. Hence in 1948 the author and his associates commenced a study of the feasibility of applying natural audio frequency magnetic fields to investigation of the electrical properties of the subsurface in order to provide a system capable of overcoming this limitation. This research culminated, in the summer of 1958, in the development of a new airborne prospecting device — AFMAG. This device has detected surface massive sulphide bodies while flown at heights as great as 3000 feet. Hence, by inference, it is deduced that it could find similar sulphide bodies if they were buried 2500 feet below surface and the aircraft flown at 500 feet. Thus a considerable improvement over conventional airborne electro-magnetic systems is obtainable with AFMAG. Airborne exploration in mountainous terrain involving deep valley fill now becomes possible. Examples are presented of the results of actual airborne AFMAG test surveys over known deposits of massive sulphide mineralization. Interpretation of the data is discussed with particular reference to the knowledge of size, dip, depth, depth extent, and conductivity of causative bodies as deduced from the flight records. The possibility of mapping major geologic structures, for both mining and oil exploration purposes, is discussed with the aid of examples of airborne AFMAG data. INTRODUCTION Electrical prospecting with natural audio frequency electromagnetic waves as a source has, within the last three years, become a practical reality. Both airborne and ground survey instruments under the trademark "AFMAG" (for audio frequency magnetics) have been used successfully in the search for conductive mineral deposits. It is the object of this paper to discuss the principles of airborne AFMAG and to illustrate its application by means of examples obtained over known geological situations. WHY AFMAG? In view of the large number of good airborne electromagnetic systems available for purchase or contract surveying, one may well ask, "Why another new system?". Primarily the answer lies in the fact that AFMAG does not suffer from the very limited depth of exploration available with, and inherent in, any conventional airborne electromagnetic system. AFMAG is not conventional insofar as an artificial transmitter is not required. Only a receiving and detecting device is employed. The electromagnetic fields measured are those from millions of electrical discharges in the atmosphere (e.g;..- lightning strokes). Their random distribution in time and space make these fields difficult to employ and it is only with recent advances in the electronics of geophysical instrumentation that this has become possible. A second reason for AFMAG and one of its

Jan 1, 1961

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-

Jan 1, 1971

By R. E. Gilchrist, R. F. Nielsen

When a gas is displaced by mother in a porous medium, and there is a relative immobile liquid present. there is a transition zone in which the gas composition varies from essentially that of the original gas to that of the injected gas. The change in extent of this zone with time may be governed by a mixing process in the direction of flow and by the rate of establishment of gas-liquid equilibrium, if the gases are appreciably soluble in the liquid. The relative importance of these two factors in deterri~ining the growth of the transition zone is discussed, with appropriate equations and experimental data. INTRODUCTION The various solution methods of oil recovery involve a transfer of the components of a mixture, whether within a single phase or between a liquid and gas. The similarity of a natural porous medium to systems used in separation and chromatographic processes makes it seem reasonable that certain concepts used by chemical engineers in "mass transfer" might be applicable to petroleum reservoirs. One approach, the HETP (height equivalent to a theoretical plate), involves a distance or length of time over which equilibrium might be con. sidered as established. Another approach involves direct use of a rate of mixing or rate of establishment of equilibrium. The latter approach has been preferred in relation to production problems. DISCUSSION AND PROCEDURE When a gas or liquid in a porous medium is displaced by one of different composition but miscible with it there will be set up a transition zone in which the composition varies from cssentially that of the original fluid to essentially that of the injected fluid. If the fluid being displaced is a gas, and there is a relatively immobile liquid present, the transition zone may be

By H. O. McLeod, J. M. Campbell

Data analysis of pentane and hexane adsorption from natural gas in a fixed bed of silica gel shows that constant length mass transfer zones form, the curvature of the adsorption isotherm controls the growth of the mass transfer zone and surface diffusion of molecules inside the silica gel particle controls the mass transfer rate. Curvature of the hexane isothem is more than the curvature of the pentane isotherm. Because of this curvature the hexane adsorption zones reached a constant length. In contrast, the pentane adsorption zones were always increasing in length during each run. A procedure was developed to obtain correct mass transfer coefficients using effluent curve slopes. These transfer roefficients increase with the amount of hydrocarbon adsorbed on the silica gel particle. The characteristic shape of the hexane effluent curves also show that molecular diffusion inside the silica gel particle controls the adsorption rate of pentane and hexane. INTRODUCTION The purpose of this study was to determine the mechanisms that control the dynamic adsorption of hydrocarbons from a natural gas onto silica gel. Before one can deal effectively with multicomponent adsorption, the transfer mechanisms by which a single hydrocarbon component is adsorbed from the gas stream must be defined. Two principal investigations of this system have been published ' and indicate that diffusion through the gas around the particle controls the adsorption rate. Some of the experimental observations in each study either do not support this transfer mechanism or are inconsistent with the mathematical model used in analysis. In this study surface diffusion of molecules inside the particle controls the mass transfer rate of pentane and hexane. This mechanism is indicated by the effluent curve shape for a constant length transfer zone and by the variation of the mass transfer coefficient with concentration of the adsorbed hydrocarbon. THEORY AND DEFINITIONS — MATHEMATICAL MODELS Mathematical solutions for the isothermal adsorption of a trace component from a carrier gas are derived from three relationships: the mass balance or continuity equation, the equilibrium relationship between the gas and solid phases, and a mass transfer rate equation. The transfer rate is proportional to the adsorbate concentration gradient within either the gas or solid phase. Mathematical solutions of these equations usually give the adsorbate concentration as a function of time and distance from the bed inlet. That part of the bed in which the adsorbate concentration changes from a maximum to a minimum value is called the transfer zone. This transfer zone is directly related to a plot of the effluent concentration vs time which has a characteristic S-shape. This general shape is determined by the continuity equation and occurs in many processes of diffusional transfer.

Jan 1, 1967

By Thomas Donnelly

Introduction THE Province of San Cristobal is situated on the south side of the island of Santo Domingo about 25 miles west of Santo Domingo city, the capital of the republic. The copper mineralization is found about 1.-CAMP BUCARO. THE TOP OF THE RIDGE IN THE BACKGROUND MARKS THE CONTACT OF THE LIMESTONE AND TUFFS. S miles north of the town of San Cristobal, in the section known as Bucaro Hill; in San Francisco Hill; on the Nigua River; and on the Jaina (Liver. The district is reached by automobile from Santo Domingo city over an excellent road for 25 miles to San Cristobal, and then, by horse-back 6 or 8 miles up the Nigua River to what is locally known as "Camp

Jan 8, 1915

By K. P. Fournier

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus:

Jan 1, 1966

By J. H. Brophy, M. H. Kamdar, J. Wulff

A constitutional diagram for the Ta-W-Re alloy system is presented. Rhenium dissolves in the complete range of solid solutions between tungsten and tantalum up to 48 wt pct in tantalum 'to about 30 wt pct in tungsten. Intermediate x and u phases only are found. X-ray diffraction and fluorescence, metallography and melting-point measurements were employed. THE constitution diagram of ternary alloys of tungsten, tantalum, and rhenium for temperatures above 1000°C is reported in this paper. Alloys in this system rich in tantalum and tungsten are of interest for high-temperature applications, and those rich in rhenium for electronic applications. No ternary phase diagram appears to be available in the literature. The three-component binary diagrams have been previously established1-3 and the present ternary data are consistent with these. EXPERIMENTAL TECHNIQUES Commercially pure tantalum (99.7 pct), rhenium (99.99 pet), and tungsten (99.9 or 99.95 pct) powders were purchased from Fansteel Metallurgical Corp., Chase Brass and Copper Co., and Fansteel or Westinghouse Electric Corp., respectively. These powders were pressed without binder and arc-melted under helium. The preparatory and analytical techniques employed were identical to those used for the Ta-Re system investigation carried out in this laboratory.324 These included X-ray diffraction and metallographic phase identification, X-ray fluorescent and wet chemical analyses, solidus determinations and heat treatments in a resistance-heated tantalum-filament vacuum furnace. For microstructural examinations standard mechanical polishing techniques were used through diamond laps. Polished speciments of all compositions were etched by swabbing with 4 parts HI?, 4 parts HNO3, and 1 part H20. Since the microstruc-tures of alloys containing one or two phases closely resembled their counterparts in the respective binary systems, typical examples are omitted in this presentation. In all the alloys examined, it was possible to observe the number of phases present. Particularly when there were small amounts of one phase involved, it was possible to identify it only by a combined conclusion based on X-ray diffraction, position of an alloy in a composition series, and the phase rule. A total of 100 different alloy compositions was arc-melted and studied in the as-cast condition metallographically and by X-ray diffraction. Specimens of each of these compositions were heat-treated at 2680, 2530, and 2020°C for 1, 2, and 4 hr, respectively. Those which were treated at 2020 were given a preliminary homogenization treatment at 2500°C for 1 hr. Specimens of 25 alloys were heat-treated at 1200o C for 168 hr. Solidus temperature measurements were made by the detection of incipient melting in eighteen alloy compositions. The metallographic and X-ray diffraction results are summarized in Table I. Graphically, this information appears in the isothermal plots of Figs. 2 and 3. Within the accuracy of the experimental methods, two such plots are sufficient to locate these data, since the results for 1200°C were similar to 2020 and those at 2530 resembled 2680

Jan 1, 1962

By J. W. Givens, P. B. Crawford

A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. INTRODUCTION One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of water-flooding or gas cycling programs.1-5 However, there arc few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures.6,7 It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee8 it has been widely used to study numerous types of fluid displacement problems. The potentio- metric model can be used for fluid displacement studies when the following assumptions are valid: (a) steady-state conditions exist; (b) the mobilicy ratio is one; and (c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN — ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattem with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattem expressed as a per cent. The cross-hatched areas of this

Jan 1, 1967

By D. F. Malott

The Michigan Dept. of State Highways makes extensive use of geophysics for subsurface surveying which would be applicable for uses in other fields. Examples of resistivity surveys are given which include a proposed large-volume excavation with suggestions for land use after excavation, subsurface evaluation for engineering design, and a subsurface survey for land appraisal. An example of a combined refraction seismic and resistivity survey is shown where the resistivity is used for outlining the unconsolidated soils, while the seismic method is used to outline bedrock and to evaluate it for rippability. A refraction seismic survey at the bottom of bridge caissons for evaluation of bedrock uniformity and a rehtive aid in assessing rock strength is reported. These past several years have been a period of unprecendented construction and commercial expansion. Vast private manufacturing complexes and government road, power, and office projects are being built or are in planning stages. Nearly everywhere, municipalities are expanding outward and upward. Many towns are developing into cities and many cities are displaying new skylines, and the building boom shows little sign of slowing down.

Jan 1, 1970

By . M. Muskat

A THEORETICAL consideration of the mechanics of various water-flooding systems with the viewpoint of comparing their relative merits involves the study of two fundamental properties of such systems. On the one hand, it is important to determine the efficiency of the flood as measured by the percentage of the total area that is swept out by the encroaching water before water actually reaches the output wells. This is really a measure of the regional tendency of the water to "bypass" the oil. On the other hand, the various systems must be compared from the viewpoint of their resistances which determine the rate of fluid production obtainable for given pressures maintained at the water input wells. The first of these questions has been studied and very definite answers have been obtained by means of simple electrolytic models.1 These models showed that, in an ideal system, the percentages of the areas flooded out before water reaches the output wells are about 57 per cent for the direct line-drive flood (the input and output wells being equally spaced and placed in alternate parallel lines), 74 per cent for the regular five-spot network, and 79 per cent for the seven-spot network. With respect to the efficiency of the usual flooding arrangements, they are, therefore, given quite accurately by the above numbers. With regard to the resistances of the flooding networks, electrical conduction models have also been used successfully2 and are well adapted to the problem of determining experimentally the pressure distribution and streamlines, or over-all resistances of specific flooding networks. However, such models do not permit readily a study of the effect of changing dimensions or configuration within a network, since a new model must be made up for each set of dimensions considered.

Jan 1, 1933

By David Cole

THE appearance of the Wilfley table in 1897 marked an epoch in the art of concentration of ores. The table has merited and received an almost unprecedented measure of public approval, lasting through its whole patent life. It has been very little improved in itself, or improved upon by competitors. The new machines bidding for popular favor have been of the Wilfley family, but without ability to do markedly better work than the parent m:-chine, or to (to more work except by the use of superimposed decks, the latter having obvious disadvantages. FIG. 1.-The- Butchart RIFFLE System. During the past three years there has been developed at Morenci a new type or arrangement of riffles applicable to the Wilfley type of concentrating table which corrects many of the objectionable features or limitations of the older system and obviates most of the difficulties encountered with it, particularly when handling ores having a low ratio of concentration. The new type is known as the Butchart1 riffle system, and its general arrangement is shown in Figs. 1 and 2.

Jan 2, 1915

Thomas Haight Leggett, London, Eng. (communication to the Secretary): Mr. Hammond has given us a concise yet complete description of the Witwatersrand gold-fields, and the character of the operations which have resulted in their remarkable development.

Jan 1, 1902

Jan 1, 1970

By C. E. Corson

THE experiments of which the results and significance are set forth in this paper do not by any means cover the whole subject of the heat-treatment of the material referred to, yet they constitute a contribution to that general subject, rather than to the special department of annealing. The material here considered is acid open-hearth steel, containing from 0.50 to 0.80 per cent of carbon, with a nearly uniform percentage of other elements. This class of steel is rapidly increasing in commercial importance. It is even rumored that the rail-specifications of some railroads will hereafter require open-hearth steel. Yet this particular grade seems to have received less study and description from the standpoint of the metallographist than many others. The investigation here described was directed to the following points:-Steel containing about 0.50 per cent, of carbon : 1. The structure as related to the temperature, at the same rate of cooling; 3. The structure and physical properties as related to temperature at different rates of cooling; 3. The structure and physical properties as related to different finishing-temperatures and different rates of cooling; 4. The bearing of these observations upon the statement of Prof. Albert Sauveur.1

Sep 1, 1906

By B. E. Warren

Jan 1, 1965

By Gorr W. W., Wyche E. H, R. Smith

The combination of high strength and corrosion resistance of cold-worked 18 Cr, 8 Ni steel has been advantageously utilized for some time, particularly in aircraft and rail car structures. There are, however, certain limitations on the use of such materials because the high strengths can be obtained only by cold-working, limiting the available products to sheets, strip, wire and tubes. The authors sought to overcome these limitations by resorting to precipitation-hardening, which has been used so successfully in nonferrous metallurgy but only to a limited extent in iron-base alloys. Accomplishment of this objective not only overcame the limitations, but also effected certain improvements in mechanical and other properties. This paper is an account of the development by Carnegie-Illinois Steel Corporation of a precipitation-hardening 18-8 stainless steel (called Stainless W‡ and tentatively identified as type 322). A description is given of its composition and metallurgical characteristics, heat-treatment, physical and mechanical properties and corrosion resistance. Development of the New Steel For a considerable length of time the authors were unable to determine the mechanism of the precipitation-hardening process that had been noted by Ffield18,19 in 18-8 Ti or 18-8 Cb after cold-working and reheating to moderately elevated temperatures. All known variables were exhaustively studied, but with little success. However, results began to indicate that chemical composition was the most important variable, particularly the ratio of austenite-forming to ferrite-forming elements. The investigators then focused their attention upon the composition, and, in particular, upon the element titanium and its mode of alloying in the presence of other elements. A heat was obtained that could not be brought to the softness level of annealed 18-8. The response to cold-straining and aging* was very marked by previous standards, and, more important, cold-straining was found to be entirely unnecessary to produce the precipitation-hardening effect. The chemical composition of this heat was: C, 0.06 per cent; Mn, 0.54; P, 0.016; S, 0.016; Si, 0.58; Ni, 7.28; Cr, 17.60; Ti, 0.90; Al, 0.17. For some time the development work, particularly on composition, was carried

Jan 1, 1947

By Gorr W. W., R. Smith, Wyche E. H

The combination of high strength and corrosion resistance of cold-worked 18 Cr, 8 Ni steel has been advantageously utilized for some time, particularly in aircraft and rail car structures. There are, however, certain limitations on the use of such materials because the high strengths can be obtained only by cold-working, limiting the available products to sheets, strip, wire and tubes. The authors sought to overcome these limitations by resorting to precipitation-hardening, which has been used so successfully in nonferrous metallurgy but only to a limited extent in iron-base alloys. Accomplishment of this objective not only overcame the limitations, but also effected certain improvements in mechanical and other properties. This paper is an account of the development by Carnegie-Illinois Steel Corporation of a precipitation-hardening 18-8 stainless steel (called Stainless W‡ and tentatively identified as type 322). A description is given of its composition and metallurgical characteristics, heat-treatment, physical and mechanical properties and corrosion resistance. Development of the New Steel For a considerable length of time the authors were unable to determine the mechanism of the precipitation-hardening process that had been noted by Ffield18,19 in 18-8 Ti or 18-8 Cb after cold-working and reheating to moderately elevated temperatures. All known variables were exhaustively studied, but with little success. However, results began to indicate that chemical composition was the most important variable, particularly the ratio of austenite-forming to ferrite-forming elements. The investigators then focused their attention upon the composition, and, in particular, upon the element titanium and its mode of alloying in the presence of other elements. A heat was obtained that could not be brought to the softness level of annealed 18-8. The response to cold-straining and aging* was very marked by previous standards, and, more important, cold-straining was found to be entirely unnecessary to produce the precipitation-hardening effect. The chemical composition of this heat was: C, 0.06 per cent; Mn, 0.54; P, 0.016; S, 0.016; Si, 0.58; Ni, 7.28; Cr, 17.60; Ti, 0.90; Al, 0.17. For some time the development work, particularly on composition, was carried

Jan 1, 1947

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By N. M. Langdon

INTRODUCTION. IN considering the magnificent success of Mr. Gayley's Bold experiment of applying dry blast to the blast-furnace, whereby , saving of 20 per cent. of fuel per ton of iron is effected, the question arises whether, still further economy in fuel is possible, and, if so, how it is to be attained? The manner in which the heat generated in the furnace is utilized in the production of pig-iron may be determined, by the method of Bell and Gruner, for any furnace for which the necessary data are obtainable ; and the study of the operation,. tinder various conditions, of a number of furnaces, for which such information has been worked out., should enable us to form some conclusion on the subject. The tables and calculations given below cover the operations of several furnaces reported in our Transactions; also the two furnaces using natural and dry blast in ,Mr. Gayley's experiment, for which the heat-equation has been worked out by Prof. Joseph W. Richards in his admirable discussion' of Mr. Gayley's paper, The Application of Dry Air Blast to the Manufacture of Iron, and, finally, various hypothetical furnaces.. The full list is as follows : A. Isabella furnace, with natural blast. B. Isabella furnace, with dry blast. The data stated. for A and B in Table III. are those given by Professor Richards; except that the heat-units are given for one unit of iron instead of 100 units, and some items of heat supplied, as stated by Richards, have been subdivided, the total being the same as given by Richards. (Columns A and B are introduced in Table III. for comparison with C and D.)

Oct 1, 1909