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By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data

By Eckley B. Coxe

The plummet lamp, to which I called the attention of the Institute, at the Bethlehem meeting, in August, 1871, with the improvement of the compensating ring, suggested by Mr. Heller, having come into general use for mine surveying in this country, and my attention having been called to the fact that it could not be employed in mines in which there was danger of meeting with fire-damp, I have so modified it that it can be used in all cases with safety. Mining engineers, who are in active practice in those districts where fire-damp is met with in the mines (and I am sorry to say it is becoming much more common in the anthracite regions), know how dangerous their work is when they are called upon to survey such mines, particularly when they are obliged to run lines in those parts of a mine which have been unworked, since by opening of doors, brattice, etc., to get the sights, they are liable to disarrange the currents of air, and cause any fire-damp that may have accumulated in the old workings to find its way into the levels, etc., where the party is at work. It is, therefore, very dangerous to leave an open light (such as the original form of plummet lamp) in an old breast or gangway, even when the safety lamp has shown that no fire-damp is present, for the opening of the doors, etc., may drive the fire-damp to the light, and thus endanger the lives of the engineers. The improved form of plummet lamp, now shown to you, can be used either with or without the safety apparatus. Upon the top of the plumb-bob portion of the old lamp a screw is cut, upon which a ring A is screwed. (See Plate 11.) On the external cylindrical part of this ring two small conical holes are drilled, 180' apart. The compensating ring, by which the plumb-bob part of the lamp is suspended, passes over the ring A, and is fastened to it by two small screws having conical points, which fit into the conical holes in the ring A. The safety apparatus resembles, to a certain extent, that of the Mueseler lamp. It consists of a ring B and plate C, which are united by four rods. The plate C has a cylindrical hole in the middle, and four apertures distributed radially around it. In the central cylindrical hole is fitted a conical brass chimney, which projects below the plate C, and is fastened to the latter, being kept ver-

By Lewis M. Haupt

IT has given me great pleasure to read, in the papers recently pub lished by this Society, the discussions on the subject of Technical Education, which were developed at the joint meeting held at the Franklin Institute in June, 1876; and since it was impossible for me to be present, I desire to improve this my first opportunity of adding the weight of my testimony and experience to what has been so ably presented by others. It is a subject about which the people need to be kept agitated, that their views may expand with the demands made for a higher and more thorough education. It is the public at large, the capitalist, the manufacturer, and the laborer, who are to be benefited more or less by this elevation of the standard of our professional schools, and it is but just, therefore, that the schools should look to them for the means with which to accomplish so de sirable an object. It is no doubt to the interest of a metallurgist to employ a skilled laborer who will prevent waste by properly proportioning his ma terials ; by regulating the supplies of air and fuel; by arranging his plant in the most economical manner, arid by disposing of his products to the greatest advantage. The engineer is benefited by selecting for an assistant a person able to determine the values of his factors of safety for the same materials in different forms and positions, avoiding expensive suits for damages and cost of reconsiruction; he should be able to so locate a road as best to fulfil the requirements of a through traffic, arid yet develop local industries. But I need not multiply instances to show what all will readily concede, viz.: the advantages of a theoretical education ; that was fully demonstrated at the previous special meeting, but it is still an open question whether the practical instruction should precede, accompany, or follow the theory.

By G. H. Pardue, L. H. Gollwitzer, J. H. Moran, R. L. Morris

Experimental and theoretical studies of casing-borne signals have provided data on the attenuation efect, compressive strength and shear modulus for different types of cement. These data resulted in the establishment of a definite relationship between the cement compressive strength and the Cement Bond log reading. The relationship is influenced by the casing dimensions, but is independent of the type of cement and the curing conditions. The theoretical analysis provides a mathematical statement of the phenomenon and shows that the attenuation rate is basically a function of the shear modulus of the cement and the thickness of the casing. The lab tests provided a connection between the shear modulus and the compressive strength, and permitted a comparison of the experimental and theoretical work. The results of the experimental and theoretical study have provided means of quantitative interpretation of the Cement Bond log. This interpretation is made more convenient with the use of a nomograph. INTRODUCTION Past interpretation of Cement Bond logs has been essenlially based upon a qualitative comparison between the log response in the zone of interest and the responses in the "fully cemented" and the "uncemented" intervals. Most of the variables influencing the magnitude of the signals were recognized in an earlier paper'; however, insufficient laboratory data were available at that time for quantitative evaluation of these variables. Early attempts to use the numerical amplitudes of the signals without full knowledge of their significance resulted in erroneous comparisons between various types of cement. An extensive program was undertaken to evaluate, both experimentally and theoretically, the attenuation phenomenon and to study the effects of the more common variables. A major objective of the experimental program was to obtain data on the relationship between cement-bond-tool response and physical property standards used by the industry so that practical interpretation methods could be devised. The studies included a comparison of attenuation rate with these properties as a function of time, temperature and pressure, using common sizes of casing. The main result was that a definite relationship was established between the compressive strength of the cement in inti- mate contact with the casing and the response of the cement bond tool. For a given casing thickness, regardless of the type of cement or the curing conditions used, the attenuation rate is a function of the compressive strength. A theoretical analysis showed that the attenuation rate for casing-borne signals should be a function of (among other things) the shear modulus of the cement and the thickness of the casing. The relationship between the compressive strength and shear modulus for curing times similar to those encountered in the field was determined from laboratory tests. Using this relationship, the computed attenuation rates showed reasonable agreement with the measured attenuation rates. The purpose of this paper is to report the results of the experimental and theoretical investigations and to present the first practical method for a quantitative interpretation of Cement Bond logs based on known variables. This method is applicable where the casing-borne signal is not affected by high-velocity formation arrivals. DESCRIPTION OF LOGGING TOOL The Cement Bond logging tool shown schematically in Fig. 1 has been described previously.' The tool consists of two sections: acoustic and electronic. The acoustic section contains a transmitter and a receiver, usually spaced 3-ft apart. Sonic energy emittted by the transmitter travels through the casing and is detected at the receiver. The electronic section measures the amplitude of the

By A. S. McLatchie, R. A. Hemstock, J. W. Young

Much attention has been given in the past few years to methods of increasing the recovery of oil from proven reserves. Numerous laboratories have made investigations to evaluate the possibilities of increased oil recovery by high-pressure injection of dry gas, injection of a propane slug followed by dry gas, solvent flooding. and by the injection at relatively low pressures of gases enriched with ethane and propane. Several years ago, Whorton and Kie-schnick' published the results of laboratory studies on high-pressure gas injection which showed that, in the case of light oils, recoveries could be considerably increased by sweeping the reservoir with dry gas at pressures in excess of 3,000 psig. The increase was attributed by those authors to the vaporization of oil at the invading gas front and viscosity and solubility effects produced at the front by the invading gas. Later, Stone and Crump' presented the results of a series of displacement experiments in which a light under-saturated crude oil was displaced from sand-packed columns with unusually high recoveries when the displacing gas was a rich condensate or a dry gas enriched with ethane or propane. They also conducted similar experiments at higher pressure on heavy undersa tu rated crude oil, although in this case the increase in recovery was not as great as in the case of the light oils. In both cases, viscosity reduction and swelling of the by-passed oil behind the invading gas front were believed to be responsible for the more favorable recovery of the original oil in place. Within the past year, other investigators", ' have presented the results of laboratory studies of miscible slug and solvent flooding recovery processes. This paper describes the laboratory methods developed for evaluating benefits to be obtained by enriched gas drive in specific reservoirs, and presents the results of several displacements of crude oils which possess a wide range of physical properties. The displacements were conducted at reservoir conditions of temperature and pressure. The apparatus used in the following experiments consisted of a sand-packed tube which served as the model reservoir, a cylinder of injection fluid, and a mercury pump. The stainless steel tube, 8 ft long and 0.53 in. I- was packed with a graded quartz sand. The high-pressure pump discharged mercury into the bottom of the injection fluid cylinder at a constant rate as low as 1 cc/hr. The average porosity and permeability of the sand column were 34.6 per cent and 3.25 darcies, respectively. In each case the tube was charged by the displacement of salt water by the reservoir oil under consideration. Recently a project was initiated to evaluate oil recovery by enriched gas drive from three oil reservoirs. Samples from a fourth reservoir (in this case high-viscosity oil) were studied with a view to obtaining recovery information of general applicability to low-grade, high-viscosity crudes. The oils from these four reservoirs exhibited a wide range of physical properties, and the reservoir conditions of pressure and temperature simulated in the laboratory represented several typical field conditions under which enriched gas drive might be employed. One of the reservoirs selected for laboratory displacement experiments produced an intermediate-gravity crude (29.6" API) by solution gas drive and a weak water drive. A low recovery in the range of 10 to 20 per cent was anticipated. Four displacement experiments were made to determine the effect of injection gas composition and initial gas saturation upon recovery of oil from the laboratory model. Two types of reservoir oil were used in these experiments. In the first run, a desaturated crude with a bubble point of 395 psi was charged to the tube. In the three subsequent runs, a simulated original reservoir oil was charged at 2,000 psi and produced by solution gas drive to 300 psi before beginning gas injec-

By C. Gatlin, F. Armstrong, K. E. Gray

This paper presents some preliminary results of two-dimensional cutting tests of dry limestone samples at utmospheric pressure. Cutting tips having rake angles of + 30°, + 15", 0°, - 15" and - 30" were used to make cuts on Leuders limestone samples at six depths of cut ranging from .005 to ,060 in. at cutting speeds of 15, 50, 109 and 150 ft/min. The vertical and horizontal force components on the cutting tips were recorded with an oscilloscope equipped with a polaroid camera. Motion pictures of the cutting process at camera speeds of 5,000 to 8,000 frames/sec were taken at strategic points in the variable ranges. The movies provide considerable insight into the brittle failure mechanism in rocks. It appears that chip-generating cracks usually have an initial orientation which is related to the resultant of the externally applied forces. The latter part of the crack curves upward toward the free surface being cut, this part being governed by some type of cantilever bending or prying. The linear and angular motion of the loosened chips also indicate the tensile nature of brittle failure. Analyses of the forces on the cutting tips indicate that: (I) relatively small increases in vertical loading result in large cut-depth increases for sharp tips (rake angles 2 0"); (2) tool forces increase at an increasing rate as the rake angle decreases, particularly for rake angles < 0"; and (3), for the range of this study, rate of loading had little effect on the maximum forces. Both the movies and visual inspection of the cuttings indicated that the volume of rock removed by chipping was much larger than that by any grinding mechanism, even for tips having negative rake angles. Cutting size increases with increased cut depth and rake angles, and decreases slightly at high cutting speeds, the depth of cut having by far the most influence. The amount of contact between the rock and the cutting tip was always less than the depth of cut and rarely exceeded 0.010 in. even for cuts of 0.060 in. INTRODUCTION The planing (or slicing) of various materials with a fixed blade has long been practiced by workers in many industries. For example, the farmer&apos;s plow, the carpenter&apos;s plane and the housewife&apos;s paring knife all employ this basic action. The casual observer might suspect that something so common must be quite simple; however, as in all problems involving the failure of materials, such is not the case. Industries concerned with the machining of metals have long studied these problems, and their literature on the subject is voluminous. Despite these efforts, basic knowledge is not very advanced, as may be noted from recent and comprehensive analyses of their literature.12 Metals are more subject to analysis by classical theories of elasticity and/or plasticity than are rocks, since their elastic constants and strengths are reasonably well established in many cases. In spite of this relative "simplicity", Hill9 refaces his discussion with an admission that the mathematical solution to the machining problem is not known. Photoelastic studies of both machining and milling have been performed and are discussed thoroughly by Coker and Filon.4 Rotary drilling of rocks with fixed blade or drag bits has long been practiced by the mining and petroleum industries, and considerable study has been given to defining their cutting action in terms of the pertinent variables. Essentially all the published mechanistic research on drag-bit drilling has been performed by mining engineers and has been concerned only with rocks in the brittle state. Fairhurst5-7 has worked extensively in this area and employed photographic techniques quite similar to those reported here, except at much lower speeds. His studies showed the periodic or cyclical nature of the brittle failure mechanism, in which instantaneous loads on the bit varied from some maximum value to near zero. Goodrichs has presented further data on the subject as well as a qualitative description of the process. Again the postulated mechanism is cyclical, with alternate chipping and grinding periods. The ploughing of coal is a practiced method and has been studied in some detail by English mining engineers."" Their findings have considerable general application to drag-bit drilling. Evans," in particular, has extended Merchant&apos;s metal-cutting theory" to brittle materials with some success, although certain aspects of his theory are open to question. Fish13 has recently summarized nearly all the published works concern-

By Hermann Wedding

I ask your permission to speak about a matter which is not of a specifically scientific nature, but more of a general—I might even say of an international—nature, and the international character which this city now presents must be my justification for introducing it. The Germans, very often, are thought to be an exceedingly warlike people, but I come to-day in the capacity of a peacemaker. Our German language is an original language; it is, therefore, a language in which it is impossible to change the meaning of a word at will. It may be, perhaps, easier in a combined language, as the English, to associate and to exchange meanings. Now, a word which we hear a great deal at the present day, is "Stahl," in English, "steel." This word means, in the German language, a substance which can be hardened. As the German literature, in relation to metallurgy, is the oldest of the modern world, this circumstance may give the German a right to ask for consideration. But I think, now, when the four languages, German, Swedish, French, and English, compete in rich metallurgical literature, it is very necessary to have uniformity in the nomenclature of iron, which would prove not only useful for science, but equally so for trade. For that purpose I propose to make the divisions of iron so that the word steel shall comprise a subdivision and not a primary division as formerly. Nature furnishes us iron mostly in the state of oxides, and if in any other condition, we must convert the ore into oxide before we can make iron. The oxides are always mixed with certain earthy substances called rock or gangue. The extraction of iron involves, therefore, the twofold process of the reduction of the iron, and imparting to it the amount of carbon necessary for technical purposes, and the separation of the reduced and carburized iron from the gangue. The reduction is always effected by carbon or carbonaceous substances (coke, anthracite, carbonic oxide, etc.), and the result is, according to the degree of heat employed, either malleable iron or a non-malleable iron. The process of malting malleable iron in this way is called, generally, the direct process—in German, Rennarbeit. It produces the iron in a solid state with a fluid cinder. By this process our ancestors made all their iron, and it has been revived in various ways in modern times up to the process of Mr. Blair, so far as I know, always without commercial success. The

By Robert H. Leach, C. H. Chatfield

This paper gives a brief summary of the process of manufacture of sterling silver, and some of its more important physical properties, as observed in conlmercial production of rolled sheet and wire. Although papers have been published by Turner and Smith,1 Rose,2 Sperry3 and Jordaq4 there are few technical data available, and unfortunately the time allowed for the preparation of this paper has not been sufficient to make it as comprehensive as the title might indicate. Analysis of Steeling Silver Fine or pure silver is too soft for coinage and the manufacture of articles in which strength and resistance to wear are desired. From the earliest times of which we have record, copper has been the metal generally used to harden silver. Analyses of coins and silver articles from ancient tombs show varying amounts of copper, and old Roman silver objects in the British Museum have approximately the same ana,lysis as our sterling. The first authentic record of the establishment of a standard alloy is during the reign of Henry I1 in England. During the twelfth and thirteenth centuries, the people in the Eastern Provinces of Germany had a reputation for the standard and purity of their silver coinage, and it is said that Henry II employed some of these Easterlings, as they were called, to improve and standardize the English coinage, which had become debased. The peculiar standard adopted is probably accounted for by the system of weights used. A troy pound contains

By J. F. Wilson

Steady-state flow theory, previously applied to displacements with two mobile phases, is extended to cover down-structure flow involving three mobile phases: oil, gas and water. When used with normal reservoir fluid properties, the theory predicts the existence of four distinct flow regimes and the conditions under which each regime exists. The predicted behavior is verified by a parallel-plate model study. INTRODUCTION Special problems exist when a water flood is contemplated in a dipping reservoir having a substantial gas cap. Normally, the gas-cap region is one of very low oil saturation. If oil is moved into the gas cap during the flood, a loss in recovery results. Efficient recovery of the oil underlying the gas is therefore difficult. In two reported field water floods, injection into the gas cap has been used to solve these problems. At the West Norfolk Garr Sand Unit, injection into the upstructure region of the reservoir was made for the stated purpose of filling up the gas cap with water.&apos; The purpose in the Sholem Alechem Fault Block "A" Sims Sand Unit was to form a continuous water barrier between the gas cap and oil band.&apos; A laboratory model study preceded this flood and was described in the same publication. Both of these gas-cap water injections gave satisfactory results, but the published data are insufficient to allow generalizing to other field conditions. The present investigation was also undertaken to obtain results for a specific field problem. However, these results will be shown to be in agreement with an extension of the Dietz3-5 mathematical model to three-phase flowing systems. The agreement between the theory and the model studies indicates that the mathematical model can be used to describe completely the flowing system under some conditions, and to indicate the general type of flow to be expected under all conditions. FLOW THEORY The Dietz equations for two-phase flow are derived "&apos; for the case of constant-velocity linear flow in a homog- eneous porous medium. The transition zone between the fluids is assumed to be of negligible extent so that the displaced and displacing fluids are separated by a sharply defined interface, as illustrated in Fig. 1. The density and mobility of the displacing fluid are constant over the region behind the interface, and the same properties of the displaced fluid are constant over the region ahead of the interface. To extend the Dietz equations to three-phase systems, we postulate the flowing system shown in Fig. 2 and determine the conditions under which it can exist. The

By Richard P. Rothwell

Though coal has been mined in this country for more than a century, no systematic effort was ever successfully made to ascertain the total amount produced. The production of the Cumberland Basin, Md., and the shipments from the anthracite fields of Pennsylvania, have been placed upon record, thanks to the intelligence and foresight of Mr. C. Slack in the former case, and to the late Mr. B. Bannan in the latter. For some of the years between 1822 and 1842, the production of the Richmond Basin was reported by Mr. R. C. Taylor, but since that date till the author undertook this work it was impossible to obtain any statement of the production of this field. A few of the newer fields, such as that of Mt. Diablo, Cal., have been fully reported, and a few of the newer States have also had this service performed by some intelligent private individuals; but no statistics of coal production have ever been collected either by the State or General Government, if we except the returns for the years 1869—70 of the census report. During the year 1875, by great exertions, I succeeded in obtaining, and July 3d, 1875, gave in the Engineering and Mining Journal what, " though not an accurate statement of our coal production," was " by far the most full and reliable that had ever been published." Though that report showed the production of bituminous coal to be 23,630,094 gross tons, or about six million tons more than had ever before been reported, it was in reality two and a half million tons below the actual output. The more full returns I obtained for 1875 gave many figures for 1874

By D. D. Dunlop, J. R. Welker

The growing interest in the use of CO, in crude oil recovery increases the need for data on the effect of CO, on hydrocarbon physical properties. Data are presented on the solubility of CO, in various dead oils, the swelling changes in CO2-oil solutions and the effect of CO, on dead oil viscosity. This latter property shows the most pronounced effect, with viscosity reductions up to 98 per cent of the uncarbonated viscosities. An empirical method of estimating the viscosity of carbonated oils is presented. The apparatus and procedures used are described in sufficient detail to allow others to make similar studies. INTRODUCTION The effect of dissolved carbon dioxide on the swelling and viscosity reduction of specific hydrocarbon oils has been observed and recorded by a number of investigators.&apos;- me object of this paper is to offer a means of predicting these effects for crude oils free from natural gas, using the dead state viscosity and gravity of the crude oils. The CO, solubility and swelling of numerous crude oils were determined in a visual cell at various pressure levels. The viscosity of the oils carbonated to various pressure levels was then determined by measuring the pressure drop across a capillary tube. From these data, the physical properties were correlated empirically. The resulting correlations allow the prediction of CO, solubility, swelling and viscosity reduction if the dead state gravity and viscosity of the oils are known. SOLUBILITY AND SWELLING MEASUREMENT EQUIPMENT AND PROCEDURE A high pressure visual cell was installed in a constant temperature cabinet. A test gauge was attached at the top of the cell for pressure measurement, and a line was run through the cabinet wall to a wet test meter which was used for volumetric measurement of the gas. The first step in making a test run was to put the oil in the cell up to a level about half to two-thirds of the total volume. This required about 50 to 65 ml of oil. carbon dioxide was then bubbled up through the oil for a time during which the pressure of CO2 in the cell was kept above 800 psia. Saturation of the oil with CO2 at this pressure and ambient temperature was confirmed by slowly bleeding CO2 through a valve to the atmosphere. If the oil was completely saturated with CO2, bubbles of gas would form in the oil at the first small decrease in pressure. If the oil was under-saturated, no bubbles formed until the pressure was decreased to the saturation pressure existing in the oil. If this saturation pressure was lower than that desired, more CO2 was bubbled through the oil until the desired level was reached. After saturation at ambient temperature was completed, the cabinet temperature was adjusted to the desired level and the cell was allowed to reach temperature equilibrium. After temperature equilibrium was reached, the pressure was again decreased slightly, and the oil again checked for full CO2 saturation at the cell pressure. The pressure now had changed because of the difference in solubility of the CO, in the oil at higher temperatures and the expansion of CO2 as the temperature increased. The outlet tube from the cell was then connected to the wet test meter and the CO2 was allowed to flow slowly out of the cell and through the wet test meter at ambient temperature and pressure. The water in the wet test meter had previously been saturated with CO2 at ambient temperature and pressure by allowing CO2 to flow continuously through it lor a period of several hours. The gas flow was stopped at several pressures during the run and the cell was allowed to come to equilibrium; this made possible the measurement of solubility and swelling data at the intermediate pressures. The volume of the oil in the cell was recorded at each of the equilibrium pressures in order to obtain swelling data. DATA AND RESULTS The solubility of CO2 in the oil was calculated by the relationship V — V, where R. = solubility of CO, in crude oil, cubic feet of CO, measured at 60F and 1.0 atm/ bbl of dead state oil at the temperature under which solubility was measured, V, = volume of gas released from the cell between the saturation pressure and zero pressure, corrected to 60F and 1.0 atm, cu ft, V, = volume of CO: contained in the gas space above the oil, corrected to 60F and 1.0 atm, cu ft, and V, = volume of the dead oil in the cell in bbl at the temperature of the run. The volumetric data of Sage and Lacey&apos; were used to calculate V., from the volume of CO2 at high pressures. The swelling factor was calculated as where V, is the volume of the C0,-

By T. Sterry Hunt

In my address on the " Geognostical Relations of the Metals," delivered before the Institute on the 20th of February last (Vol. I Transactions, p. 331), I spoke of the rocks in the vicinity of Thunder Bay, Lake Superior, where I indicated two series of uncrystalline rocks resting upon the Huronian schists, the lower one consisting of dark-colored argillites and sandstones overlaid, apparently in slight discordance, by nearly horizontal red and white sandstone and marls, which were compared with those of Sault Ste. Marie, and those of the Portage Lake district, on the south shore. These latter sandstones, according to Brooks and Pumpelly, overlie uncomformably the Keweenaw series of copper-bearing amygdaloids, sandstones, and conglomerates, and are in turn overlaid by the Trenton limestone. I then proposed to call this lower series of Thunder Bay, that is to say, the dark-colored argillites and sandstones which are traversed by the silver-bearing lodes of that region, the Animikie group. Shortly after the publication of that address I received an abstract of a paper on the geology of that region by Professor Robert Bell, read before the Montreal Natural History Society, February 24th. He there confirms the statement made in my address that the gold of Lake Shebandowan occurs in the Huronian, which is also seen to be cut by the silver-bearing lodes just mentioned. Professor Bell, in this paper, proposes to designate both what I have called the Animikie group, and the overlying red and white sandstones, by the name of the Nepigon group, for the reason that the upper series is best displayed about Lake Nepigon. This latter series is by Logan supposed to be overlaid by the copper-bearing amygdaloids with conglomerates and sandstones of the north shore (apparently identical with those of Keweenaw); and the whole together, inclnding the Animikie group, constitute his Upper Copper-bearing group. These copper-bearing strata are by him supposed to be overlaid by the red and white sandstones of St. Mary, which are apparently the same with those sandstones which, according to Brooks and Pumpelly, overlie unconformably the similar cupriferous rocks of Portage Lake, and are, in their turn, overlaid by the Trenton limestone. Thus the sandstones which at Thunder Cape overlie the Animikie group are by Logan placed in the midst of the Upper Copper-bear-

By J. E. Warren, J. H. Hartsock

In the receipt of J. E. Warren and J. H. Hartsock&apos;s comments on our paper, "Aspects of Gas Deliverability", We wish to point out that all the physical characteristics we conceived as constant were absorbed in the gas deliverability constant of the individual well&apos;s performance, listed

By F. J. Fayers, S. A. Hovanessian

The one-dimensional displacement equation for a homogeneous porous medium, including the effects of gravity and capillaty forces, has been solved by a numerical method. A finite-difference scheme is developed for obtaining saturation, pressure and fractional flow profiles in waterflood recovety problems. From the numerical examples given, it is concluded that the gravitational forces have a pronounced effect on the saturation profiles and the pressure distribution curves of the system. INTRODUCTION Within the past 20 years, a number of papers have appeared in the literature dealing with the quantitative treatment of waterflood recovery problems. In their celebrated paper, Buckley and Leverett1 described a method for calculating saturation profiles when the effects of capillary pressure and gravity are excluded. Terwilliger, et al,2 included the effect of gravity in their theoretical and experimental investigation of oil recovery problems and obtained close correlation between experiment and theory. welge3 described a simplified method for obtaining the average saturation and the oil recovery from an oil reservoir. The effect of gravity can be included in this calculation. More recently (1958) Douglas, et al,4 presented a method for calculating saturation profiles which includes the effect of capillary pressure. The authors start with the one-dimensional displacement equation (which is nonlinear in the derivative) and, by a change of variable, transform this equation to a semi-linear partial differential equation. This equation is then solved by a finite-difference method on a high-speed digital computer. Fayers and Sheldon5 obtained the solution of the one-dimensional displacement equation by directly replacing the differential equation by a finite-difference equation. The effects of capillary pressure and gravity were in- cluded in their solution. Here, since the movement of the foot of the saturation front is governed by a separate equation, the elapsed time in attaining a particular saturation profile cannot be obtained. The results of these two papers indicate that the inclusion of capillary forces eliminates the triple-valued Buckley-Leverett saturation profiles. In the present paper, the one-dimensional displacement equation for a homogeneous permeable medium, including the effects of capillary and gravity forces, is solved. The method of solution resembles that described in the paper by Douglas, et al, since it involves a similar transformation of variable. However, it extends their work in that the effect of gravity is included and, in addition, pressure profiles may be calculated. Also, the functions of saturation [kro(S), krw(S) and Pc (S) ] required are entered in tabular form rather than as low-order polynomials. This simplifies data preparation and permits the use of a greater range of function types. Unlike the method of Fayers and Sheldon, the corresponding elapsed time required for the development of each saturation profile is calculated and, also, saturation profiles may be calculated after breakthrough. THEORETICAL CONSIDERATIONS The dimensionless form of the one-dimensional displacement equation for a homogeneous porous medium as obtained from Darcy&apos;s law and material balance relations can be written as follows.

By R. J. Blackwell, A. L. Pozzi

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments. If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascer tain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media. From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion. Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion. These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. INTRODUCTION One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated. Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies. Craig,et al,1 demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled. The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. Consequently, laboratory investigations were made of the dependence of recovery on dispersion and other variables,

By P. D. White, J. T. Moss, J. S. McNiel

Results of experimental work on the in situ combustion process were first published in this country in 1953&apos; when Kuhn and Koch described results of a three-well test in Jefferson County, Okla. Shortly there-after Grant and Szasz2 described field studies in Nowata County, Okla., in which several modifications of the basic combustion process were investigated by injection of various oxidizing gas mixtures other than air. In the past five years speculation concerning this method of oil recovery has continued, with a number of interesting papers on various aspects of in situ combustion appearing in the literature3,4,5,6,7. However, only one of these&apos; provided actual engineering information on pattern-type field experiments. The primary objectives of the Oklahoma three-well test were to check operation of specially designed electrical ignition equipment and evaluate problems associated with initiation of combustion in a natural oil sand reservoir. Immediately following successful completion of this test in the Pontotoc sand, plans were activated for a second field experiment to be conducted in the same sand a short distance away. The objective of this second field test1 as to establish a relationship between field observations and information derived from laboratory experimentation and computations. Secondary objectives of the test were to develop operating tech- niques and define operating problems, and to obtain information that would assist in the economic and engineering appraisals of the process. Careful planning was required since this test was designed with the hope of providing basic information on the characteristics and operation of a combustion drive. It was necessary to include test facilities which would not only permit precise control and measurement of the process variables but would also provide sufficient flexibility of control to insure that variables in the combustion process could be studied during the course of the test under a wide range of conditions. In order to accomplish these objectives elaborate instrumentation and several control wells were included in the design of the test installation. This type installation was felt to be well suited for an experimental study, but was in no respect intended as a counterpart of a commercial-scale operation. PRELIMINARY LABORATORY WORK An important objective of the field experiment, as stated previously, has been to obtain reliable data on operating variables which might be compared with similar data obtained in laboratory combustion tests. The value of successful correlations between quantities that can be measured in the laboratory and those obtained in a full-scale commercial venture has been well established for other industrial processes. The difficulty of following a process underground should make such correlations even more essential here. Also. approaching the field test phase of development of in situ combustion, it was considered desirable to precede design of test equipment with laboratory combustion studies under a variety of conditions to establish likely ranges of variables. These included temperature, air injection rate, frontal advance rate and produced gas composition.

By Thomas Egleston

DURING the year 1873, my attention was called to the frequent accidents, resulting from the breaking of rails, on the different railroads in this&apos; country, and I was requested to investigate the subject. The plan of investigation I proposed was to ascertain, in as many cases as possible, the exact hist* of broken rails, both in this country and in Europe; to collect information in Europe relating to the tests which rails used there were required to undergo, and to experiment upon the pieces of rails broken on the road, with a view to ascertain whether their fracture was due to their chemical constitution, bad manufacture, to a reduction in strength owing to temperature, or to physical changes in the constitution of the rail. The investigation was commenced by the collection of statistics, and for this purpose I spent several months in Europe, collecting information on the subject of broken rails, as well as the life of iron and steel rails generally, and inquiring into the systems of purchasing and of testing them employed by the railroads there, intending, on my return, to make a series of analyses of rails broken, both in this country and in Europe; to ascertain, if possible, how far great cold had an influence on the fracture; to examine whether the rail broken, either on the road or afterwards, underwent, at or about the fracture, any physical change, and to make a series of experiments on the strength of rails manufactured in the United States or sold in the American market. Unfortunately, the panic of 1873 came on, just before my return from Europe, and prevented the carrying out of the larger part of the plan proposed; as, however, I had collected in the meantime, a large number of statistics of different kinds from all parts of Europe, and had made a number of interesting experiments and investigations, I have thought it would be worth while to communicate some

By B. L. Landrum, J. Simmons, J. M. Pinson, P. B. Crawford

Patentiometric model data have been obtained to estimate the effect of vertical fractures on the areas swept after breakthrough in water flooding and miscible displacement programs such as gas cycling where the mobility is near one, The data are presented for the case of the fire-spot pattern in which the cemer well is fractured various lengths and orientations, the data indicate that for 10-acre spacing, fractures extetidirrg over 1300 ft in either directior1 from the fractured well may re.srrlt in reductions in sweep efficiencics from 72 to approximately 34 per cent. However. the area swept after break through may be quite largr and only 10 or 12 per cent 1ess than would be obtained if the reservoir were trot fractured. For the specific case when the volume of fluid injected is equivalent to 100 per cent of the pattern vol-unie, the swent area may vary from 80 to 88 per cent, depending on the lenght of the fracture. The former value is that which occurs when the break through or sweep efficiency was orrly 34 per cent and the latter figrrre of 88 per cent is that which is obtained if the reservoir were unfrac-ttm&apos;d. It is pointed out that although the sweep efficiency may he very low in vertically fractured five-spot patterrz.s, the area swept at low water-oil ratios may be only 5 to 10 per cent less than those achieved if the reservoir were unfractured. INTRODUCTION Since the initiation of commercial reservoir fracturing techniques it has been desirable to determine the effect of fractures on the areas swept after breakthrough. Most water flooding or gas cycling projects are continued for substantial periods after the brcakthrough of the injected fluid. Although the sweep efficiency serves as one criterion for rating various flooding patterns. the area swept after breakthrough for various water-oil ratios or percentage wet gas, if cycling. is of perhaps more importance than the sweep efficiency alone. Sweep efficiency data on the vertically fractured five-spot have been presented3. Previous work on the line-drive pattern has shown the effect of vertical fractures on the area swept after breakthrough for the case in which the distance between injection and producing wells divided by the distance between adjacent input wells was equivalent to 1.5 (see lief. 2). The data indicated that for the line-drive pattern it may be desirable to flood or cycle substantially perpendicular to the fractures in order to achieve the greatest recovery for the smallest volume of fluid injected. For this study the center well of a five-spot is assumed as the fractured well. All fractures were assumed to originate at this well and extend into the reservoir for various distances and orientations. All the fractures are straight and are of large permeability compared to the matrix proper. These data are presented to aid the engineer in estimating fractured five-spot pattern performance. ANALOGY The potentiometric model was used in making this study. The model used was 20 20 in. by approximately 1-in. deep. For certain portions of the study one corner of this model was considered to be an injection well and the opposite corner a production well. To simulate vertical fractures a copper sheet was soldered to the wire well and made to conform to the desired length and orientation. In other studies the same model was used except that the four corners of the model might be considered as the corner wells of a five-spot pattern and a fifth well was placed in the center of the model. The well placed in the center of the model was fractured. The total fracture length is L and the well spacing. d. The complimentary fracture angles will be obvious from Figs. 3 and 4. The data obtained on the potentio-metric model assumes the pay to be uniform and homogeneous, the mobility ratio is one, steady-state conditions exist and gravity effects arc neglected. The permeability of the fractures is very great compared to that of the matrix proper. The po-tentiometric model has been used widely both in water flooding and gas cycling projects, and may be used for miscible displacement; how-ever. it is believed that the poten-tiometric model data are more properly applicable to gas cycling than water flooding because the model as-