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By William I. Gardner

Optimum design of a structure obviously requires a thorough knowledge of the materials to be utilized in its construction. When the structure is a tunnel, a most important element in its design and construction is the geology. As a tunnel may be many miles in length and at depths of hundreds or thousands of feet, we face a real problem to meet the needs of the designer and builder. How can we determine the properties of our construction materials in this situation? Engineering geology has had a formidable challenge to meet the requirements of conventional excavation methods; the advent of machine methods for rapid excavation compounds the requirements for more detailed and more precise geological knowledge of the tunnel site. This chapter will discuss the means now at our disposal to meet the challenge to produce the required data on the tunnel site in the preconstruction stage. Our considerations will be directed towards construction of a free-flow tunnel, primarily in fractured rock formations, without any requirements for the rock mechanics type of in-situ tests that might be made for a pressure tunnel or for a large opening for an underground power plant. In essence the investigation must determine: (1) The geologic conditions affecting the type of construction equipment and excavation method of the rock to be broken and removed. (2) The quantities of water and gas to be encountered. (3) The strength and stability of the material surrounding the bore and its need for support and lining. GEOLOGICAL FACTORS AFFECTING TUNNEL DESIGN AND CONSTRUCTION The engineer or contractor may classify the rock as either competent or incompetent or more pointedly as "good" or "bad" ground. The geologist may bestow a precise petrographic name upon the rock, such as granodiorite or indurated tuff breccia or name the formation, as Mancos shale, for

Jan 1, 1970

By James Gayley

The atmosphere, which plays such an important part in the manufacture of iron and steel, is the most variable element involved in its several processes; and particularly is this true of the blast-furnace process, which consumes air in large quantitiee. At no time since the blast-furnace became an important and widely used apparatus—even when it was operated in the most crude manner—have the variations in composition of the raw materials used been as frequent and as great as the variations in humidity of the atmosphere. Important improvements have been made in the blast-furnace and its accessories, such as the hot-blast stoves, the increase in size and change in the shape of the furnace, more efficient blowing-engines, the increased protection given to the bosh-walls, and the careful preparation of the raw material, all of which have exerted a pronounced influence on the furnace-operations from a metallurgical standpoint. But during the past eight years little advance has been made in this direction; the fuel-consumption has not diminished, nor has there been any material increase in production. Within that period, however, there has been witnessed the greatest development in appliances for the economical handling of material. So complete has been the work in this direction, that, except in isolated cases, in this country at least, a further extension does not hold out much promise of a satisfactory return on the investment required. It seemed that, with the exception of the gas-engine, we had about reached the limit, for like a strong wall, the atmosphere, with its humidity as variable to-day as when first blown into a primitive blast-furnace, appeared to stand as a barrier to

Jan 1, 1905

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation' y = 100 (x/k)a [1] in which y — cumulative percent finer, x = particle size, a -= distribution modulus, and k = size modulus. Charles3 found that the energy consumption in comminution is usefully expressed by another empirical relation, E = Ak(1-D) [2] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; (1-n) is the slope of a plot of log E vs log k. Holmes3 has presented energy equations similar to Eq. 2. The constants a and n in Eqs. 1 and 2 have been shown to depend both on the nature of the material and on the comminuting device. Moreover, Charles showed that within experimental error a and n are a — n+1 = 0 [3] Combining Eqs. 2 and 3, E = A k-a [4] In the first sections of this article it is shown that the energy equation, Eq. 4, can be derived directly from the size distribution equation for the fine sizes, Eq. 1. The derivations are made without assuming any of the specific relationships between energy and particle size which have been common in previous literature. For comminution processes in which Eqs. 1 and 4 adequately represent the experimental data, the constant A in Eq. 4 is found to be a simple and useful inverse measure of grindability. That is, A is the energy consumption per unit volume of comminution product finer than unit size as determined from the straight line portion of the log-log plot of the size distribution. These considerations all lead to a unifying hypothesis of comminution mechanism from which both Eq. 1 and Eq. 4 can be derived. Finally, it is pointed out that this hypothesis raises serious questions as to the significance of the Rittinger hypothesis, the Kick hypothesis, and other theories in which energy numbers are systematically assigned to various size fractions of comminution products in order to calculate theoretical energy consumptions. Derivation of the Energy Equation from the Size Distribution Equation: For simplicity, consider the comminution of 100 volumes of a feed material of relatively uniform particle size. The comminution process may be considered as the summation of many individual and independent comminution events. The extent of comminution is most easily expressed as the number of comminution events, z. In the first derivation, the key assumption is that the characteristics of the comminution events in a given crushing or grinding process are substantially constant and do not vary with the progress of the comminution process. Accordingly the characteristics of an average comminution event may be defined. In one such event, a quantity of energy $E is applied to a single particle of size f and volume $v. The crushing of this particle produces fine particles with a size distribution similar to that given by Eq. 1: yw=100(x/ka)a0 [51 In this equation yo, a0, and k0 are used to characterize the product of an individual comminution event rather than the product of the comminution process as a whole. In using Eq. 5, we will not be concerned with values of x close to the feed size f and will therefore assume only that the equation is applicable to the finest sizes of the material. In 100 volumes of total product, the actual volume of product finer than x from a single comminution event, or dy, is given by The total volume of material below size x, resulting from z events, is then given by y = z(dy) =z(dv) (x/ka)a0 =" Eq. 7 reduces to Eq. 1 when we let a, = a and [8a] z =100/dv (ka/k )1 or k = ka (zdv/100)-1/a [8b] Eq. 8a shows that the distribution modulus of the comminution product is the same as for the product of an individual comminution event. Eq. 8b shows how the size modulus of the comminution product k varies with the extent of comminution as measured by the number of events, z, or as measured by the fraction of the feed actually subjected to com- minution1 zdv/100. The energy input to 100 volumes of total feed, or 100E, is the sum of the energy inputs for all the comminution events: 100E =z (dE) [9]

Jan 1, 1961

The mining fraternity of North America was grieved and shocked to learn of the death of Dr. Willet G. Miller on Feb. 10, 1925. Doctor Miller was for many years the Provincial Geologist of Ontario and the one who more than any other had contributed by his personal work and the reports of his subordinates to the recent extraordinary mineral development of the Province. Doctor Miller was fifty-eight at the time of his decease. A man of unusually stalwart physique, he seemed destined to many years of useful service. His friends in both the American and Canadian Mining Institutes can with difficulty reconcile themselves to his loss. Doctor Miller was born in 1867 in Port Rowan, Ont., on the shores of Lake Erie. After preparation in the high school of his native town, he entered the University of Toronto and took his bachelor's degree in 1890. He pursued graduate studies in geology at Chicago, Harvard, and Heidelberg Universities. In 1893, he was first appointed lecturer and soon thereafter Professor of Geology in Queens University, Kingston, Ont., a chair which he held until 1902. He was then appointed Provincial Geologist of Ontario and was placed at the head of the Survey which was attached to the Department of Mines. Within the next year, 1903, he performed the service that made him famous. In the summer of 1903, in connection with the building of the Ontario Government Railway toward an objective on James Bay, veins had been noticed by construction parties just north of what is Cobalt Lake today, and in the rocky pass that is now traversed by the main line of the Canadian National Railway en route to Vancouver. The pink stain of cobalt bloom on the vein, known later as La Rose, caught the eye of a workman; in November, Doctor Miller recognized the silver in it, and brought the possibilities of the district to general attention. In December, he published an article in the Engineering and Mining Journal, stating that the veins could be worked at a handsome profit. During the winter and spring, the mining interest awoke, which resulted in the astonishingly productive silver district of Cobalt; but in which, Doctor Miller, because a government official, scrupulously refrained from having any financial interest whatever. Seldom has so high a sense of honor been manifested; and as the result, Doctor Miller commanded confidence and respect to an extraordinary degree. Hard on the discoveries at Cobalt came, in the next few years, those at the other famous camps in Northern Ontario; and step by step with them, reports issued from

Jan 1, 1925

By Oswald J. Heinrich

The responsibility resting upon the owners and managers of mines where fire-damp is generated, renders it a matter of imperative duty that a frill and correct statement of any explosion that occurs should be given to the public. But such a statement must be based on the testimony of impartial eye-witnesses or trained experts. Then a sad experience may result in the adoption of effective preventive measures. In the absence of any official and professional body of mining experts in the State of Virginia, the writer desires to submit to his professional brethren of the American Institute of Mining Engineers an account of an explosion which recently took place in a colliery under his management, and earnestly desires a thorough and impartial discussion on the Fats submitted. Description and Plan of the Mine.—The "Grove" shaft is situated at the nearest point 825 feet from the last old workings upon the Midlothian property, south of the old Pump shaft works. (See Plate 111.) The shaft was sunk by the former company, some thirty years ago, to the depth of 622 feet. An incline over 230 feet long, starting in a northwest direction at a depth of 105 feet above the shaft bottom, had been driven to explore the coal on the dip. A return of very small dimensions had been driven round the shaft on the south side, entering the upcast chamber. With the information obtained from the former company that a seam of coal about four feet thick, at a depth of 490 feet, had been found, and with the information obtained by the present proprietor, R. T. Burrows, of Albion, N. Y., by means of two boreholes on the dip west of the old shaft, in both of which workable seams of coal at various depths had been ascertained, the clearing out and thorough retimbering of this shaft were commenced in March, 1873. Borehole No. 1, at a depth of 4773 feet from surface, revealed a seam of coal. This borehole was afterwards carried to a depth of 1140 feet to the granite, without finding any other seam of coal. Borehole No. 3, at a depth of 608 feet, revealed the first coal-seam, 14 1/2 feet thick; at 633 feet, the second, 12 feet thick; at 662 feet the third, 1 foot thick, and at 692 feet the fourth, 43 to 5 feet thick. The borehole was stopped at a depth of 715 1/2 feet.

By Oswald J. Heinrich

THE responsibility resting upon the owners and managers of mines where fire-damp is generated, renders it a matter of imperative duty that a full and correct statement of any explosion that occurs should be given to the public. But such a statement must be based on the testimony of impartial eye-witnesses or trained experts. Then a sad experience may result in the adoption of effective preventive measures. In the absence of any official and professional body of mining experts in the State of Virginia, the writer desires to submit to his professional brethren of the American Institute of Mining Engineers an account of an explosion which recently took place in a colliery under his management, and earnestly desires a thorough and impartial discussion on the facts submitted. Description and Plan of the Mine.-The "Grove" shaft is situated at the nearest point 825 feet from the last old workings upon the Midlothian property, south of the old Pump shaft works. (See Plate III.) The shaft was sunk by the former company, some thirty years ago, to the depth of 622 feet. An incline over 230 feet long, starting in a northwest direction at a depth of 105 feet above the shaft bottom, had been driven to explore the coal on the dip. A return of very small dimensions had been driven round the shaft on the south side, entering the upcast chamber. With the information obtained from the former company that a seam of coal about four feet thick, at a depth of 490 feet, had been found, and with the information obtained by the present proprietor, R. T. Burrows, of Albion, N. Y., by means of two boreholes on the dip west of the old shaft, in both of which workable seams of coal at various depths had been ascertained, the clearing out and thorough retimbering of this shaft were commenced in March, 1873. Borehole No. 1, at a depth of 477 1/2 feet from surface, revealed a seam of coal. This borehole was afterwards carried to a depth of 1140 feet to the granite, without finding any other seam of coal. Borehole No. 3, at a depth of 608 feet, revealed the first coal-seam, 142 feet thick; at 633 feet, the second, 12 feet thick; at 662 feet the third, 1 foot thick, and at 692 feet the fourth, 4 1/2 to 5 feet thick. The borehole was stopped at a depth of 715 1/2 feet.

Jan 1, 1877

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's law and material balance relations can be written as follows.

By R. G. Grieves, G. Thodos

A method is presented for the accurate calculation of the cricondentherm and cricondenbar pressures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain six and quite possibly any number of components including paraffins, isoparaffins, olefins, acetylenes, naphthenes and aromatics. The approach is similur to that used for calculating critical pressures and cricondentherm and cricondenbar temperatures. The critical pressure, the normal boiling point and the approximate vapor pressure behavior of each component are all that art required. A stepwise culculation procedure is necessary for mixtures containing more than two components. From an analysis of 22 binary systems and 118 mixtures, the average deviation of calculated cricondentherm pressures from reported values is 2.4 per cent. For nine multicomponent mixtures the average deviation is 1 per cent. Considering 19 binary systems and 108 mixtures, the average deviation of calculated cricondenbar pressures from reported values is 1.7 per cent. For 15 multi-component mixtures, the average deviation is 2.2 per cent. INTRODUCTION A knowledge of the phase behavior in the critical region of multicomponent hydrocarbon mixtures is of value both in industrial processing operations and for the optimum operation of gas condensate reservoirs. Accurate methods of calculating the critical temperatures and critical pressures4,6,7,8,9,23 and cricondentherm and cricondenbar temperatures6p10 of multicomponent hydrocarbon mixtures are available in the literature. If the cricondentherm and cricondenbar pressures could be calculated with equal accuracy, the entire phase diagram of a multicomponent hydrocarbon mixture could be well approximated. The work of Etter and Kay6 is limited to systems containing the normal paraffins and has not been tested on systems containing a heavier component than heptane. In addition, the development of their multicomponent equations is based upon a limited number of mixtures containing from three to six components. Silverman and Thodos have considered systems containing both paraffinic and non-paraffinic hydrocarbons, but their correlation is limited to binary systems and is highly inaccurate for methane systems. Eilerts has done extensive work on the cricondenbar pressure; he has produced an excellent correlation for binary systems. However, his procedure for multicomponent mixtures is chiefly useful for highly complex mixtures requiring a knowledge of the vapor-liquid equilibrium behavior of the mixtures; he has not considered the cricondentherm pressure. The objective of this study was the development of an accurate and rapid method for the calculation of the cricondentherm and cricondenbar pressures of multicomponent mixtures containing all types of hydrocarbons and having a wide volatility range. The approach that was adopted is similar to that used by Grieves and Thodos for cricondentherm and cricondenbar temperaturesl0 and for critical pressures.9 However, methane systems had to be considered separately and a modified stepwise calculation procedure was utilized for the cricondertherm pressure. The correlations were developed in a manner similar to those for critical pressures and cricondentherm and cricondenbar temperatures. Based upon binary data reported in the literature it was observed that the ratios of cricondentherm and cricondenbar pressure to the pseudocritical pressure (molar average), pt/ppc and pp/ppc, respectively, in two-component systems depended upon the mole fraction of the low-boiling component and upon the diversity in properties of the two components. A dimensionless boiling-point parameter Tb,/Tb was chosen to represent the diversity in properties of the components. For a binary system, Ti,'is the molar average of the normal boiling points of the two components involved. For a multicomponent system it is either the molar average of the normal boiling points of all of the components involved or the molar average of the normal boiling point of the pure low-boiling component and of the atmospheric boiling point of the low-boiling-free mixture of

Jan 1, 1965

By D. L. Murphy

As the world's demand for iron ore increases and available sources are depleted, increasing attention will be centered on deposits in the Quebec and Labrador portions of the Labrador Trough. Improvements in the beneficiation of low grade iron ore stimulate exploration for deposits amenable to concentration. This study is centered on the Mt. Wright-Lake Carheil area, lying between Wabush Lake and Mt. Reed in Quebec. Described in detail are the general lithology, structural and economic geology, and mineralogy of the iron-formation. The iron ore province of Quebec and Baffin Island extends from the southern shore of Baffin Island southeasterly through the Labrador Trough to Matonipi Lake, approximately 185 miles northwest of Seven Islands. (See Fig. 1.) Future geologic field studies will very likely extend the limits of the province to include the ferruginous and associated rocks of the Lake Mistassini area. At present, only the deposits near Knob Lake and Lake Jeannine (Mt. Reed) have been brought into production although in the near future several other properties including those at Wabush Lake will commence operations. Within the next decade or so, as the world's demand for iron ore increases and available sources are depleted, this region will undoubtedly become a major mining district. Initial reports of iron-rich rocks in Labrador date back to the investigations undertaken by A. P. Low near the turn of the century. During the ensuing years the country was prospected chiefly for precious and nonferrous base metals because of its inaccessibility and the low tenor of the iron ore. In 1945 an evaluation of the direct shipping ores near Knob Lake indicated that sufficient reserves were present to justify the enormous capital expenditure required to bring the deposits into production. Initial open-pit mining began in 1954 following the construction of a townsite, a 360-mile long railway to Seven Islands, and an elaborate loading dock. Recent improvements in the beneficiation of low-grade iron ore have stimulated widespread exploration for deposits amenable to concentration, particularly along the southwest extension of the Trough. The Mt. Wright-Lake Carheil area, bounded by longitudes 66O45' and 67 30' west and latitudes 52 30' and 52 45' north, is a nearly rectangular tract of slightly less than 500 sq miles. It is in Saguenay County, 174 miles north-northwest of Seven Islands (see Fig. 1). Except for the periods of the spring breakup and the fall freeze up, the area is readily accessible by air.

Jan 1, 1962

By J. H Lightfoot, Stuart E. Buckley

Deep drilling has led to the development of numerous pools which yield products consisting predominantly of natural gas accompanied by high-gravity water-white or slightly straw-colored liquid. Yields of this "condensate" or "distillate," as it is commonly called, vary from traces to over a hundred barrels per million cubic feet of gas. The fact that this liquid exists in the reservoir as an integral part of the gas phase and is formed by condensation attending simultaneous reduction of pressure and temperature after its entry into the well was apparently first recognized about 1932.l The nature of the physical phenomena involved in this condensation was clarified for the petroleum industry in 1933 by a report by Sage, Schaafsma, and Lacey2 of the results of an experimental investigation of the behavior of mixtures of methane and propane. Search of the literature has revealed that the condensation of liquid from gaseous mixtures by isothermal pressure reduction is not a new discovery. Kuenen was led by theoretical considerations to expect such a phenomenon, and in 1892 reported3 the results of experimental verification of his deductions. This was followed by a considerable amount of work on the phase relations of mixtures by Kuenen 4,5,6 and by 0thers,7,8 mostly in European universities. Since 1930 investigators in this country have reported experimental data on the properties and behavior of a number of hydrocarbon systems."' It is now generally known that in the presence of natural gas the solubility in the gas phase of the heavier and normally liquid hydrocarbons increases rapidly with increasing pressure above 500 to 1000 Ib. per sq. in. Thus, at pressures of 2500 Ib. per sq. in. or higher a gas may contain appreciable quantities of hydrocarbons with normal boiling points as high as 6o0°F., which in turn may be condensed from the gas phase by the reduction of their solubility therein attending pressure reduc-tion. The combined effects of pressure and temperature on condensation and vaporiza-tioi of mixtures are most readily visualized by the study of phase diagrams. Since the construction, application, and interpreta-tion of such diagrams have been described fully in readily available literature, 18-20 this paper will not review the theoretical aspects of this subject. While the behavior of gas-distillate sys tems is now clearly understood, at least in a qualitative way, most of the published work deals with the results of laboratory studies of binary systems or of synthetic mixtures of hydrocarbons, and although several systematic investigations of the effects of separator pressure and temperature on the yields of liquid product from gas-distillate wells have been made21,12z it appears that in all cases the limitations have precluded the construction of even approximately complete phase diagrams for naturally occurring systems. There has 2

Jan 1, 1941

By V. V. Valleroy, A. J. Cornelius, B. T. Willman, G. W. Runberg, L. W. Powers

This paper reports the results of an investigation into the use of steam as a recovery agent. High oil recoveries by steam, as much as 100 per cent greater than by water flood, were demonstrated in laboratory linear cores. The principal mechanisms responsible for the additional oil have been identified as (1) thermal expansion of the oil, (2) viscosity reduction and (3) steam distillation. Although the first two also enhance recovery by hot water flood, they are effective with steam injection at lower volumes of produced fluids. Steam-zone residual oil saturation is independent of initial saturation. Recovery by steam is greater for lighter oils because they contain a greater fraction of steam-distillable components. Equations for the steam-zone advance in a radial homogeneous system are presented; these show the effect of reservoir parameters. The displacement in the hot liquid region moving ahead of the steam front can be estimated by a calculative procedure which is suggested. The method which takes account of the temperature gradient is applicable also to a regullar hot water flood. INTRODUCTION Considerable industry interest in the application of heat to petroleum reservoirs as a means of increasing oil recovery has been evident in the past few years. Three thermal methods which have attracted interest are (1) the injection of saturated steam, (2) the injection of hot water and (3) the injection of air into a formation to support combustion within the reservoir. Much has been published in recent years on underground burning, and there have been several papers on hot water injection. Although there are several early reports1,2 on steam injection, no recent experimental studies have been published on this recovery method. In our early thermal methods research, a marked improvement was found in oil recovery by steam injection compared with recovery by water injection in the same system. An investigation subsequently was undertaken to obtain quantitative information from which to evaluate steam injection as an oil recovery method. In addition, it was desired to investigate the recovery mechanism of hot water as compared with that of "cold" water and steam injection. An understanding of the mechanisms by which these processes operate would generally define favorable field conditions for their successful application. This paper reports the results of the laboratory study and suggests calculative approaches to estimate the field behavior of the steam-injection process. EXPERIMENTAL METHOD EQUIPMENT A schematic diagram of the equipment used for the displacement tests is shown in Fig. 1. Essentially, it consisted of a core with suitable means for recording temperatures, a feed system for injecting steam or cold or hot water, and a receiving train for condensing, cooling and measuring produced fluids. For the steam experiments, air-free saturated steam was piped from the boiler to the core face in insulated lines that were provided with steam traps and bleeds to remove any condensate formed in the lines due to heat losses. A 12-in. section of the line immediately ahead of

By J. H. Lightfoot, Stuart E. Buckley

Deep drilling has led to the development of numerous pools which yield products consisting predominantly of natural gas accompanied by high-gravity water-white or slightly straw-colored liquid. Yields of this "condensate" or "distillate," as it is commonly called, vary from traces to over a hundred barrels per million cubic feet of gas. The fact that this liquid exists in the reservoir as an integral part of the gas phase and is formed by condensation attending simultaneous reduction of pressure and temperature after its entry into the well was apparently first recognized about 1932.l The nature of the physical phenomena involved in this condensation was clarified for the petroleum industry in 1933 by a report by Sage, Schaafsma, and Lacey2 of the results of an experimental investigation of the behavior of mixtures of methane and propane. Search of the literature has revealed that the condensation of liquid from gaseous mixtures by isothermal pressure reduction is not a new discovery. Kuenen was led by theoretical considerations to expect such a phenomenon, and in 1892 reported3 the results of experimental verification of his deductions. This was followed by a considerable amount of work on the phase relations of mixtures by Kuenen 4,5,6 and by 0thers,7,8 mostly in European universities. Since 1930 investigators in this country have reported experimental data on the properties and behavior of a number of hydrocarbon systems."' It is now generally known that in the presence of natural gas the solubility in the gas phase of the heavier and normally liquid hydrocarbons increases rapidly with increasing pressure above 500 to 1000 Ib. per sq. in. Thus, at pressures of 2500 Ib. per sq. in. or higher a gas may contain appreciable quantities of hydrocarbons with normal boiling points as high as 6o0°F., which in turn may be condensed from the gas phase by the reduction of their solubility therein attending pressure reduc-tion. The combined effects of pressure and temperature on condensation and vaporiza-tioi of mixtures are most readily visualized by the study of phase diagrams. Since the construction, application, and interpreta-tion of such diagrams have been described fully in readily available literature, 18-20 this paper will not review the theoretical aspects of this subject. While the behavior of gas-distillate sys tems is now clearly understood, at least in a qualitative way, most of the published work deals with the results of laboratory studies of binary systems or of synthetic mixtures of hydrocarbons, and although several systematic investigations of the effects of separator pressure and temperature on the yields of liquid product from gas-distillate wells have been made21,12z it appears that in all cases the limitations have precluded the construction of even approximately complete phase diagrams for naturally occurring systems. There has 2

Jan 1, 1941

By D. M. Kehn

A method has been devloped for chromatographic analysis Of the vapor and liquid phases Of a a system containing methane to components having 20 or more carbon atoms. The method uses a windowed equilibrium cell in which volumetric phase behavior of the system can be observed accurately and from which small samples of gas or liquid can be withdrawn for analysis. Analyses are made using two chromatographs, one for the lighter and one for the heavier components in a sample. Combination of the two analyses yields a detailed analysis of the gas or liquid sample. The complexity of the condensate heavy ends is evident from the chromatograms of these fractions, and the predominance of the paraffin hydrocarborn serves as a useful marker in interpreting the chromatograms. The K-values obtained in this analytical method are presented for a high-pressure condensate system and predict closely the observed volumetric behavior of the system. INTRODUCTION Quantitative analysis of hydrocarbons from natural gas reservoirs is necessary for several reasons—to calculate the amount of sales gas produced, to calculate the amount of natural gasoline produced, to plan a liquid recovery system, or to calculate the potential economic value of a reservoir produced under one or more of several different conditions. Analysis of natural gas fluids produced to the surface consists of identifying and computing the mol fraction of each component of the mixture. Although methane is the predominant component, varying amounts of ethane, propane, butane, pentanes and heavier components are also present. Materials containing up to 30 carbon atoms occur in amounts which decrease with increasing molecular weight. However, the quantities of components in the 20 to 30 carbon atom range are usually so small that their importance is negligible, and they are undetect-able in natural gas by ordinary analytical methods. All the components up to those having 20 carbon atoms may sigsficantly affect phase behavior, however. Commonly, only the methane-through-pentane fraction is analyzed quantitatively for each component, while components heavier than Pentane are lumped and repored as "hexane- plus". Expensive, tedious techniques are required for analysis of this fraction. Consequently the detailed analyses needed for prediction of reservoir behavior are usually undertaken only when major gas fields are being developed. The need for complete analyses of condensate systems is apparent when it is recalled that most gas fields are produced by pressure depletion. As the pressure declines, some of the heavier hydrocarbons are lost as liquids which are in the reservoir. In many instances the amount of liquid in equilibrium with the gas phase at high pressure constitutes only 1 or 2 mol per cent of the total system. Flash calculations generally must predict the actual amount of liquid with an accuracy of a few per cent in order to be useful. This retrograde condensation has been understood for years, but accurate correlation methods to permit quantitative prediction of phase behavior in the retrograde region are not presently available. The increasing importance of natural gas has made accurate prediction of phase behavior and composition of produced natural gas streams an economic necessity. The work reported here was undertaken to provide a rapid, economical method for obtaining the vapor-liquid equilibrium information needed to predict accurately the composition of the fluids produced from a gas reservoir throughout its life. TO develop this method, a pressure cell equipped with windows was designed and built for observing the volumes of liquid and gas present at reservoir pressures and temperatures. Use was made of established chromatographic methods for rapid and detailed analysis of both phases. This paper describes the equipment and techniques developed for obtaining vapor-liquid equilibrium data, presents the results of analyses of a condensate system, and indicates the usefulness of these data in predicting hydrocarbon phase behavior. DESCRIPTION OF EQUIPMENT USED The equipment used in obtaining the required information on phase behavior and the complete analysis of hydrocarbon mixtures through C, will be described first, followed by a discussion of the operation of the equipment. It will be helpful, however, to consider first a brief outline of the technique used. A sample of separator gas and liquid is charged to the windowed cell (see Figs. 1 and 2) where volumetric equilibrium phase behavior at reservoir pressures and temperatures can be determined. Then samples of the coexisting phases are withdrawn. The methane-through-pentane fraction is analyzed with a chromatograph equipped with a hot-wire detector, and the pentane-plus fraction is analyzed with a second chromatograph equipped

Jan 1, 1965

By H. K. van Poollen, H. C. Bixel

A treatment is given of the transient pressure behavior of a well located at the center of a circular region surrounded by a radial discontinuity. On either side of the discontinuity, the values of permeability, viscosity, compressibility and porosity are uniform but may be different from those on the other side of the discontinuity. The results are obtained by solving a pair of finite difference equations. The numerical solution to these equations is obtained using a digital computer. The results are compared with previously published, approximated analytical solutions to the same problem. Solutions, presented graphically, show pressure decline for constant rate fluid production. The range of variables studied include dimensionless time from '0.001 to 100 and storage capacity ratio from 0.001 to 1,000. The well behaves as if it were in an infinite reservoir for dimensionless times less than 0.25. Reservoir properties near the well can be estimated in the usual manner. An overlay technique is used to match an experimental curve with one of the theoretical curves. It is possible to estimate the distance to a discontinuity by substituting the actual time t and the corresponding dimensionless time tD at which a match occurs into the equation a = (0.000264 tk1/tD , µ1 cI)I/2 where kI/ I µI cI is the diffusivity near the well, and may be estimated from data taken at early time. Several buildup curves are computed. These curves show that for early shut-in times, correct values for transmissibility are obtained from conventional analysis. However, erroneous values of static reservoir Pressure are obtained unless data at large shut-in times are taken. INTRODUCTION A mathematical treatment of the transient pressure response of a well located at the center of a region bounded by a circular discontinuity is given. Within a region (Fig. 20) the properties of both the rock and the fluid are considered to be constant on either side of the discontinuity. While these properties are considered constant, they may be different on opposite sides of the discontinuity. A discontinuity of this type could be a fluid-fluid contact or a sudden change in rock characteristics such as thickness, porosity or permeability. Analytical solutions to this problem are available. 1-3 However, they are so involved that they are of little practical use. An approximate solutionl is available but the range of times over which it is valid has not been specified. A numerical solution to a pair of finite difference equations is used to obtain the solution given in this paper. PREVIOUS WORK One of the first solutions to the problem was published by William Hurst.1 Hurst considered unsteady-state flow of fluids through two sands in series with different mobilities in each sand. He used Laplace transforms to obtain a solution for a single well located at the center of the circle enclosing the first of the two sands. In this case, the solution for the pressure change in Region I (Fig. 20) is2

By J. E. Warren

The mathematical problem considered by the author1 can be given another physical interpretation which is of some practical significance. The alternative physical problem involves the approximate behavior of a single well which is producing at a constant rate through an axially symmetric, horizontal fracture of infinite flow capacity which is located at the center, top or bottom of a uniformly thick, horizontal, homogeneous, anisotropic reservoir of infinite lateral extent which contains a single, slightly compressible fluid. Using Coats' asymptotic results, the wellbore pressure in the fractured system is given by the following equation.

By F. G. Miller, T. D. Mueller, L. B. Davidson

A mathematical model of reservoir behavior during one cycle of the intermittent steam injection process is presented in this paper. A cycle of the process is considered to be composed of three stages: injection, condensation and production. The model concentrates on behavior during the production stage. The influence of several parameters on production improvement is described, using the results obtained with a numerical equivalent of the model. Reservoir system parameters considered are thickness, reservoir thermal conductivity, oil viscosity, solution gas-oil ratio and the change in oil effective permeability with temperature. Operating parameters investigated are heat injection rate, steam temperature and cumulative injection time. In the face of considerable uncertainty, the model appears to give a fair prediction of the behavior observed during an actual test. This makes the model a useful means of selecting projects. It is shown that the model may also be utilized to select an optimum set of operating conditions for a particular project. Results of this study show the extent to which production improvement depends on each of the parameters investigated and give an indication of the range of system conditions within which the process would be effective. INTRODUCTION In recent years the intermittent steam injection or steam soak process of oil recovery has become a popular method of improving recovery in reservoirs bearing high-viscosity hydrocarbons. Production improvement due to the process results from heating the reservoir near the wellbore. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three stages: injection, condensation (the soaking period) and production. During the injection stage, high-pressure steam is injected into the reservoir surrounding the well-bore. This study assumes that injection is carried out over the entire vertical section of the reservoir rock that can be exposed to fluid injection. The condition of steam entering the reservoir is considered to fall within the following limits: (1) steam pressures less than 1,000 psig, (2) steam temperatures between 300 and 700F and (3) steam quality less than 90 percent. The last restriction is due to equipment limitations. Normally, injection re maintained for less than 3 weeks. After termination of injection, the condensation stage begins. The well is shut in for several days, supposedly to make certain that the injected steam condenses. This condensation would insure the retention of injected heat. The production stage is initiated when the well is opened again. Reservoir response during this stage determines the effectiveness of the process (response is defined as the oil production rates, the water production rates and the wellbore temperatures observed during the entire production stage). The immediate response of the reservoir is sometimes quite good. Sets of case histories by Longl and by Owens and Suter2 give some typical figures for response. Duration of the production stage is equal to the time needed for the oil production rate to decline to some predetermined value. This usually requires 4 to 6 months. Termination of the production stage coincides with the start of the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable to continue. One simple model2 and two more sophisticated models3,4 of the process have been presented. These are based on fundamentally different assumptions than those used in this investigation. Although the three models might be modified to fit the assumptions used in this study, it is felt that greater rigor would result by developing a

By Francis Collins, E. R. Brownscombe

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949

By E. R. Brownscombe, Francis Collins

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949

By K. H. Coats

This paper presents the development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertical direction due to router flow are taken into account. A vertical permeability equal to a fraction of the horizontal permeability is also included in the model. The solution is given in the form of a dimensionless pressure-drop quantity tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservoir pressure from a known water-influx rate, to predict water-influx rate (or cumulative amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. The model is applied in example problems to gas-storage reservoirs, and the difference between reservoir performances predicted by the thick sand model of this paper and the horizontal, radial-flow model is shown to be appreciable. INTRODUCTION The calculation of aquifer water movement into or out of oil and gas reservoirs situated on aquifers is important in pressure maintenance studies, material-balance and well-flooding calculations. In gas storage operations, a knowledge of the water movemenr is especially important in predicting pressure and pore-volume behavior. Throughout this paper the term "pore volume" denotes volume occupied by the reservoir fluid, while the term "flow model" refers to the idealized or mathematical representation of water flow in the reservoir-aquifer system. The prediction of water movement requires selection of a flow model for the reservoir-aquifer system. A physically reasonable flow model treated in detail to date is the radial-flow model considered by van Everdingen and Hurst.1 In many cases the reservoir is situated on top of the aquifer with a continuous horizontal interface between reservoir fluid and aquifer water and with a significant depth of aquifer underlying the reservoir. In these cases, bottom-water drive will occur, and a three-dimensional model accounting for the pressure gradient and water flow in the vertical direction should be employed. This paper treats such a model in detail — from the description of the model through formulation of the governing partial differential equation to solution of the equation and preparation of tables giving dimensionless pressure drop as a function of dimensionless time. The model rigorously accounts for the practical case of a vertical permeability equal to some fraction of the horizontal permeability. The pressure-drop values can be used in given equations to predict reservoir pressure from a known water-influx rate or to predict water-influx rate (or cumulative amount) when the reservoir pressure is known. The inclusion of gravity in this analysis is actually trivial since gravity has virtually no efFect on the flow of a homogeneous, slightly compressible fluid in a fixed-boundary system subject to the boundary conditions imposed in this study. Thus, if the acceleration of gravity is set equal to zero in the following equations, the final result is unchanged. The pressure distribution is altered by inclusion of gravity in the analysis, but only by the time-constant hydrostatic head. The equations developed are applied in an example case study to predict the pressure and pore-volume behavior of a gas storage reservoir. The prediction of reservoir performance based on the bottom-water-drive model is shown to differ significantly from that based on van Everdingen and Hurst's horizontal-flow model. DESCRIPTION OF FLOW MODEL The edge-water-drive flow model treated by van Everdingen and Hurst1 is shown in Fig. la. The aquifer thickness b is small in relation to reservoir radius rb. water invades or recedes from the field at the latter's edges, and only horizontal radial flow is considered as shown in Fig. 1b. The bottom-water-drive reservoir-aquifer system treated herein is sketched in Fig. 2a and 2b. Here the aquifer

By F. H. McDowell

The increasing interest in the subject of electrical separation warrants the addition to what has already been written of a few lines covering the practical workings of the Tilly Foster mill under the direction of Mr. E. S. Moffat, General Manager. Since my last paper was presented to the Institute, Mr. S. P. Tomkins, the superintendent, has had thrust upon him for solution several problems complicated by the introduction of new conditions. 1. The richer portion of the lean ore dump, and that nearest the railroad track, having been worked up in 1890, the handling of the balance, including a largely increased amount of rock, could only be accomplished at an increased cost. 2. The tailings had accumulated close about the mill to such an extent that arrangements had to be perfected to move them further away.

Jan 1, 1893