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By H. O. Jahns

This paper describes the application of regression analysis for obtaining a two-dimensional areal description of heterogeneous reservoirs from short-term pressure-time data such as that obtained in interference tests. The method replaces the time-consuming trial-and-error procedure commonly used to match field data on an electric analyzer or digital computer with a systematic search which is programmed for a computer. The computer program adjusts the properties of a reservoir model automatically until a least-squares fit is obtained between observed and calculated pressure data. The reservoir is simulated by a single-phase, compressible, two-dimensional model. It is divided into a number of homogeneous blocks whose transmissibility (kh/F) and storage (Fch) values are varied to obtain the least-squares fit. The reliability of these values is determined from their standard deviations and correlation coefficients. Although the method is rigorously applicable to single-phase flow only, multiphase flow can be handled provided saturation changes are small during the test. Possibly the method can also be used to obtain a reservoir description from pressure-production history, but this application is outside the scope of this work. The paper includes, in addition to a description of the numerical procedure, a discussion of some of the problems associated with the method. Rules are given to help in selecting the number of homogeneous blocks and deciding upon their arrangement. The uniqueness of a reservoir description is considered. Finally, the use of the method is illustrated by the interpretation of field data from two interference tests. INTRODUCTION Pressure data from short-term transient tests, such as single-well and interference tests, are widely used to obtain reservoir properties. These tests are usually analyzed by assuming a simple reservoir model; very often, a homogeneous one is used. As a result, analysis of the transient data from each well frequently gives different values for reservoir properties. The problem then arises to combine all these differing results into a more detailed picture of the reservoir. One technique is to simulate the reservoir with a digital computer or with an electrical analyzer and to adjust the reservoir parameters by trial and error until the simulated pressure data are in reasonable agreement with the observed pressure data for all wells. Although this method has been used for both transient tests and pressure-history data, it is time-consuming and subjective. A second technique uses regression analysis to replace the trial-and-error procedure with a systematic search that can be programmed for a digital computer. Use of regression analysis in reservoir description was proposed recently by Jacquard and Jain.1 They divided the reservoir into a number of homogeneous blocks whose properties are varied until a least-squares fit is obtained between observed and calculated pressures. However, they did not consider their technique to be operational, mainly because of ".. .(I) the lack of experience in using the method .. . notably for the improvement of convergence; and (2) limitations imposed by the insufficiency of available computers". 1 While the analysis presented in this paper applies the same general principle used by Jacquard and Jain, the specific method is significantly different. Some differences are (1) the regression problem is solved in a different way which requires less computer time in most cases; (2) a stepwise solution, in which the detail in the reservoir description is increased from step to step, is used to improve convergence; and (3) the reliability of the estimated reservoir .properties.. as measured by their standard deviation and correlation coefficient, is estimated'

Jan 1, 1967

By David W. Brunton

(San Francisco Meeting, October, 1911.) MINE-DRAINAGE and the ever-increasing demand for water on the plains have within the past few years necessitated the driving of a great number of adits and tunnels, including many of considerable size and great length. In most instances, ex isting conditions have called for extreme rapidity of execution; and this necessity, coupled with the high altitudes at which most of the work has been carried on, excessive freight-rates, and difficulty -of access, has involved many complex and interesting problems. One of the most rapidly executed undertakings of this class is the Laramie tunnel, recently completed for the Laramie-Poudre Reservoirs & Irrigation Co. This tunnel is driven through Green ridge, a spur of the Continental Divide, which separates the Laramie river from the Cache-la-Poudre in Laramie county, Colo. Green ridge is extremely persistent, and further northward in Wyoming is known as Sherman hill, the highest point on the Union Pacific railway. At the point where the tunnel is driven, two opposing bends bring these streams within 2.5 miles of each other, with a difference in elevation of 500 ft. The rock exposed on the banks of the two rivers does not differ materially in hardness; and, without a geological study of the conditions involved, it would appear that the difference in the depth of erosion of the two streams is due principally to the greater volume of water at this point in the Cache-la-Poudre, which has a drainage-area above the tunnel-portal of 110 sq. miles, as against 30 sq. miles of natural drainage for the Laramie. To increase the water-supply at the tunnel, however, this latter amount has been augmented by two side collection-canals, which bring the available drainage-area up to 84 square miles. The nearest railroad shipping-point to the eastern portal is

Apr 1, 1912

By Herty, C. H.

Iron oxide (FeO) plays an extremely important part in the manufacture of iron and steel. In the three major processes- blast-furnace, open-hearth, and Bessemer converter-iron oxide is the chemically predominant compound and controls to a large ex- tent the operation of the furnaces and the composition and quality of their respective products. In order to emphasize the importance of iron oxide in each process, they will be considered individually in some detail. THE OPEN-HEARTH FURNACE. Iron oxide is introduced into the open-hearth furnace in four ways : 1. The scrap charged into the open hearth is oxidized by the furnace gases, the amount of oxide formed depending primarily on the amount and type of scrap charged. It has been found' that with large scrap, 1.7 Ib. of FeO is formed per 100 Ib. of scrap charged, whereas with scrap of medium size about 5.3 Ib. of FeO is formed per 100 Ib. of scrap charged, when the period between the charging of the scrap and the addition of hot metal is 3 hours. 2. The decomposition of the limestone sets free CO, by the reaction

Jan 1, 1957

By W. R. Ingalls

DUPING the last two years, and especially during the last six months, a number of important articles upon the new methods for the desulphurization of galena have been published in the technical periodicals, particularly in the Engineering and Mining Journal and in Metallurgie. I proposed for these methods the type-name of "lime-roasting" of galena as a convenient metallurgical classification,' and this term has found some acceptance. The articles referred to have shown the great practical importance of these new processes, and the general recognition of their metallurgical and commercial value which has already been accorded to them. It is my present purpose to review broadly the changes developed by them in the metallurgy of lead, in which connection it is necessary to refer briefly to the previous state of the art. The elimination of the sulphur-content of galena has been always the most troublesome part of the smelting-process, being both costly in the operation and wasteful of silver and lead. Previous to the introduction of the Huntington-Heberlein process at Pertusola, Italy, it was effected by a variety of methods. In the treatment of non-argentiferous galena concentrate, the smelting was done by the roast-reduction method (roasting in reverberatory furnace and smelting in blast-furnace); the roast-reaction method, applied in reverberatory furnaces; and the roast-reaction method, applied in Scotch hearths 2 Precipitation-smelting, simple, had practically gone out of use, although its reactions enter into the modern blast-furnace practice, as do also those of the roast-reaction method.

Sep 1, 1906

By AIME AIME

IT IS impossible in this short sketch to give a detailed description of each part of the plant at Bethlehem, therefore, only such facts will be touched on as are necessary to give a general idea of the works. The extent of the plant, and the fact that the units making up the various departments are located in different parts of the works, make it impracticable to mention the departments in any regular order with regard to their location. They are, therefore, mentioned approximately in the order of their relation to each other with reference to their functions in the making of the various products.

Jan 1, 1924

By T. W. Beck

Roof bolter occupations in underground coal mines continue to experience overexposure to respirable dust. One potential source of dust in roof bolting operations is the exhaust from the roof bolter dust collection system. A wet exhaust conditioner (water box) has been developed to reduce dust emissions from the exhaust of the vacuum dust collection system on roof bolting machines. The exhaust conditioner consists of a muffler chamber and a water chamber with four internal partitions to direct airflow over the surface of the water. The National Institute for Occupational Safety and Health conducted a series of laboratory tests to assess the respirable dust capture ability of this device as compared to the standard exhaust muffler. To determine the dust collection efficiency, both devices were placed in the exhaust stream of a simulated roof bolter dust collection system. Gravimetric samplers were operated upstream and downstream of the exhaust conditioner and muffler to evaluate the ability to capture both respirable coal and limestone dust. Researchers observed a 41 % reduction in dust concentrations for the water exhaust conditioner in the laboratory configuration. Significant levels of dust deposition in the sampling chambers may have contributed to this effective capture rate.

Jan 1, 2012

By Jay A. Carpenter

IN six years the construction of Hoover Dam and the power plants probably will have reached the operating stage and this vast new source of power will then be continuously available for industry. The height of the darn will be 580 ft. and the average annual flow of the Colorado River is calculated at approximately 24,000 cu.ft. per sec. If this full head and average flow can be maintained the year round, about one million horsepower will be generated. The U. S. Reclamation engineers, taking into consideration the probable range in flow and head, have set the figure for power contracts at 660,000 firm horsepower, which can be assured at all times of the year. During the months of heavy run-off of water from the Colorado River Basin the power plants should be able to generate the full 1,000,000 hp. capacity of the power plants, so there will be 340,000 excess or secondary horsepower. The cost of firm power at the switchboard will be close to 2.15 mills per kw.-hr., equal to $14.05 per hp.-yr., and the cost of the secondary or off-peak power will be close to 0.8 mills per kw.-hr., or $5.22 per hp.-yr. In no place in the country can such cheap power be obtained today. The electrochemical industry is in a state of flux because the power costs from its old sources have increased so much (to $30 per hp.-yr. at Niagara) that the industries have had to seek new sources, so they have gone to Canada and Norway and built new plants.

Jan 1, 1932

By M. E. Lombardi

IN comparison with the mining industry the petroleum industry is new and inexperienced, and until now it might have been called the fortunate industry. Its great good fortune consisted in two things; a bountiful supply hidden by nature in the rocks of the earth, and a steady and large increase, during the past twenty-five years, in the demand for petroleum products. It is a remarkable fact that consumption of gasoline in the United States has shown an increase every year since automobiles first became important, and even in 1930 there was a four per cent increase, in spite of the universal depression; the estimated increase if the times had been normal, was ten per cent. This industry has, therefore, not passed

Jan 1, 1931

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

By Bjorge, Guy N.

MINING method improve through the gradual process of evolution and in 1340 there were no marked outstanding innovations. On the other hand refinements of detail and betterment: in equipment design continued to progress. Among the most important changes have been the increased application of trucks and highway equipment, including tractors and bull- dozers, to open-pit mining as exemplified by Phelps Dodge's Morenci operations; the Mesabi iron range; and the Tri-State district. Mass or bulk handling contributed its part underground with slurhers and conveyors at Consolidated Coppermines and slushers at Climax; and in open-pit mining. conveyors found increased use on the Mesabi range.

Jan 1, 1941

By E. L. WOOD

IN ATTEMPTING to summarize briefly the reconstruction of the Hecla plant since the fire, three important facts must be held in mind; namely: a hurry-up job with the shadow of an insurance company in the background; restriction of working space in the narrow Burke Canyon; and building two-thirds of the plant on a filled area. Construction work was carried on without interruption through the winter season. These adverse conditions have contributed many obstacles not ordinarily encountered in mining work. The first problems immediately after the fire were organization and policy; the-former to create an efficient construction crew out of a mining organization; the latter to determine the type and extent of surface plant to be built. The new crew was organized from a nucleus of mine employees, 25 per cent. of the old crew remaining for construction work. Permanent fireproof buildings were decided upon, the general arrangement of the new plant to be similar to the old one as far as possible, at the same time enlarging it 100 per cent. in anticipation of the demands which would be made upon it when the Star Mine began operating. Cleaning up the wreckage was a big job, the extent of which is indicated by the fact that 30 carloads of scrap iron and steel were moved off the property. In re-establishing transportation facilities at the plant, a previous disadvantage of a steep grade on the high line was obviated by excavating 1600 yd. of solid rock; the fire having destroyed all town buildings below, made this work possible.

Jan 1, 1924

By J. E. Brantly

THE oil-producing industry may logically be 'divided into four independent branches: (1) Acquisition of possible productive lands by lease, fee purchase, concession, or otherwise and the perfection of titles thereto. (2) Studies of the geology of the properties, leading to the location of exploratory wells. These involve reconnaissance and detailed surveys and the use of geophysical instruments, where conditions do not permit surface determination. (3) Drilling of exploratory or test holes and, later, exploitation wells. (4) Actual recovery of the oil from the wells by flowing, pumping, or other methods. These four divisions of the industry are unrelated in detail of accomplishment, but they are entirely complementary, one to the other, and must, in any efficient' organization, harmonize in their respective efforts toward the desired ultimate end. The relative order for the first two branches is not necessarily the proper one; in fact one should have knowledge of the favorable possibilities of a given property before it is acquired, and preferably, also, final opinions as to then proper location for an exploratory well, if such is justified in the light of

Jan 1, 1937

By Donald F. Hammer, Donald W. Peterson

The Magma mine at Superior, Arizona, has produced over 13 million tons of ore yielding 1.5 billion pounds of copper. It is a mesathermal deposit, and, although the bulk of the ore has come from the Magma vein, most of the recent production has come from replacement deposits in limestone. The mine lies in a Precambrian and Paleozoic sequence of rocks that includes schist, diabase, quartzite, shale, and limestone; nearby, these rocks are intruded by igneous bodies of Mesozoic age that were probably the source of the ore-bearing fluids. Locally, these rocks are overlain by Cenozoic volcanic rocks and conglomerate. Layered rocks at the mine dip eastward about 30°. The area is extensively faulted, and surface faults are grouped into an earlier east-trending set and a later northtrending set. An additional set of diagonal faults that trends northwest and northeast is recognized underground. The east-trending Magma vein-fault, with its splits and branches, is the principal mineralized structure of the district. The bulk of the ore occurs in large ore shoots that plunge steeply westward and are sporadically connected by irregular ore shoots dipping gently eastward. The main ore controls apparently are selective zones of permeability related to the transverse faults. A bed of crystalline limestone near the base of the Martin Limestone (Devonian) is the host for the replacement ore bodies-discontinuous tabular pods dipping eastward parallel to the bedding. Selective permeability is again the apparent ore control, caused both by local hydrothermal solution of limestone and by deformation along faults. The principal copper minerals in the vein are chalcopyrite, bornite, enargite, tennantite, chalcocite, and digenite; these minerals vary in abundance according to a distinct zoning pattern. The upper part of the mine yielded considerable zinc as sphalerite, and the oxidized zone was rich in silver. The chief gangue minerals are pyrite, quartz, and hematite. In the limestone replacement bodies, chalcopyrite and bornite are the chief ore minerals.

Jan 1, 1968

By Roy E. Dickerson

CUBA differs considerably from the other Greater Antilles in many geologic fundamentals. Cuba is geosynclinals; whereas Jamaica, Hispaniola. (Haiti), and Puerto Rico are geoanticlinal. (Scliuchert, Chas., Historical Geology of the Antillian. Caribbean Region, p. 13, 1935.) Rocks of lowermost Cretaceous age exist in large volume in Cuba, where- as they are generally absent in the other islands. Since many of the surface indications of petroleum are intimately associated with lowermost Cretaceous rocks, the Vinales limestone,, this difference is most important. The Vinales limestone in many places in Pillar del Rio and Santa Clara provinces reeks with light tars when broken with a hammer. The late David White and his associates on the U. S: Geological Survey studied

Jan 1, 1937

By W. H. Adams

One of the most attractive subjects for technical writers is the gigantic industry of the manufacture of sulphuric acid. This is no doubt, natural when we take into account that it has grown in this country during the past twenty years, from a production of 60,000 tons in the year 1867, to that of nearly 450,000 tons in 1887. We may well excuse much of the literature which but repeats the same old story, as it serves to bring to the public notice, at proper intervals, the hidden resources of our land; and this constant application of essential truths will sooner or later be the means of freeing us from dependence upon the Old World for necessary chemical products. The present increase in manufacture of this acid in the United States is almost wholly from pyrites ores, which we have in unlimited quantities close at hand. The largest consumption of such acid is for treatment of other native products, petroleum, rock-phosphates, etc.; and, considering the knowledge we have gained during the past twenty years, it is safe to say that the industry is but fairly established, and the causes which have operated to place us in our present proud position are but natural incentives for a further growth and an increased consumption of the many other undiscovered or undeveloped resources of our American soi1. In one of his earlier editions Muspratt says: " It would seem that the manufacture of sulphuric acid, though as extensively carried on as any other business, yet seems to be the least understood; and the ignorance of some manufacturers appears to be only equalled by that of writers, who, in their description of the production of this acid, give figures of apparatus, and vaunt as improvements, things which have been exploded for years. It is possible to find in the works of eminent men drawings of apparatus, for the production of sulphuric acid, which never could possibly have worked one day—some, in fact, could never have worked at all."

Jan 1, 1888

By Burk, Hugh A.

AT THE inception of the cyanide process and its adaptation to the practice of gold and silver metallurgy much difficulty was experienced in applying it to auro-cupriferous ores, both in economy of treatment and recovery of the gold from solution. The presence of copper in the ore effected a high chemical consumption of cyanide during treatment, and in the solvent solution, it retarded the precipitation of the gold on zinc shavings. The coating of the copper on the zinc shavings presented even worse difficulties than the increased cyanide consumption as most ores contain a small amount of copper. This interference of copper led to the use of other precipitating methods and attempts to recover the cyanide which was consumed during ore treatment. Of the other methods used, electrolytic precipitation was the most practical until a better understanding of the application of zinc shavings and zinc dust developed. In September, 1905, a patent entitled, "Method for Recovering Precious Metals from Solution," was granted to Isaac Anderson and Michael Scanton. This method is adaptable to precious metal ores containing a small percentage of copper but has never been extensively used or perfected. The process has

Jan 1, 1925

By W. E. Wrather

CURTAILMENT of production was a matter of far more serious concern to the oil industry through 1933 than the search for new supplies of oil. The huge reserves of crude, built up during past years, instead of inspiring a feeling of security, were viewed apprehensively. The status of past laws and court decisions seemed to guarantee to operators the right to produce oil at will, and this entrenched privilege was so widely adhered to that the market was-in a constant state of chaos. The more modern idea of the ownership of oil in place and correlative rights gained headway slowly, since usually there were enough belligerent producers, staunch believers in the old established order, to defeat the efforts of the majority who sought to' introduce order and restraint. State regulatory commissions were unable to cope, with the rebellion among producers with the result that those who abided by proration rulings were penalized, while those who flouted the rulings and produced unrestrainedly were able to make profits on large volumes of flush oil even at low prices. This situation, known in the vernacular as the "hot 'oil" problem, became so acute that the industry was threatened with ruin. The low price for 36c A.P.I. in the Mid-Continent came in April. at 25c per barrel 'but gradually moved upward to the long-hoped for price of $1.00 per barrel in October, after the Federal Government had taken a hand in the matter and effectively allocated production among the oil producing states and materially curbed the "hot oil" runs.

Jan 1, 1934

By ALBERT F. J. BOARDEAUX

(Canal Zone Meeting, November. 191(j.) I. GENERAL INTRODUCTION. 1. Historical. ALLUVIAL gold was first discovered in Guiana in 1852, in the sands of the Arataye river; by Paulino, a Brazilian convict. During the following years, gold was found also in the rivers Orapu, Cirubé, etc. In 1873 the famous placers of the Sinnamary system were opened: Saint-Elie, Dieu-Merci, Adieu-Tat, and Couriége. This group of mines has produced nearly $10,000,000, according to official records, not including the gold that escaped the taxes. The discoverer was a mulatto named Vitalo. Except in a few rich spots, the gold was rather evenly distributed along the creeks. In one instance, gold was found in the red dirt from the slope of a hill, which, after transport to the creek, gave an amount of 150 kilograms. The placers of the Mana system, Enfin, Elysée, Pas-Trop-Tot, date from 1878, and their production has been about $5,000,000. In 1888, the Awa placers, along the boundary between the French and Dutch Guianas, on the Maroni and its tributaries, were discovered. They have yielded $12,000,000. The only industrial company,, the Dutch Guiana French Mining Co., produced in 15 years about 2,500 kg. of gold, worth $1,500,000. From 1893 dates the famous Carsewene discovery, in territory then in dispute between France and Brazil. A settlement was made recently in favor of Brazil, by arbitration of the Switzerland State Council. Carsewene is said to have pro-duced about $18,000,000 in six years (1894-1900), but not even one-fourth of the production went through French Guiana and

Nov 1, 1910

By J. G. Thompson

PROJECT 8411 of the U. S. Bureau of Standards, sponsored by the Iron and Steel Division of the A.I.M.E., is an attempt to define more concisely than has been possible heretofore the accuracy and the Limits ' of usefulness of the ' various methods now in use for the determination of oxygen as it exists in ferrous materials. It originated in correspondence between John Johnston and other metallurgists, and was brought to the attention of the Iron and Steel Division of the Institute at the Annual Meeting in February, 1933. As reported in MINING AND MET,ALLURGY, Vol. 14, page 152, March, 1933, "Dr. Johnston introduced, and those present adopted, a resolution that the Iron and Steel Division of the A.I.M.E., believing that a careful comparison of the several methods now in use for the analysis of steel for nonmetallic elements such as oxygen is highly desirable, heartily endorses the proposal that the U. S. Bureau of Standards act as a clearing house " in this matter, undertaking the final preparation and allocation of identical samples to those laboratories willing to collaborate in this important question, and collate the results re- ported back to the Bureau.'"

Jan 1, 1934

By Joseph A. Holmes

(Pittsburg Meeting, March, 1910.) AT the Mining Experiment Station of the U. S. Geological Survey, in Pittsburg, an investigation of the process of combustion is being carried on in a specially-designed furnace having an unusually long combustion-chamber. This work is conducted by a committee consisting of H. Kreisinger, mechanical engineer; Dr. J. C. W. Frazer, chemist; and Dr. J. K. Clement, physicist. The problem, essentially one of physical chemistry, is extremely interesting to all who are concerned in the burning of coal or the construction of furnaces. The main object of these experiments is to ascertain the relation between the amount of the volatile combustible driven from the coal and the combustion-spaces necessary to burn it completely. Our best steam-coals vary from 15 to 45 per cent. of fixed combustible. The greater part of the latter is burned on the grate; but the volatile combustible leaves the freshly-charged coal and must be burned in the combustion-space. If this space is not large enough, the volatile combustible will leave the furnace only partly burned, and the result will be a considerable heat-loss and a smoky stack. Strictly speaking, the factor which determines the completeness of combustion of the volatile matter, after it has been mixed with a certain amount of air, is the length of time the mixture is allowed to remain in the combustion-space; but this length of time depends on the extent of the space itself. Let us suppose, for instance, that, when a given coal is burned at a certain standard rate, the volume of the volatile combustible driven off per second is 10 cu. ft. Adding, say, 10 cu. ft. of air, the volume of the resulting burning mixture is increased to 20 cu. ft. If the combustion-space is 20 cu. ft., the burning mixture will stay in it,

May 1, 1910