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By Bruno KERL

THE list of deaths reported during the year 1905 comprises the following names (the figures in parentheses indicating the year in which the persons named were elected to membership:- Honorary Member.-Dr. Bruno Kerl. Members and Associates.-Charles Christy Adams (1903), John Wesley Anderson (1898), William Burton Barber (1901), Thomas A. Bennett (1900), Luke W. Bryan (1901), Edwin S. Daugherty (1905), William Scott de Camp (1875), George H. Eldridge (1889), B. W. Frazier (1871), John Broome Guinn, Jr. (1897), Dana C. Irish (1900), Harry Hugh Lee (1899), William Alfred Lindsay (1902), Roland C. Luther (1884), James MacNaughton (1890), Gordon McLean (1899), Herbert Holmes McNamara (1902), August R. Meyer (1886), William Orr (1897), William J. Parker, Jr. (1898), Joseph Phillips, Jr. (1895), Charles O. Ripley (1902), Emmerich J. Schmitz (1883), Ludwig Philip Seeger (1900), Jacob Johnston Sperry (1900), Gustavus H. Stoiber (1902), William L. Study (1905), Robert Macnair Wilson Swan (1900), Richard Henry Terhune (1886), Joseph Thiry (1892), John N. Tisdale (1903), Alfred Isham Totten (1897), Walter H. Virgoe (1902), Charles H. Wellman (1890), Harvey L. Williams (1903). Of these, Dr. Bruno Kerl and Prof. B. W. Frazier have been made the subjects of special Biographical Notices in the Bi-Monthly Bulletin 1 the former in No. 4, July, 1905, p. 743, and the latter in No. 5, September, 1905, p. 1097. Concerning the remainder of the list, the following paragraphs comprise such information as could be obtained by the Secretary. Charles Christy Adams, who had been a member of the Institute since 1903, died in Johannesburg, South Africa, August 31. 1905. He was born in New York City, July 13, 1849, and received his technical training at the Colorado State School of

May 1, 1906

By TENNEY C. DeSOLLAR

TRADITION tells us that the earliest use of Alabama iron was to make shoes for the horses of General Andrew Jackson and his men during the first part of the nineteenth century. The first recorded incident in the making of iron was the request of U. S. Indian Agent Benjamin Hawkins "that a crew of blacksmiths be sent to the Creek Nation in the lower Mississippi territory." These frontiersmen made up the first body of pioneer iron makers in the territory. The first known blast furnace was built by Joseph Heslip in 1818 at Russellville, named after Major William Russell, who was General Jackson's chief of scouts. The Tannehill furnace was built in 1830 in what is now Tuscaloosa County and its ruins, as shown above, can be seen today.

Jan 1, 1937

By John S. Alexander

By S. F. Shaw

Tars paper is a review of the principal details of cyanide practice in several of the modern plants in America, mainly during the year 1908. Two of the mills, the Goldfield Consolidated and the Vets, Colorado, are not yet prepared to give data, the former having started about Jan. 1, 1909, and the latter not yet being completed. These two mills embody most of the latest methods and are therefore described as far as possible. I. CRUSHING. The principal methods of crushing ores for treatment by the cyanide process are with gyratory and jaw-crushers, stamps, Bryan and Huntington mills, and tube-mills. The first stage is usually done by gyratory or jaw-crushers, in a few cases sup-\

Jul 1, 1909

By J. E. Harris

By elimination of other possible nucleation processes, it has been demonstrated, for commercially pure magnesium and a Mg-Al alloy, that at stresses less than that necessary for triple-point cracking creep cavities are most probably nucleated heterogeneously at second-phase particles. Evidence for the existence of such particles is presented and the role of grain boundary sliding in the nucleation process is examined quantitatively. DURING creep deformation of polycrystalline magnesium and its dilute alloys in the temperature range 0.45 to 0.7 Tm (Tm = absolute melting temperature) cavities form mainly along grain boundaries oriented normal to the stress axis and failure eventually occurs by their growth and impingement.' The possibility of low-ductility creep failure of magnesium-alloy reactor cans during service has prompted a number of studies of cavity formation in these materials.2-5 In this paper divergent theories of cavity nucleation6-10 are examined critically and conclusions drawn regarding the most probable mechanism of formation of cavities in magnesium. The paper is divided into two parts. The first section consists of the review and quantitative assessment of the possible role of grain boundary sliding in the nucleation process. In the second part an experimental program is described where an electron-microscope technique has been used to determine if second-phase particles exist in as-received commercially pure magnesium and in a magnesium alloy 1) THEORETICAL REVIEW Possible nucleation sites for creep cavities are: a) high-angle grain boundary triple points,11-14 b) subboundary/grain boundary intersections,15-18 c) ledges in the grain boundary, 19-25 d) second-phase particles. 9,26-30 Each of these possibilities is now considered with special reference to deformation of magnesium. 1.1) Triple-Point Cracking. The stroh31 condition to nucleate fracture is: " > vr [1] where ss = applied shear stress, ? = surface energy, C = shear modulus, L = length of sliding interface. This relationship is independent of the nature of the interface and it is possible to calculate the stress concentration at the end of a sliding high-angle grain boundary and thus deduce, approximately,* the minimum applied stress necessary to nucleate triple-point cracking. Such theoretical predictions for Nimonic alloys have been made by McLean13 and found to agree quite closely with the minimum stress determined by experiment. Stresses capable of nucleating triple-point cracking should also be sufficient to nucleate fracture at a grain boundary due to intragranular slip, for the lengths of sliding interface in the two cases are approximately equal. Thus the minimum stress for triple-point cracking should represent a demarcation between failure due to general "cracking" and that due to cavitation. Hauser, Landon, and Dorn32 have demonstrated that for polycrystalline magnesium in the temperature range 78° to 298°K the fracture stress is inversely proportional to the square root of the mean grain diameter. As pointed out by stroh31 this result indicates that Eq. [I] describes the fracture characteristics of magnesium at low temperatures. Heal3 has reported that for rapid deformation (112 pct hr-1) of polycrystalline magnesium the transition from cracking to cavitation occurs in the temperature range 175" to 275°C. He also presented the fracture-stress values for the same material tested under similar conditions. From Eq. [I] taking G = 1.3 x 10" dynes , ? = 600 ergs . cm-2,33 and L = 0.017 cm, a Stroh-McLean13,31 tensile stress of -266 kg. cm-2 is calculated, corresponding to a transition temperature of -190°C; this is in

Jan 1, 1965

By D. H. Newland

On the bulk basis New York's contribution to the production of oil is small, representing, as it does, a bare half of one per cent of the annual total for the United States. Yet it has more importance than is implied by such a statement. Petroleum includes a variety of organic compounds, some more and some less valuable. It would be a fairer estimate of the situation to say that New York in recent years has produced around 10 to 12 per cent on the average of all Pennsylvania grade oil, the supply of which is strictly limited and the demand steady even in times of overproduction of other grades. One may not infer from this that New York and other Appalachian states enjoy an independent position in the market with a price structure uninfluenced by that of the Mid-Continent, Gulf or California fields. On the other hand, the recent market demoralization in the South and West brought about by uncontrolled production caused prices to drop to a point where the life of the local industry was seriously threatened. The current cost of producing oil in New York under the methods of water-flooding, by which most of the output is now obtained, has been estimated by competent authority at not less than $2.50 a barrel. The

Jan 1, 1934

By Charles Austin

IN an earlier series of studies on 18-8 stainless steel at 600°, 700°, and 800°C.1 one pretreatment was used throughout; viz., 15 min. in hydrogen at 950°C., followed by an air quench. Several manufacturers of this alloy since have expressed doubt as to the suitability of the temperature employed, recommending instead the more customary Strauss treatment as promising superior results. In this subsequent investigation on the effects of the temperature of pretreatment several interesting points have arisen, which are described in this paper. Previous work on our equipment had shown a marked difference between alloys of "similar chemical composition" that had been manu-factured by different companies. Accordingly, one mill-bar length was selected from which to prepare all specimens. It could then be assumed that any marked differences in creep characteristics would be due to effects resulting from variations in the pretreatment of the alloy. The material was furnished by the Allegheny-Ludlum Steel Co. in the form of 5/16-in, dia. rod, finished by air cooling from a mill anneal at 1950°F. (1066°C.). It was analyzed only for the elements shown: carbon, 0,07 per cent; chromium, 18.73; nickel, 9.46; manganese, 0.40. Three pretreating temperatures were chosen, the specimens being held for 15 min. in hydrogen at either: (1) 1150°C., to conform to the recom-mended Strauss treatment; (2) 950°C., to compare with the results of previous tests; or (3) 750°C., to initiate precipitation of carbides in the material before testing. As the test cross sections were only 1/8 -in. dia., air cooling followed the annealing treatment. These treatments per-mitted two direct comparisons: (1) between the 1150° and 950°C. treat-ments to indicate the effect of grain size when all carbides were probably in solution at the start of the test; and (2) between the 950° and 750°C. treatments to indicate the effect of carbide "nucleation" for similar grain sizes.

Jan 1, 1940

By V. F. STANLEY

THERE is not the slightest doubt that the present recoveries of valuable minerals by the Broken Hill mills could be improved, and that further machinery would be installed for the purpose if it could be assured that a high price of metals would be maintained; but concentration, like all other com¬mercial propositions, is a question of profit and loss, and no sensible metallurgist would carry out his work in such a manner as to obtain high recoveries at a financial loss to his company. There is a point in all concentration at which the added money obtained from the higher recovery of minerals is balanced by the extra cost of obtaining the last part of the recovery; a wise metallurgist will be content with his work before his working-expenditure reaches this point. To a casual observer, the work being done by the various Broken Hill mills is identically the same. A closer investigation will show that this is far from being the case, for it is a remarkable fact that, although the larger mines extend over a length of approximately only 2 miles, such a difference in the physical and chemical properties of the ores exists that, from the first reduction downwards, special treatment is necessary in each case, and hardly any two mills are identical in operation. The details of this paper refer directly- to the work of one . particular mill in Broken Hill, for the reason that the ore from each mine presents special difficulties and requires its own special treatment. I have selected the mill referred to because it has been constructed and modified under my supervision.

Sep 1, 1909

By Hugh S. Spence

IN MAY, 1930, G. LaBine and E. C. St. Paul, prospect¬ing round the southeastern shore of Great Bear Lake, in the North West Territories of Canada, discovered pitchblende at what is now LaBine Point. At the same time, they also found native silver in a small sheared break on an island lying off the point. Late in 1930, samples of the pitchblende were sent to the Mines Branch, at Ottawa. The material consisted of several fair-sized slabs of botryoidal pitchblende banded with a brownish quartz. A small amount of chalcopyrite was visible as small particles and fine veinlets, and the pieces were rather heavily stained a yellowish-green by secondary copper-uranium salts. Analyses were run in the Mines Branch Ore Dressing Laboratories on two samples, and small-scale concentration tests were made on one of them. The results of this work were published in a Memorandum Series report (No. 48) of the Mines Branch, in March, 1931.

Jan 1, 1932

By ROBERT H. BOOTH

THE happy intra-plant relationships of the Bridgeport Brass Co. are largely attributable to the interest of the management in this important business factor. In furtherance of this development Carl F. Dietz, President of the Company and a member of the Institute, has contributed the novel plan for the objective presentation of business economics, described herein. All of the officers of the corporation are active in its management and they together with many other workers filling both executive and subordinate positions have a substantial financial interest in the enterprise. The viewpoint of this organization is fairly reflected by the following quotation from Roosevelt's "The Foes of Our Own Household."

Jan 1, 1924

By Max Hebgen

Within the State of Montana the streams rise in the high mountains at. an elevation of from 5,000 to 8,000 ft. These streams leave the State line both east and west at elevations from 3,500 to 2,400 ft. It is, therefore, apparent. that all these streams have an average fall of 3,000 ft. within the confines of the. State, and many opportunities are presented on all streams. for the development of power, by taking advantage of the natural fall. It is probable that 1,000,000 h. p. can :be developed in the State of Montana. I. NATURAL FEATURES OF STATE AFFECTING POWER DEVELOPMENT. The main. range of the Rocky mountains, forming the Continental Divide, cuts the State of Montana into two parts. The eastern part is drained by the Missouri river and its tributaries, the Madison; Jefferson, Gallatin and Yellowstone, rivers. The western part is drained by tributaries to the Columbia river, the Clarks fork and the Kootenai river. The Clarks fork in turn is formed by the junction of Missoula and Flathead rivers, the latter, draining Flathead lake. The western part of the State. is mountainous and the eastern part is comparatively level. As a natural result the rivers in the western part are capable of generating large amounts of power, while in the eastern part of the State natural power sites are much fewer and farther apart. It also follows that in the mountainous districts large amounts of power are required for the mining industry, while in the eastern part of the State, which is principally devoted to agriculture, power is required in smaller quantities. ?

Jan 8, 1913

L. D. GODSHALL, Everett, Washington: This very interesting paper cannot fail to command the attention of every one who has ever had experience in the amalgamation of gold-ores. I wish to call attention to three very important facts brought out very prominently by the paper, namely: 1. The extent of accumulation of amalgam on copper plates in the form of scale, not removable in the ordinary manner; 2. The change in the relative quantity of the two metals in the amalgam as we. recede from the battery-discharge; 3. The difference in fineness of the bullion obtained from the above-mentioned scale as compared with the bullion from the daily clean-ups. From Mr. Bayliss's figures we find that during the life of the plate in question 14,942 tons of ore were crushed, yielding amalgam of the value of $5.03 per ton, or a total value of $75,158.26. The amalgam accumulating on the plate during this time as scale, we find to have had a value of $8340.54, or $0.558 per ton of ore treated, representing 11.09 per cent. of the total amount of amalgam saved in the ordinary clean-up; or, taking the amalgam saved by daily clean-up plus the amalgam-scale as representing the total saved on this plate, or 100 per cent., we find that the daily clean-up saved 90.01 per cent., while the scale represented 9.99 per cent. The above figures do not include some additional amalgam still adhering to the plate after scale had been removed. We are told that this was not an exceptional case at the Drum Lummon, but that other plates have even yielded a third more than the one in question. The interesting query now comes up, whether this experience at the Drum Lummon is exceptional or universal at all mills; and another question arises, as to how long such an accumulation might continue,

Jan 1, 1897

By James Hance

INTRODUCTION SEVERAL years ago the writer was connected with the Mint and Assay Service of the Federal Government as Assistant Assayer at the-Salt Lake Assay Office. At that time cyanide bars formed approximately half of the bullion purchased by that office. Disagreement in valuation between the producer and the office was not infrequent and to a lesser extent between the Assay Office and the Mint, this latter issue being soon obviated, however, by adopting uniform methods of sampling the bars. A nice problem seemed to offer itself for research and the writer began a series of experiments which were soon terminated, however, by his going into other work, and which he regrets have not since been completed. The results attained may suggest lines of approach to this problem and are, therefore, offered in this article. Frederick P. Dewey, Assayer of the Mint Service, U. S. Treasury, has had abundant opportunity to study this phase of metallurgy, and has published several articles relative thereto.1 In the last article cited Dewey quotes analyses of cyanide bullion similar in content to that with which the writer worked, and which show some of the variations met with. In the discussion of these papers,2 comparison has been made in terms of copper bullion, but to the writer this seems of questionable value. Copper bullion may resemble silver bullion, but its similarity to, gold bullion with little or no silver content is another thing. The freezing-point diagram of Roozeboom, reproduced on page 881 of the discussion cited, is for the gold-silver series as stated. The original problem under discussion, however, is not this alloy but gold with base metals other than copper. As for the statement that the corners are the worst places or

Jan 2, 1916

By H. O. Hofman

WHEN dry chlorine gas is made to act in the cold upon finely¬divided gold,' it converts the latter with evolution of heat into auro-auric chloride, Au2CI4, a hard, dark-red, hygroscopic salt. Moisture splits this salt into aurous and aerie chloride, Au2C14 = AuCI + AuCI3; treatment with water converts it into auric chloride and gold, 3 Au2CI4 = 4 AuC13 + Au,. Aurous chloride, when stirred with water, undergoes a similar decomposition, 3 AuCI = AuCI3 + Au,. These decompositions of auro-auric chloride and of aurous chloride furnish the explanation for the practice of moistening an ore before it is treated by the Plattner chlorination-process; practical experience having shown that gaseous chlorine gave an unsatisfactory extraction with dry ore. According to Rose,' fine gold is acted upon more slowly by chlorine than gold containing some base metal, e.g., copper. He also states that small quantities of silver increase the rate of solution, but adds that the coating of silver chloride formed checks, and finally stops, further action, if the percentage of silver be increased beyond a certain undetermined amount. Bromine' acts upon finely-divided gold in a manner similar to chlorine; the auro-auric bromide, Au2Br4, however, is not hygroscopic. Upon treatment with water it is decomposed as is the corresponding chlorine salt. It is generally believed that bromine does not act as energetically upon gold as does chlorine. This seems to be borne out by the results in the leach-

Mar 1, 1905

By Royal Preston Jarvis

minerals of different specific gravities. It is simple in construction, easily operated, capable of treating large quantities in a short time, and highly efficient under various conditions. The question, whether the material to be jigged has first been sized, determines the two principal methods of jigging. Jigging preceded by close sizing, generally known as the Continental or German system, involves a more or less elaborate series of screens or trommels, with attendant cost for installation, operation, and repairs. Jigging without sizing, known as the English system, is, according to Munroe,1 a development of the hand-jigging formerly employed in Cornwall . and introduced by English miners to this country." In its simplest form, the method consists in jigging an ore-mixture previously crushed to some maximum size (although, in some cases, even this preliminary is omitted) oil a relatively coarse sieve, and then jigging again on a filler sieve, the material passing through the first sieve and bedding. While many modifications have been necessary to adapt it for use in mills of large capacity, where hand-work was necessarily, replaced by machines, the principle remains the same; the fact that the English system has been successfully employed, both in this country and abroad, is well known; and arguments have been made for its efficiency and applicability in a wider sphere than it has occupied hitherto. II. REVIEW OF PREVIOUS INVESTIGATIONS. The fact that treating a mixture of minerals under jigging conditions increased the amount of mineral saved, or, as Professor Richards aptly terms it, 1 ?the extra jig-catch," has long been known. To account for this fact a number of theories have been proposed. The work of Rittinger2 in this field has, for many years, been a classic in the literature of ore-dressing. For the purposes of my present paper, however, the work of two American investigators, Prof. H. S. Munroe and Prof. R. H. Richards, is chiefly concerned. Professor Munroe has given the results of an elaborate series of experiments,3 and his deductions, based largely oil theoretical grounds, of this work. After reviewing briefly the two systems of jigging, followed by a discussion of Rittinger's formulas and

Sep 1, 1908

By J. S. UNGER

A LARGE proportion of the coke used is made in the by-product oven from the high-volatile coals mined in the adjacent district. At the beginning it was feared good by-product blast-furnace coke could not be made with our coals. By experimenting with various mixtures of coals, coking time, oven design, and coking temperatures, much has already been accomplished. The results show that a hard, dense coke, not easily broken by handling, can be produced. In its present state it is not all that could be desired, but it is being constantly improved. Such coke has been used alone as the fuel on several of the blast furnaces producing the highest daily production in the Pittsburgh district. Many of the coals in the Pittsburgh district when coked in the by-product oven yield a gas which contains a high percentage of sulfur, which is objection- able for many metallurgical operations. As this fuel is gradually replacing the ideal fuel, natural gas, which is becoming less plentiful, studies are being made of the best methods for purification. Some metallurgists believe sulfur to be a very injurious element in steel. Recent investigations by Government bureaus, scientific bodies and private firms, seem to indicate that a reasonable amount of sulfur may exist in steel without detriment. Without wishing to provoke any metallurgical controversy on the subject of sulfur, the fact remains that the daily purification

Jan 1, 1926

By R. V. Norris

The anthracite coal trade, with a shipment averaging about 70,000,000 tons per year, differs essentially from other coal business, iii the fact that the larger sizes, comprising about 65 per cent. of the total, are used almost exclusively for domestic purposes, principally during the winter months; and that for proper combustion close-sizing is imperative, so that eight sizes are made; broken, egg, stove, and nut, known as prepared sizes, and pea, buckwheat, rice, and barley, known as steam sizes. These sizes are made in the regular course of preparation, and but little variation in the natural percentage of each is practicable. Thus it is necessary either to work the collieries intermittently, or to dispose of all the varying sizes in their fixed proportions. Unfortunately, the market does not at all times absorb the coal in proper proportions, and rather than interfere with the regular operation of the mines it has been found economical to provide storage for the excess. While the cellars of' the consumers are the great storage-plants of the country, this capacity is not under the control of the trade, except so far as reduced prices during the spring and summer months may tempt the use of this reserve. The same remark applies but with less force to the retail yards, which, though usually small, store in the aggregate a large amount of anthracite. While every effort is made to utilize to the utmost the individual storage-capacity of the country, there still remains the necessity for taking care of the irregularities of the market by the construction of storage-plants under the direct control of the producers. Such plants are usually the property of the railroads, and are situated at points most convenient from a traffic stand-point.

Jan 1, 1912

Remarks of Mr. Robert W. Hunt, General, Superintendent, Albany and Rensselaer Iron and Steel Company., Troy N. Y.—In discussing Dr. Dudley's two most interesting papers, I feel a natural hesitancy in disagreeing with conclusions formed after such careful and conscientious work. But I think he has made his deductions from too meagre premises. The analyses of but twenty-five samples are entirely too few to justify the establishment of so important a formula. When we consider that he indirectly proposes to regulate an interest amounting, even at the present low prices, to over $20,000,000 per annum, we may well hesitate before accepting a formula based upon the chemical and physical analyses of but twenty-five steel rails. Dr. Dudley touches the keynote in referring to the proposed labors of the Government Test Commission. They based their hopes of attaining success upon the chemical and physical analyses of a very large number of samples, and in the only branch of investigation which the short-sighted policy of Congress has allowed them to complete, i.e., chain cables, we find that a dozen, twenty-five or one hundred tests gave no satisfactory results. It was only after many hundreds that they were enabled to' draw conclusions. There are so many circumstances hearing upon the life of a rail, that the task of extracting a correct result seems herculean. I presume I am right in stating that in our Northern latitudes early winter and spring months witness the breaking of the greatest number of rails, thus seeming to prove that an unstable road-bed has much to answer for. Then, again, broken and flattened wheels must be taken into account, but I am convinced that more rails have been broken by the treatment which they received before leaving the rolling-mill

Jan 1, 1879

Remarks Of Mr. Robert W. Hunt, General Superintendent, Albany And Rensselaer Iron And Steel Company., Troy N. Y. - In discussing Dr. Dudley's two most interesting papers, I feel a natural hesitancy in disagreeing with conclusions formed after such careful and conscientious work. But I think he has made his deductions from too meagre premises. The analyses of but twenty-five samples are entirely too few to justify the establishment of so important a formula. When we consider that he indirectly proposes to regulate an interest amounting, even at the present low prices, to over $20,000,000 per annum, we may well hesitate before accepting a formula based upon the chemical and physical analyses of but twenty-five steel rails. Dr. Dudley touches the keynote in referring to the proposed labors of the Government Test Commission. They based their hopes of attaining success upon the chemical and physical analyses of a very large number of samples, and in the only branch of investigation which the short-sighted policy of Congress has allowed them to complete, i.e., chain cables, we find that a dozen, twenty-five or one hundred tests gave no satisfactory results. It was only after many hundreds that they were enabled to draw conclusions. There are so many circumstances bearing upon the life of a rail, that the task of extracting a correct result seems herculean. I presume I am right in stating that in our Northern latitudes early winter and spring months witness the breaking of the greatest number of rails, thus seeming to prove that an unstable road-bed has much to answer for. Then, again, broken and flattened wheels must be taken into account, but I am convinced that more rails have been broken by the treatment which they received before leaving the rolling-mill * The remarks of the participants in this debate have been written out by the speakers, and are here given without any attempt to retain the order of the dis¬cussion. While the report does not, therefore, preserve the vigor and spontaneity of the debate, it is believed that it gains in value by giving the matured views of the speakers. The continuation of this discussion at the Pittsburgh Meeting, May, 1879 (beginning with remarks of Mr. Cloud on page 401), is appended for convenience of reference.-T. M. D., Sec'y

Jan 1, 1879

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958