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L. C. UREn,* BerkelEy, Cal. (written discussion).—I heartily concur with Rlr. .Fobs concerning the need for advanced courses on various phases of Petroleum Engineering. I think that his criticism is probably true of most of the engineering schools that are specializing at all in Petroleum Engineering, that is, that most of their so-called graduate courses are not of graduate caliber but are merely more specialized aspects of undergraduate subjects. It would undoubtedly be to the advantage of the petroleum profession if more advanced work could be offered in a few of the leading engineering institutions so that there would be something substantial to offer graduate students wishing to return after a period of undergraduate work, for additional training. There is no doubt but that a better trained engineer, more useful to the oil industry, could be secured from schools offering such advanced training. The problem of adpting our instruction to fit the needs of engineers trained along other lines who wish, after completion of their undergraduate work, to enter thc petroleum engineering field, is a more difficult one. It has been my experience that such men are usually sadly deficient along certain lines and that they are really not prepared for the more advanced work in Petroleum Production Engineering until they have gone back over the work which they have missed in their undergraduate training. I note that Mr. Fohs suggests that other eastern and western colleges not now stressing Petrolelim Engineering, should be encouraged to take up advanced work of this character. With this, however, I cannot agree unless the institutions arc also prepared to offer a full sequence of undergraduate work on which the more advanced courses may be superimposed. Whether or not there is a need for additional engi-ncering colleges entering the petroleum engineering field is an open qucstion. I believe that we arc turning out enough petroleum engineers at the present time and that none of the six institutions now specializing in this field arc overcrowded. Morc-ovcr, they are fairly well distributed over the country, though there may be room for an additional school in the field in the eastcrn section of the United States. F. W. Padgett, Norman, Okla. (written tliscussion).—Assuming that the stnclcnt has the proper fundamentals, that is, general science and a knowledge of the technology of the industry, then the problem is: What courses should be offered from the graduate standpoint? (a) Course Work.—His knowledge of the technology of the industry can be extended advantagcously by means of one and two-hour courses, which consist in a more detailed survey of the various branches of the industry. (b) Lilerdure.—This work may, or may not, be connected directly with his research problem. The student should become familiar with methods of locating articles in the 1iterature; should also become familiar with all the important original

Jan 1, 1928

H. W. Turner, San Francisco, Cal. (communication to the Secretary*): This excellent paper apparently represents the results of extensive observation and experience among the mines of the Mother-Lode, but I strongly question its relegation of the dioritic intrusions to the period of fissuring and ore-deposition. The dioritic rocks referred to are evidently those areas represented by Ransome in the Mother-Lode folio1 as meta-diorites, and, as he says, are merely basic facies of the great granodiorite batholite of the Sierra Nevada. If followed downward I venture to predict that these meta-diorite areas would be found to connect with the great batholite, and to be in fact mere apophyses of it. I see no reason for supposing that these apophyses were intruded into the Mother-Lode slates at a period later than the intrusion of the granodiorite in general. The period of fissuring was subsequent to this intrusion; the basic granodiorite or quartz-diorite areas of the foot-hill region are themselves fissured extensively; and the fissures were filled with quartz, apparently during the same general period of the formation of the Mother-Lode veins. Prichard and Ransome2 both refer to the deposition of quartz in the same lode at different periods resulting from a reopening of the fissures. Some time since, I saw in the stopes of the

Jan 1, 1904

By Donald B. Gillies

PROBABLY the most critical and difficult period in an engineer's career is that between the completion of his college work and his attainment of professional recognition and accepted status in the industrial world. Upon leaving school the young graduate breaks his immediate ties with his educational institution and in a sense finds himself adrift. At this time in his life a society like our Institute has both the responsibility and the privilege of meeting a vitally important need in his professional life. Some of these young men are Student Associates, in the year after graduation, and some are Junior Members, but all need advice and assistance. In some respects this situation will be accentuated by the war. Not only will thousands of young engineers be mustered out of military service but the process we describe generally as industrial reconversion will make necessary many readjustments in personnel. About two years ago the Institute recognized the opportunity of helping the younger member to help himself by appointing a new standing committee to be known as the Committee on Professional Development of Junior Engineers. Herbert Hoover is Honorary Chairman and it is my privilege to serve as Chairman. The name of the Committee is not entirely satisfactory but it expresses the general objective. The present article is in the nature of a progress report of the work of this Committee.

Jan 1, 1945

G. M. TAYLOR,* Colorado Springs, Co1o.-I do not think the plan outlined in this paper would work at Cripple Creek. Most of our men have had a pretty good education. The Cripple Creek district is a lessee district-I do not think there is one mine operating in Cripple Creek to-day that does not have the leasing system. We have as many men leasing on our property as we have mining and every plan who is working for wages is looking for n lease-everyman has mined for him- self, he has been his on7n boss on n lease, either on our own property or

Jan 1, 1919

By P. H. Mell

AMONG the minerals exhibited at the Atlanta Exhibition of 1881, soapstone, kaolin, and asbestos were well represented. The first two occur in large quantities, of very pure quality, throughout the South. The last is somewhat limited in amount, yet in certain localities it exists in masses sufficiently large to pay for working; in North Carolina, Georgia, and Alabama it has been mined with some profit. I would, in this paper, call special attention to the minerals soapstone and kaolin, because their many valuable qualities seem to have been al most entirely overlooked by our Southern manufacturers. Steatite, particularly, occurs in such large quantities, and generally in such close proximity to the great iron regions of Alabama and Georgia, that it is amazing that the iron companies will persist in sending abroad under. heavy expense for firebrick. It would require a much smaller sum of money to quarry this rock and place it at the various furnaces ; and the results obtained, I am sure, would prove its superiority over the majority of firebrick brought into this region. Soapstone, as well as kaolin, is found throughout the metamorphic regions of Alabama, Georgia, South Carolina, and North Carolina. Below-will be found seven analyses that I have made of this mineral, taken from various points in the four States above mentioned. I have also subjected these same specimens to severe fire-tests, and the results were very satisfactory. The tests were conducted in the following manner: Small portions of the compact variety were carefully weighed and placed in a Fletcher's new crucible furnace for gas, and subjected for half an hour to a heat that will in 12 minutes fuse iron. The only effect upon these specimens was a slight change in color .to a darker shade, a small loss in weight, due evidently to the evaporation of water, and, in one or two specimens, a slight degree of fusion on the sharp edges. The first specimen subjected to investigation was taken from a large outcropping in Tallapoosa County, Alabama. Specific gravity, 2.88 ; hardness, 1.9; color, blue gray. Composition Water, - 2.68 Silica, - 65.46 Iron oxide, - 2.10 Alumina, - 15.02 Magnesia, - 15.35 100.61

Jan 1, 1882

Jan 1, 1922

Jan 1, 1897

Jan 1, 1914

By P. H. Mell

AMONG the minerals exhibited at the Atlanta Exhibition of 1881, soapstone, kaolin, and asbestos were well represented. The first two occur in large quantities, of very pure quality, throughout the South. The last is somewhat limited in amount, get in certain localities it exists in masses sufficiently large to pay for working; in North Carolina, Georgia, and Alabama it has ken mined with some profit. I would, in this paper, call special attention to the minerals soapstone and kaolin, because their many valuable qualities seem to have been almost entirely overlooked by our Southern manufacturers. Steatite, particularly, occurs in such large quantities, and generally in such close proximity to the great iron regions of Alabama and Georgia, that it is anlazing that the iron companies will persist in sending abroad under heavy expense for firebrick. It would require a much smaller sum of money to quarry this rock and place it at the various furnaces ; and the results obtained, I am sure, would prove its superiority over the majority of firebrick brought into this region. Soapstone, as well as kaolin, is found throughout the metamorphic regions of Alabama, Georgia, South Carolina, and North Carolina. Below will be found seven analyses that I have made of this mineral, taken from various points in the four States above mentioned. I have also subjected these same specimens to severe fire-tests, and the results were very satisfactory. The tests mere canducted in the following manner: Small portions of the compact variety were carefully weighed and placed in a Fletcher's new crucible furnace for gas, and subjected for half an hour to a heat that will in 12 minutes fuse iron. The only effect upon these specimens was a slight change in color to a darker shade, a small loss in weight, due evidently to the evaporation of water, and, in one or two specimens, a slight degree of fusion on the sharp edges. The first specimen subjected to investigation was taken from a large outcropping in Tallapoosa County, Alabama. Specific gravity, 2.88 ; hardness, 1.9; color, blue gray. Composition: Water,....2.68 Silica,..........65.48 Iron oxide,.........2.10 Alumina,.........15.02 Magnesia,... 15.35 10061

Jan 1, 1882

Gus C. Henning, New York City: In taking up the discussion of these specifications it is necessary that I give definitions of what I understand under the term " Specifications." There may be three kinds, viz.: (1) Specifications in general; (2) Standard Specifications; (3) Standard International Specifications. 1. A Specification is a document used in commerce which should clearly define the qualities of material to be supplied by the producer, the tests which shall be applied for their determination, and the methods which shall be applied for the purpose of determining that the entire product shall possess such qualities, properties and finish as are desired. The terms used in such document must be applied in accordance with their strict technical definitions as used by those most conversant with them, and the language should be of such accuracy that there can be but a single interpretation of each and every clause. A specification is a part of a contract, and should be legally perfect and accurate. Inaccuracy of definition and dic-

Jan 1, 1903

By J. W. Cuthbertson, R. A. Cresswell

THE constitution of Cu-rich alloys with 1.5 to 13.5 pct Sn and 0.25 to 3.0 pct Be and the precipitation-hardening characteristics of alloys with 1.5 to 13.5 pct Sn and 0.25 to 1.0 pct Be have been examined. The hardness and tensile strength of the alloys examined increase markedly after solution treatment at 700°C followed by heat treatment at temperatures between 200" and 450°C. By a combination of cold work and heat treatment, hardness values similar to those exhibited by commercial Be-Cu alloys containing 2.25 pct Be can be obtained with ternary alloys containing 9 pct Sn and 0.75 pct Be and containing 10 pct Sn and 0.5 pct Be. Marked hardening effects occur with alloys containing even less beryllium. By heat treatment alone, a hardness value of 310 diamond pyramid hardness can be obtained from an alloy containing 10 pct Sn and 0.75 pct Be. Preliminary tensile tests have shown that an ultimate tensile strength of 110,000 psi with an elongation of 23 pct is obtainable by precipitation hardening an alloy with 8 pct Sn and 0.75 pct Be. The precipitation-hardening process has been followed microscopically for certain alloys and the inference is that, while the initial hardening effect is probably explained by the precipitation of the ß phase of the Cu-Be system, further hardening, proceeding at a much slower rate, also occurs, apparently as a result of precipitation of phases of the Cu-Sn system, particularly precipitation of the 6 phase at temperatures below 350". The presence of the e phase of the Cu-Sn system in certain alloys at temperatures below 350°C has been confirmed. Tin-bronzes are widely used in engineering applications where a combination of high strength and good resistance to corrosion is wanted. The maximum strength is induced in these alloys by cold working, and it would be an advantage for many purposes if high strength could be achieved alternatively by an age-hardening process. While Cu-Sn alloys have a good fatigue resistance they can be surpassed in this respect by Cu-Be, but the use of the latter alloy is limited by its high cost. If, by adding beryllium to tin-bronze, the properties of the respective binary alloys could to some extent be combined, a most attractive alloy should result. As pointed out by Raynor,¹ beryllium is on the borderline of the zone of favorable size factors for copper, and the solid solubility of beryllium in copper is consequently much more restricted than if the size factor were strongly favorable. The size factor is sufficiently favorable, however, to permit an increase in solid solubility with rise in temperature, and there is thus a composition range in which CU- Be alloys are susceptible to hardening by precipitation heat treatment. Although the a phase of the Cu-Sn system is similarly susceptible to precipitation treatment, the time necessary to establish equilibrium in commercial alloys of this type is usually so great that age hardening becomes impracticable. The addition of beryllium to Cu-Sn alloys would appear to offer a means of conferring on the latter useful age-hardening properties. Masing and Dahl² and others have, in fact, shown that the addition of beryllium to Cu-Sn a solid solutions renders these alloys susceptible to precipitation hardening and after such hardening confers on them an encouraging improvement in physical properties. If this improvement could be achieved by the addition of substantially smaller amounts of beryllium than are customarily found in binary Cu-Be alloys, the ternary alloys should possess economic advantages which might make them more attractive than the binary alloy for some applications. Binary Systems Copper-Tin: The constitution of these alloys is now reasonably well known and is summarized in the equilibrium diagram published by Raynor.³ The following observations, due to Raynor,¹ on the structure of those phases of the Cu-Sn system that are likely to be found in the ternary alloy system will facilitate the subsequent discussion on the examination of that system. The ß phase is an electron compound at the electron-atom ratio 3:2 and has a body-centered cubic crystal structure. This phase is stable only down to 586°C, at which temperature it decomposes eutectoidally into the a and y phases. The y phase has a structure that is also based on the cubic system. This phase is stable down to 520°C, at which temperature it decomposes eutectoidally into the a and d phases. The d phase is an electron compound (Cu³¹Sn8) which has a crystal structure analogous to that of 7 brass. This phase is stable from 590" to 350°C; on prolonged annealing at the latter temperature it breaks down into a mixture of the a and E phases. The e phase is an electron compound (Cu³Sn) having the electron-atom ratio 7:4. Its structure may be regarded as a superlattice based on the close-packed hexagonal system. This phase is stable from 676°C to room temperature. The primary solid solubility of tin in copper increases to a maximum of 15.8 pct as the temperature falls from that of the peritectic reaction to 586°C. The solid solubility remains constant from 586" to 520°C. At lower temperatures the solubility decreases progressively. Below 350°C the fall in solubility is pronounced and is associated with the precipitation of the e phase. This precipitation is very sluggish and does not normally occur under service conditions. Copper-Beryllium: The Cu-Be system has been investigated by Borchers' and others. Raynor5 summarized the present state of information on it.

Jan 1, 1952

ZAY JEFFRIES (written discussion*).-I have read with much interest Mr. Ruder's discussion of Professor Howe's paper, "The Supposed Reversal of Inheritance of Ferrite Grain Size from that of Austenite." I am yet of the opinion that my first explanation' of Mr. Ruder's samples is substantially correct. In that explanation I did not intend, however, to convey the impression that "reversed inheritance" was the general rule nor even of common occurrence but rather that." Non-inheritance" was the general rule. Mr. Ruder suggests that a " perfectly formed" grain is an indication of inheritance. The grains in my Fig. 52 are perfectly formed and in fact more nearly equiaxed than those in Mr. Ruder's Fig: C,3 yet the grains in the former are known not to be inherited but to have been formed by the partitioning of larger austenite grains. On close examination of Mr. Ruder's Fig. C the very shapes of the grain suggest partitioning. Again, the grain size (25 to 30 grains per square millimeter) is at least 10 or- more likely 20 times smaller than might be expected of the austenite from which these grains were .formed under the given time and temperature conditions. Mr. Ruder's newer results on electrolytic and Armco iron are most interesting and instructive. His results fit in. nicely with my conclusions 5, 6 and 10.4 His photographs, however, indicate that the thickness of the pieces of sheet metal are such that abnormal grain growth is promoted. He indicates that equilibrium grain size after heating to 950° C., with furnace cooling, is about the same as his Fig. 1, above. I estimate this to be approximately one-half -grain per square millimeter, or 40 times as large as I have obtained with the same material (Armco iron) after heating Y4-in. bars to 1300° C. for 2 hr. and cooling in the furnace. The effect of thickness of sample on grain size is one which needs more attention.

Jan 3, 1918

By Nathan C. Rockwood

BASIC mineral commodities may be divided into two general classifications in their market or price characteristics. In one class are commodities sold on a world-wide basis, as gold, silver, nickel, asbestos and petroleum, and in the second are those produced and sold locally. Of course, no precise line of demarcation exists between the two; coal, for instance, belongs more or less in both. If there are enough producers of any commodity to prevent control of production by any one person or group, a free market then exists and the price in a buyer's market is determined by the most favored producer-meaning the producer, with the lowest production cost or the lowest cost of transportation, or both, to the particular market, or place of use. With minerals in the first classification, their high intrinsic value far outweighs the transportation cost and a uniform market price is accepted as an essential element in the economy of distribution. But with common minerals of small. intrinsic value and relatively high transportation costs, economists are reluctant to admit that a uniform price may also be an essential element in distribution.

Jan 1, 1940

By F. O. Willhofft

The symposium on mine safety held in connection with the annual meeting of the Institute three years ago, it. was pointed out that "at present no convenient, reliable, accurate means for determining the gas content of mine air is available, for use by the ordinary mine man." In a letter addressed to Coal Age and published on Feb. 25, 1925, Thomas T. Read, then Director of the Safety Service of the Bureau of Mines, stated: "It is to be hoped that sometime in the near future some-one will invent a reliable methane indicator that is con-venient to, use and will permit the keeping of all flames of every character out of bituminous mines, through doing away with the safety lamp." The Martienssen methane detector, which has re-cently received the official approval of the Bureau of Mines, is intended to. meet the demand for such an in-strument as expressed at that meeting and on many other occasions. The characteristics which qualify it for the task are the following: (1) simplicity; (2) small bulk and light weight; (3) ruggedness; (4) accuracy sufficient for the requirements; (5) safety; and (6) dependability. The principle on which the working of the instrument is based may best be explained by giving a brief out-line of the various stages of development through which the inventor, Professor Martienssen of the University of Kiel, Germany, advanced to the final solution of the problem which he had undertaken to solve.

Jan 2, 1928

Executive. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANE WAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY.

Jan 4, 1913

By George S. Rice

STUDIES of ground movement and subsidence caused by mining necessarily chiefly deal with causes and effects of making extensive excavations underground with spans beyond the strength of the un- supported or temporarily timbered roof or hanging wall. Perhaps no other phase of engineering is so de- pendent for results upon the assemblage of what may be called "experience data." That this is the case is cot surprising when one considers the number of variables involved in any at- tempted mathematical formula to determine the angle of draw or the angle of permanent slope of the rocks in any particular case. It is not like dealing with construction materials in which, through testing of. small specimens, in conjunction with the tests of large built- up specimens, relative stresses and strains may be deter- mined and formulas closely approximated for still larger constructions.

Jan 1, 1931

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting passed the following resolution: "The Board of Directors, having been appealed to by several Local Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of

Jan 1, 1938

By Alan M. Bateman

POSSIBLE postwar trends of the more important world minerals will be determined in part by their present world position and by the acts and forces that have operated during the war period, so it is desirable first to review briefly what has been happening in the foreign field of metals and minerals. When we first entered this war we of the mineral profession were all acutely conscious of our lack of strategic minerals and other materials, which had to be imported in great quantities-minerals such as manganese, chrome, tin, mercury, nickel, and antimony. But we realized also that we had to acquire vast quantities of those minerals of which we had thought we were bountifully supplied. Our assumed domestic abundances turned out to be woefully deficient, and demands also arose for new minerals never before produced in large quantities. Some threescore minerals entered the strategic list of our imports. Ores from new sources had to be sought, developed, and transported. Tonnages in the millions of such bulk materials as zinc, lead, copper, chrome, and manganese flowed to feed our war efforts. Sparsely distributed minerals such as tin, mercury, antimony, tungsten, cobalt, mica, and corundum had to be lured from their rock lairs in greatly increased quantities to feed the hungry maw of war industry, and the rare minerals such as tantalite, columbite, beryl, and quartz crystals had to be developed and procured in quantities never before dreamed of. New uses such as radio and radar created demands for many minerals formerly thought of only as adornments of museum collections and not as pressing industrial minerals. Such minerals were never before mined in quantity.

Jan 1, 1945

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating