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By F. W. Davis

SOME idea may be gained of the tremendous consumption of refractories by the open-hearth steel manufacturers from a statement made by A. T. Green at a meeting reported by T11.e Industrial Chemist of London, as follows: "At a very progressive steel plant in the Midlands, with a battery of five open-hearth furnaces working. twelve months and making 3000 tons of steel per week, the cost of refractories per ton of steel produced averages about $0.50 for the actual open- hearth casting and $0.12 for those operations incidental to the rolling of the metal." .These figures, when translated into the annual tonnage of steel, represent a very considerable expenditure.

Jan 1, 1930

By JAMES J. PURDY

The great majority of stokers used in residential heating installations are of the clinkering type. Because of inherent characteristics of the under- feed combustion process as it occurs in these small stokers, and because of the wide range of operating conditions encountered in residential heating schedules, not all bituminous coals can be used successfully in residential underfeed units. The problem of providing consumer satisfaction has been attacked by the joint efforts of the stoker manufacturers and the coal industry; the stoker manufacturers have been concerned with improving their product to permit the use of a wider range of coals, and coal operators have made every effort to market selected and better prepared coals. In view of the wide range of physical characteristics and chemical properties of bituminous coals, the problems are real and are receiving increased attention.

Jan 1, 1949

By Ernest G. Enck

Expanding markets and technological investigations now in progress for commercial production of titanium metal and alloys, as well as expanding uses for the oxide, have resulted in greater production, increased prices, and accelerated search for additional commercial occurrences of titanium minerals. For more than 50 years rutile has been used in moderate quantities in ceramics, in the production of ferrotitanium, as well as nonferrous titanium alloys. During the early 1930's, use of pure titanium dioxide was introduced as an ingredient of coatings for electric welding rods. For technical and economic reasons rutile was soon found to be as good or better for mild steel welding rods, and this use continues to account for a good share of the rutile sales in the U. S.

Aug 1, 1956

California Academy of Sciences, Golden Gate Park, San Francisco, Calif C E Grunsky, President A price list of the publications of the Academy will be sent upon request The voluminous literature issued by the Academy deals principally with subjects in the fields of botany, zoology and biology. The Proceedings are issued as volumes, but separates of each paper contained in the proceedings may be obtained at prices indicated in the list of publications A few of the papers which may be of interest to geologists, follow, and indicate the scope and character of the papers of the Society

Jan 1, 1933

By R. J. Robbins, D. L. Anderson

A tunnel boring machine has potential use in al- most any type of mining where the access shaft (or adit) is large enough or can be made large enough for its initial entry and where the orebody is of sufficient size to warrant its use. Some time will inevitably be lost in negotiating curves or making lateral moves and moving from level to level. Nevertheless, if the orebody is sufficiently large, advance scheduling can minimize the lost time encountered in such moves. Ideally, a mine will be planned for the use of these machines, thus eliminating access and transport problems. From the viewpoint of time involved, the rate of advance by boring as compared to conventional means is worthy of review. For instance, the Blanco Tunnel, one section of the Bureau of Reclamation's San Juan-Chama Project in southern Colorado, was bored in competent sedimentary rock with the following performance:

Jan 7, 1967

By WALTER B. JONES

IN ALABAMA there are three distinct groups of bauxite deposits, as follows: (1) Cambro-Ordovician contact with the principal-deposits located in Talla-dega, Calhoun, DeKalb, and Cherokee Counties, and in adjacent portions of the State of Georgia. (2) Midway-Nanafalia contact, with the principal deposits in Barbour and Henry Counties, and in adjacent portions of Georgia; also in North-eastern Mississippi. (3) Mississippian - Cretaceous contact, with a group of deposits centered around Margerum in Colbert County. For the purpose of more clearly describing bauxite mining in the state, past, present and possible future, these three groups will be described separately.

Jan 1, 1934

By Fred H. Lippold, Wm. H. Wolf

Methods of fair payment for excavating, supporting, and concrete lining tunnels have been sought by various owners for years. Tunneling techniques have changed with the development of equipment-from the hand-mucking operation to the machine mucker and, most recently, to machine-boring; from tunnel supports using timber sets to steel sets to rock bolts and, most recently, to shotcrete support; and from hand-placing the concrete lining using wooden forms to pumping or pneumatic placing using steel forms. As tunnel construction techniques advanced, so did methods for payment for the work performed. The recent development of tunnel-boring machines, or "moles," is precipitating another change. These changes have led to some difficulty in providing proper payment for the various items of work for different types of tunnels. As a major construction agency engaged in water-resources development in the western states, the U.S. Bureau of Reclamation has long been aware of the need for clarification of payment provisions in tunnel construction. The Bureau has some 150 miles of tunnels completed on its projects and about 50 miles of tunnels under construction. In this construction, the Bureau has benefited by the advance made by contractors in improving the techniques of tunnel excavation. To assure that the Bureau has an up-to-date approach to payment provisions, the Chief Engineer recently established a "standard" method of payment for all types of tunnels. It is believed that this new method of payment will be equitable for all contractors bidding on various types of tunnels using the diversity of methods of excavation now available to them. These payment provisions provide for different quantities for excavated tunnels using the blasting technique or using machine-boring techniques. In this way, the contractors have a choice in excavation methods and an equal opportunity to be low in their bids. We believe this will be an incentive to all contractors to be as progressive as the development of new equipment economically allows.

Jan 1, 1970

By E. H. Herron, J. H. Perry

Mathematical simulation of reservoir behavior may be used to help understand reservoir processes and to predict reservoir behavior, thereby leading to the most economically desirable form of exploitation. In addition, simulation can be used as a tool for reservoir description to learn more about the physical nature of the reservoir and the mode of primary recovery. This use is essential in most reservoir studies and represents one of the more significant applications of simulation. Prediction of reservoir behavior provides information concerning displacement efficiency, optimum well locations, and the comparison of alternative producing processes. Since oil, water and gas all commonly occur in many reservoirs, a simulation that takes into account the simultaneous flow of three immiscible phases is a prerequisite for obtaining such information. Furthermore, a simulation that describes this flow in two dimensions provides the capability of evaluating combination gas- and water-drive reservoirs with either an areal or a cross-sectional description. Many reservoir problems require such a simulation. The objective of the research described here was to develop a mathematical model and associated computer program for accurate, efficient, and economical prediction of the reservoir flow of three phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases.l-3 Gottfried et al.' presented an analy- sis of three-phase simulation in one dimension. Fagin and Stewart" and Garrett6 have discussed the simulation of three-phase flow in two dimensions, but their solution techniques were different from the method discussed in this paper. In particular, previous models and computer programs have usually involved either fewer capabilities or inefficient and less rigorous descriptions resulting in limited applicability. In the following sections, we present a description of the model, an evaluation of the method, and the application to reservoir problems. Additional and supporting material is presented in the Appendix. The Three-Phase Model General Description The three-phase model consists of the mathematical description of the flow of oil, water and gas in a reservoir. Conceptually this description considers flow in all three space dimensions, but in the subject simulator it is assumed that no flow occurs in the third dimension. The model includes the effects on reservoir behavior of fluid and rock compressibility, viscosity, gravity, capillary pressure, relative permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. The differential equations governing multiphase, multidimensional flow in a reservoir are too complex to be solved analytically, so they are approximated by a system of finite difference equations and solved

Jan 1, 1970

By Spruille Braden

My attendance at this seventy-fifth Anniversary banquet of the A I M E is for me a homecoming, It means renewing associations with old friends, breathing again 'the invigorating mining atmosphere in which I was born and reared, and being among those who remember with affection and esteem the man from whom I inherited a name so intimately linked to-the mining profession Tonight, like a prodigal son strayed from mining into the far countries of diplomacy, I return, to eat and be merry over the fatted calf on this pleasurable occasion , While there is no riotous living in modern diplomacy, you are no doubt convinced that neither did I suffer a mighty famine in those far lands When I entered the Foreign Service, a few mining friends, viewing diplomats as sartorial perfectionists, or "striped pantsers" preoccupied with the art of cookie pushing, no doubt thought me a lost soul Conversely, some of my new colleagues at first looked upon me captiously and later as a reformed character, because they believed all miners to be rough customers, attired in muddy boots and given to direct action and equally direct or even explosive speech In point of fact, these two professions have much in common I do not have in mind the parallel cynicisms that "a miner is a liar with a hole in the ground" and "a diplomat a man sent abroad to lie for his country " I do

Jan 1, 1947

By D. G. Swarthout, J. W. Savage, R. W. Guard

The Nb-N constitution diagvam has been examined from 1100° to 1450°C at 1 atm N2 pressure. On the basis of- our work plus that of Brauer and coworkers the stable nitvide Phases are: a) a solid solutlion, basic niobium (bcc) with nitrogen contained interstitially; NbN,, x = <0.40; b) ß NhNx,x = 0.39 to 0.45; hexagonal (W2C type) (NbzN); a =3.058A,c = 4.961 + 0.001A c) y NbNx x = 0.75 to 0.80; tetragonal (distorted NaCl type) (Nb4N3); a = 4.386A,c = 4.332 + 0.001A; d) 6 NbN,, x = 0.88 to 0.91; cubic (NaCl type); a = 4.3885 + 0.0007A; e) E NbNx x = 0.92 to 1.00; hexagonal (Tip type); a = 2.958A, c = 11.272 * 0.0015A. In addition, a metastuble transition phase 6&apos; has been observed and occurs only during the transition 6 — E. 6&apos; NbN has these distinguishing parameters: NbNx,x = 0.96; hexagonal (anti-NiAs type); a = 2.94A, c = 5 .46A. The high-temperature phase fields in the system are governed by two reactions: a) 6 + Y + E, a entectoid reaction occurring at 1270" ± 20° C; b) o + N2 = E, a 2 012 1 reaction occurring at 1370" ± 20° C. As part of a study of the electronic low-temperature. properties of transition metal nitrides, a number of specimens of niobium nitride were prepared. Preliminary observations on these specimens showed several points of disagreement with data already in the literature. It was, therefore, decided to determine the constitution diagram for the Nb-N system between 1100" and 1450°C. The objective of this research was to define the temperature and composition regions of stability of the various phases and to explain the differences among previously proposed diagrams. Review of Previous Literature. The research on the Nb-N system to 1964 has been summarized by storms.&apos; Although he does not present a phase diagram, his review covers the research on the system thoroughly. One of the earliest works on NbN is that of Ascher-mann and coworkers2 who studied the superconductivity of the cubic 6 NbN. Subsequent work by Horn and ziegler,3 Cook, Zemansky, and Boorse,1 Rögener:5 Schroder6 and sellmaier7 has qualitatively confirmed the first results on superconductivity, although their methods of preparation differed considerably. The constitution diagrams proposed for the system by Brauer and Esselborn8 and Elliott9 are shown in Fig. l(a)and (b). The diagram in l(a) has been modified by more recent results in Brauer&apos;s laboratory (private communication). Although 6&apos; is shown on this diagram, Brauer has indicated that he now believes 6&apos; to be a metastable phase in the temperature range shown. The diagram of Elliott, Fig. l(b), is based primarily on the results of Elliott and Komjathy10 on ni-trided niobium strip or rod specimens examined by X-ray diffraction and metallography. It will be noted that these proposed diagrams are in conflict with respect to the temperature and composition ranges of

Jan 1, 1968

By N. O. Johnson, J. Boyer, D. H. Sargent, R. B. Frahme

Although the Western bentonite industry has grown rapidly, it is facing major challenges to sustained growth. The fundamental penalty of costly overland transportation to both domestic markets and to US seaports is of increasing importance; as both substitute materials and foreign bentonites present more formidable competition in the historic market areas of drilling muds, foundry sands, and iron ore pelletizing; and as foreign demand grows more rapidly than domestic demand. The Western bentonite industry is facing these challenges by altering its transportation patterns, by upgrading of products, and by emphasizing customer service and stringent quality control.

Jan 9, 1979

By R. Schuhmann

Jan 1, 1965

Later this month (June 24-27) in San Francisco, the Society of Mining Engineers of AIME, together with the American Society of Civil Engineers, the Canadian Institute of Mining & Metallurgy and the Engineering Institute of Canada, is sponsoring the second biannual Rapid Excavation and Tunneling Conference. The dominant theme of the Conference is the practical application of techniques and research relating to underground rapid excavation and tunneling. In the following pages, ME gives highlights of many of the 24 technical sessions and some of the papers being presented. The full proceedings of the Conference will be published by SME-AIME later this year.

Jan 6, 1974

By O. C. Wheeler

The activity in exploration and in the acquisition of prospective oil lands that reached such a high level in Colombia during 1936 gained momentum and reached unprecedented proportions during 1937. Both national and private lands were taken up. In the Magdalena Valley above Puerto Berrio, leases on large tracts of private lands are held by Richmond (Standard of California), Shell and Texas. Tropical also owns leases covering a block of acreage in this area near Honda. From Puerto Berrio to El Banco most of the acreage is of national ownership, and concessions covering parts of this area have been granted to Tropical, Socony Vacuum, Shell and others, while applications for additional concessions are pending. Latterly leases on private lands below the Lebrija River have been taken out by Shell and Richmond. In the drainage basins of the Meta and Guaviare Rivers of the Llanos region of eastern Colombia, several of the major companies have carried on geological exploration and it is understood that some private properties have been leased or optioned. Under Colombian law, subsoil rights are reserved to the nation on all lands that passed from Government ownership after Oct. 28, 1873. Private titles antedating that day carry both surface and subsurface rights. Conditions under which lands may be acquired, explored and

Jan 1, 1938

By J. R. Campbell

THE need for standardizing methods of arriving at definite conclusions regarding the cleanability of a given coal, and for measuring the performance of coal-cleaning equipment, is constantly increasing. Earlier notes by the author on this subject are amplified in this paper, because he believes that better preparation of bituminous coal is a partial solution of the coal operators&apos; troubles. WASHABILITY STUDIES The term "washability" of coal was coined when washing was the universal method of separating coal from its impurities by utilizing their difference in specific gravity. This and analogous terms are still used in their broad sense although pneumatic or air separation is now used to clean coal. These terms are so used in this paper. Too much time or money, can hardly be spent on "feed surveys" to get a "picture" of the coal that is to be cleaned. There have been too many "rule of thumb" methods used. Screen analyses and "sink-and-float" tests on the raw coal enable the coal operator and washery man to predict within reasonable limits the results that may be expected from any efficient cleaning apparatus.

Jan 1, 1928

By Arthur Bell

(San Francisco Meeting, September, 1915) . PRIOR to 1908 the oil production in the State of California, had been almost entirely a heavy fuel, oil, with a high flash point, hut changed within a-short period to a large percentage of refining oil with a low flash, by reason of the coming in of the Santa Maria field, the Midway field, and the increased production of the Fullerton field. This is clearly shown in the following tabulation of California&apos;s production: Year Barrels . Below -20° Be, Above 20° Be,, Per Cent_ Per Cent. 1905 48,307,000 90 10 1910 77,698,000 SO 20 1912 90,075,000 6o 31 1914 10:3,600,000 47 53 The bringing in of these high percentage&apos;s of light oil with their dangerous low flash and the increasing demand for the refined products necessitated the devising of some cheap and efficient means of quickly separating the lighter elements either in the field or at the main distributing points; also it became necessary to remove the excessive percentage of water which many of the light oils carried in emulsion.

Jan 9, 1915

By N. O. Johnson, J. Boyer, D. H. Sargent, R. B. Frahme

Although the Western bentonite industry has grown rapidly, it is facing major challenges to sustained growth. The fundamental penalty of costly overland transportation to both domestic markets and to US seaports is of increasing importance; as both substitute materials and foreign bentonites present more formidable competition in the historic market areas of drilling muds, foundry sands, and iron ore pelletizing; and as foreign demand grows more rapidly than domestic demand. The Western bentonite industry is facing these challenges by altering its transportation patterns, by upgrading of products, and by emphasizing customer service and stringent quality control.

Jan 1, 1980

By Paul M. Tyler

YEAR after year, the kaolin industry of the United States has been setting new production records and making better products. High-grade paper, pottery, and rubber clays are produced in this country mostly in the South. Georgia alone contributes over 70 pct and South Carolina almost 20 pct of the total domestic output. Residual kaolin is mined in North Carolina, highly plastic but naturally sandy Tertiary (Eocene) potting clays are worked in north central Florida, and good white clays are produced in several other states, but the main sources of kaolin or china clay have been numerous deposits in the Tuscaloosa (Upper Cretaceous) formation. This formation of generally sandy sediments is called the Middendorf member in older geologic reports and corresponds in age with some of the New Jersey clays. As shown in fig. 1, it crops out almost continuously in a generally southwesterly direction across South Carolina and Georgia and into Alabama. Clay is mined from this formation in all three states but the principal producing centers lie within about 10 miles of a straight line drawn between Aiken, S. C., and a point about 10 miles south of Macon, Ga. The white kaolins of the South were recognized and used prior to the Civil War but suitable treatment processes were not introduced until World War I when imports, chiefly from England, were curtailed. Although imports of high-grade clays were resumed after 1918, the domestic industry managed to treble its prewar production record during the early 1920&apos;s and has continued to grow. Whereas the 1909 to 1913 average total production in the United States was only 132,104 short tons valued at $705,352 f.O.b. mines, the output in 1948 was 1,-568,848 tons worth $19,756,738. Paradoxically, it seems in retrospect that the early failure of the American industry to meet foreign competition was due to the superior quality of our sedimentary clays in their natural state. Kaolin, of course, is the principal decomposition product of feldspars which originate in acidic igneous rocks such as granite, aplite, alaskite, granodiorite, quartz porphyry, etc. English china clays occur in residual deposits and before they can be marketed they have to be treated to remove accompanying quartz, mica, and other impurities. Notwithstanding the relatively crude methods employed, the final product is a beneficiated clay which is subject to a certain amount of technical control as to quality and uniformity. Although the naturally concentrated deposits in Georgia and South Carolina contain some of the finest crude white kaolin in the world, even it can be made better by suitable treatment. In recent years well over half of the high-grade china clay produced in the United States has been used in making paper. Some qualities of paper clays are still produced by the dry process, or air flotation, but the paper industry&apos;s specifications have grown so exacting that wet processing was adopted and more refined methods had to be perfected. Notwithstanding notable advances in clay-preparation technology during the past decade, or possibly because these advances have implemented and encouraged technologic changes in consuming industries, demand has grown for products of higher uniform quality than can be obtained from even the best natural deposits without rigidly controlled fractionation. Largely as a result of the wide adoption of machine coating for paper, the clay industry has been obliged not merely to eliminate virtually all mineral impurities but also to segregate the clay substance itself into narrow particle-size ranges. By extraordinary coordination of sales effort and production technology, several Georgia companies manage to market a wide variety of specialized joint products but the commercial success of many producers depends upon their mining only the best parts of their deposits and then skimming the cream of this almost pure clay in order to obtain a maximum yield of kaolinite finer than about 2 microns in maximum particle size and possessing low viscosity as well as the more familiar attributes of suitable color and brightness, or reflectance. To the casual visitor from another mineral industry, the kaolin mines and plants may appear to be

Jan 1, 1951

By Paul M. Tyler

YEAR after year, the kaolin industry of the United States has been setting new production records and making better products. High-grade paper, pottery, and rubber clays are produced in this country mostly in the South. Georgia alone contributes over 70 pct and South Carolina almost 20 pct of the total domestic output. Residual kaolin is mined in North Carolina, highly plastic but naturally sandy Tertiary (Eocene) potting clays are worked in north central Florida, and good white clays are produced in several other states, but the main sources of kaolin or china clay have been numerous deposits in the Tuscaloosa (Upper Cretaceous) formation. This formation of generally sandy sediments is called the Middendorf member in older geologic reports and corresponds in age with some of the New Jersey clays. As shown in fig. 1, it crops out almost continuously in a generally southwesterly direction across South Carolina and Georgia and into Alabama. Clay is mined from this formation in all three states but the principal producing centers lie within about 10 miles of a straight line drawn between Aiken, S. C., and a point about 10 miles south of Macon, Ga. The white kaolins of the South were recognized and used prior to the Civil War but suitable treatment processes were not introduced until World War I when imports, chiefly from England, were curtailed. Although imports of high-grade clays were resumed after 1918, the domestic industry managed to treble its prewar production record during the early 1920&apos;s and has continued to grow. Whereas the 1909 to 1913 average total production in the United States was only 132,104 short tons valued at $705,352 f.O.b. mines, the output in 1948 was 1,-568,848 tons worth $19,756,738. Paradoxically, it seems in retrospect that the early failure of the American industry to meet foreign competition was due to the superior quality of our sedimentary clays in their natural state. Kaolin, of course, is the principal decomposition product of feldspars which originate in acidic igneous rocks such as granite, aplite, alaskite, granodiorite, quartz porphyry, etc. English china clays occur in residual deposits and before they can be marketed they have to be treated to remove accompanying quartz, mica, and other impurities. Notwithstanding the relatively crude methods employed, the final product is a beneficiated clay which is subject to a certain amount of technical control as to quality and uniformity. Although the naturally concentrated deposits in Georgia and South Carolina contain some of the finest crude white kaolin in the world, even it can be made better by suitable treatment. In recent years well over half of the high-grade china clay produced in the United States has been used in making paper. Some qualities of paper clays are still produced by the dry process, or air flotation, but the paper industry&apos;s specifications have grown so exacting that wet processing was adopted and more refined methods had to be perfected. Notwithstanding notable advances in clay-preparation technology during the past decade, or possibly because these advances have implemented and encouraged technologic changes in consuming industries, demand has grown for products of higher uniform quality than can be obtained from even the best natural deposits without rigidly controlled fractionation. Largely as a result of the wide adoption of machine coating for paper, the clay industry has been obliged not merely to eliminate virtually all mineral impurities but also to segregate the clay substance itself into narrow particle-size ranges. By extraordinary coordination of sales effort and production technology, several Georgia companies manage to market a wide variety of specialized joint products but the commercial success of many producers depends upon their mining only the best parts of their deposits and then skimming the cream of this almost pure clay in order to obtain a maximum yield of kaolinite finer than about 2 microns in maximum particle size and possessing low viscosity as well as the more familiar attributes of suitable color and brightness, or reflectance. To the casual visitor from another mineral industry, the kaolin mines and plants may appear to be

Jan 1, 1951

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well&apos;s shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner&apos;s&apos; theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner&apos;s widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs&apos; analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner&apos;s&apos; method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner&apos;s method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner&apos;s original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner&apos;s approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink