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By C. S. Herzig

In the Engineering and Mining Journal of Jan. 27, 1900, there appeared an article by Fred T. Greene, describing a method of measuring stopes by the use of strings, a clinometer and a tape. In the early part of 1899 I had occasion to use a somewhat similar method, for the purpose of accurately ascertaining the volume of a very irregular drift connecting two mines. This drift was an important factor in a lawsuit for $150,000, in which it was necessary to determine accurately the volume originally occupied by the material extracted from the drift. While it is unnecessary to give all details of the controversy, some explanation of the conditions is required for a clear understanding of the following description. This drift was started by the a E." Co. from its workings, in about 7 ft. of ore, and headed toward the " G " property, the plan being to extract all the ore between foot- and hanging-walls, but to take out nothing but ore. As the " G." workings were approached; the ore-body became very irregular and much thinner. It was, however, very closely followed, and where the drift broke through into the " G." workings, the hole was only 11 inches high by 14 inches wide, or just about the size of a man-hole in a boiler.. Thus, this connection-drift tapered sharply; and the very irregular foot-wall sloped toward the " G." workings, and entered them at a place where the stope was only about 3 ft. high, and the ground had already commenced to cave. It may be added that the ore-body was a nearly flat deposit of lead carbonate in limestone, the ore and gangue being quite soft. I was called upon by the " G." people to make the survey

Jan 1, 1901

By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986

By R. A. Stauffer

The chief ore of lithium is spodumene, a lithium-aluminum silicate containing up to 3 pct lithium. The preparation of lithium salts from spodumene is costly because of the low concentration of the metal and the difficulty of separating it from the other alkali metals present. Dr. Kroll's and Dr. Schlecten's recent paper1 has reviewed various methods proposed for preparation of lithium. It will be seen from this paper that the methods proposed to date have required one or another of the lithium salts as a raw material. The high cost of these salts has been the chief item of expense in the lithium metal produced. This situation has made it interesting to investigate the possibility of producing the metal directly from spodumene. When spodumene is calcined at 1000ºC in the presence of lime, lithium oxide is replaced in the ore as is evidenced by the fact that it may be leached from the reaction mixture with water.2 Free energy calculations suggested that lithium oxide might be reduced with aluminum or silicon and the lithium produced distilled from the reaction mixture by heating-to about 1000ºC in a vacuum. These facts taken together suggested that it might be possible to prepare lithium metal directly from spodumene by heating a mixture of the ore, lime, and a suitable reducing agent in vacuum and distilling off the lithium metal as formed. The Replacement of Li2O in Spodumene A series of experiments were undertaken to determine the ratio of lime to spodumene necessary to free substantially all the lithium oxide Present in the Ore. The spodumene used in these experiments was supplied by Foote Mineral Co. in the form of powder of about 200 mesh' Analysis of the spodumene was as follows: PCT SiO2......................... 62.7 Al2O3........................ 29.9 Li2o......................... 4.9 Na2O........................ 0.89 CaO......................... 0.75 MgO........................ 0.49 K2O......................... 0.44 Lime (cp —200 mesh) was added in various ratios to spodumene and thoroughly mixed in a ball mill. Two hundred gram samples of spodumene-lime mixtures were charged loosely in fireclay crucibles and held at 1000ºC in a gas-fired furnace for 5 hrs. The product in each case was ground to pass 140 mesh and then placed in a thimble in a soxhlet extractor. Extraction with water was carried on for 6 hrs. After this period the extract was reduced in volume by evaporation in order to precipitate dissolved lime and was then filtered and titrated with 1/4 normal hydrochloric acid. After correcting for residual calcium oxide in solution, the alkali present was calculated as lithium oxide. The results of these experiments are shown in Table I and Fig I. At lime-spodumene ratios less than 1.5, the products were invariably fused. At the ratio of 1.5 and above, the product was loosely sintered with little evidence of fusion. When the ratio of lime to spodumene was three, replacement of alkali oxides in the

Jan 1, 1949

By E. P. Whittemore

Experience with the ASC multipoint gas lift system was obtained in Colonia zone of the West Montalvo field near Oxnard, Calif. The wells in this pool produce from depths varying from 10,500 to 12,000 ft. Oil gravity is generally 14 to 15' API with a few extremes of 12 and 20" API. Some salt water is produced which causes some very viscous emulsions. Viscosities at 150F (which is the approximate wellhead temperature) vary from 5,000 to 100,000 SSU. Most of the production is by gas lift, although a few wells are produced by rod and hydraulic pump. About half of the gas-lift wells are on continuous flow and the remainder are on intermittent lift using large, ported, pilot-operated valves for single-point transfer of gas from casing to tubing. Gas-liquid ratios vary from about 6 to 10 Mcf/bbl of gross fluid lifted. Wells are produced to a 450-psi trap system. The following remarks will be confined to intermittent lift only, since this is the type of lift which has been achieved with the ASC valve system. The maximum gross fluid which has been produced by single-point intermittent lift is about 350 B/D in 3-in. tubing and 200 B/D in 21/2-in. tubing with gas-liquid ratios of approximately 7 to 9 Mcf/bbl. Some design changes could reduce this ratio. The ASC multipoint system has provided production as high as 480 BOPD in 21/2-in. tubing with gas-liquid ratios just under 4 Mcf/bbl. To be able to apply the multipoint system, it is recommended that a detailed explanation be obtained concerning transition-point pressure and stabilizer setting—what its significance is to the string design, how it may work for or against the operation of the well, how it is related to tubing sensitivity and how it affects the unloading operation. The unloading operation may only be of academic interest in a technical paper, but to the production foreman, unloading and setting the valves in operation is a very real problem and should be understood in detail. One item touched lightly in the paper was the unloading valve. This valve controls the maximum pressure at which the well can be operated. When lifting heavy viscous fluids, it is most important to set this valve for the maximum possible realistic operating pressure at the surface. If the well lifts easily, it is simple to set the ASC valves at a lower operating pressure and the unloading valve will remain closed; but if the well happens to be heavier to lift than anticipated, it may be desirable to operate on the unloading valve itself and use all the energy obtainable at the bottom of the hole. In the Colonia pool very heavy wet-gas gradients are experienced due to the viscosity of the liquid and the dense mist which is left behind a slug of fluid. There are many combination strings of 3- and 21/2-in. tubing. This aggravates the wet-gas gradient problem and provides wet-gas gradients of about 50 to 70 psi/1,000. An advantage which multipoint lift has provided is increased slug efficiency through better maintenance of pressure under the slug and decreased fall back as the slug passes up the tubing. By using multipoint injection, wet-gas gradients have been reduced to about 30 psi/1,000. This has reduced bottom-hole operating pressure and given a production increase. The ASC valve is not a simple device. It's operation is difficult to understand, and it must be understood to be used efficiently in gas-lift design. Operating problems are difficult to diagnose—whether they be caused by the fluid lifted, valve malfunction, lift gas rate, or operating pressure. Calculations and reasoning are required to find out what is causing the problem. Inherent in the ASC valve is the inability to create large pressure differentials across a slug. Large differentials may be required to overcome the inertia of very viscous fluid as it is being accelerated in the bottom of the hole. This is tied back to the design of the unloading valve and is one reason for the importance of setting the unloading valve for the highest possible operating pressure. ~u; to the narrow spread the ASC valves provide, it is impossible to cycle slower than about 24 cycles/day on choke control. If small production of 150 BOPD and less is expected, a surface time-cycle controller will be required if the most economical operation is to be achieved. To achieve a satisfactory operation, the operator must keep a record of any changes made in the operating pressure of the ASC valves. Anything which may cause changes in casing pressure in excess of the stabilizer setting will change the valve operating pressure, and if this is not noted from daily inspection of the well casing-tubing pressure recorder charts, the operator will lose control of the well. Significant results can be achieved using ASC valves; however, considerable knowledge is required to design with them, and attention to detail is required for satisfactory field operation.

Jan 1, 1965

By B. E. Mix, L. M. Barker

THe present methods of unloading ore and coarse-crushing at the Magna plant of the Utah Copper Co. are the developments of the pas five years. Hand dumping and breaking have given way to the rotary car dump and large gyratory; and the bucket elevators and stationary screens have been replaced by conveyors and shaking screens. The coarse-crushing plant may be broadly divided into two units the primary crushing and the secondary crushing, or primary roll, unit The former was erected in 1923; with the exception of the excavation the construction was carried on by forces of the company. Excavation was started in the middle of March, the first concrete was poured July 16, erection of the steel building started Oct. 30, and the unit was com pleted and operating Dec. 30. The unit has a capacity of over 24,001 tons of ore per day, and cost more than a million dollars. Remodeling of the primary-roll unit extended over a period of years preceding this some of the work having been done as early as 1918. Delivery of Ore from Mine, Yard Storage, and Handling Ori Cars to and from Primary Crushing Plant The ore is transported, in steel cars of 80 tons capacity, from the min' to the mill, where a reserve tonnage of loaded cars is maintained. Malle locomotives, handling trains of 45 cars, or approximately 3600 tons o ore per train, deliver the trains to a storage yard which contains thre tracks—a passing track and two storage tracks. All of this trackage i equipped with an overhead trolley system, so that electric locomotive can be used in yard switching. The storage tracks have a total length of 4500 ft. and provide storag space for 140 cars. The passing track, besides permitting switchin room for locomotives, is used for storage purposes between train arrivals thus giving intermittently a total storage capacity for the yard of approxi mately 200 cars. The amount of ore stored at any one time, howeve

Jan 1, 1926

By Thomas Fraser, David R. Mitchell

THE primary purpose of the loading plant is to transfer the finished product from the preparation machines to the railroad car, truck, or barge in which it is to go to market. Secondary purposes of the loading plant are: to prevent excessive degradation of sizes during loading, to reduce segregation as much as possible, and to prevent excessive quantities of very good or off-grade coal from entering any one car. Nonuniformity of consignments is one of the chief sources of com- plaints by consumers and coal merchants. A properly designed loading plant will do much to reduce complaints and ensure uniformity, not only from shipment to shipment but also in each individual consignment along the length of the car and in cross section. DEGRADATION IN STORAGE, LOADING AND SHIPMENT The object in loading is not only to handle the coal without breakage and segregation, but also to produce a well-trimmed load that will ride to its destination without spillage or breakage en route. The small sizes present in a car of prepared coal as received by the purchaser consist of: missed small sizes not screened out in the preparation plant, breakage during loading, and breakage caused by handling en route. For domestic sizes of anthracite shipped from the Pennsylvania anthracite field to Atlantic coast cities, the dealers' loss because of break- age in loading and shipment amounts to from 2 to 5 per cent and for anthracite shipped to Middle West cities, the loss is 8 to 9 per cent. This difference is in part because dealers in the Middle West rescreen their coal more thoroughly than is usual in the East. One dealer handling Illinois No. 6 coal shipped from southern Illinois mines to Chicago reports an average size loss of 10 per cent when lump coal is unloaded with a fork. This runs as low as 5 per cent for carefully loaded coal and as high as 15 per cent for carelessly loaded coal.

Jan 1, 1943

By J. J. Becker

BEAN1 has discussed the magnetic behavior of mixtures of small ferromagnetic particles on the order of 20 to l000A in diam. As he points out, there are three size categories with characteristic properties: 1) Particles large enough to contain many ferromagnetic domains magnetize initially by the motion of domain walls. The initial susceptibility of such particles, if domain-wall motion is assumed to be perfectly easy, depends only on their shape. It is equal to the reciprocal of the demagnetizing factor (and is thus 3/4 tt for a sphere) and is independent of temperature. 2) Smaller particles find it energetically undesirable to contain domain boundaries. They are always spontaneously saturated, and reverse their magnetization only by rotation of their entire magnetic moment. As assemblage of such particles has a remanence which is a large fraction of the saturation of the assemblage; its coercive force is on the order of 2K/1,, where K indicates magnetic aniso-tropy from any source, and I, is the saturation magnetization of the substance of which the particles are made. 3) Particles which are still smaller continue to be single-domain, but the direction of their magnetization fluctuates thermally, as first pointed out by Neel.' They have no remanence and no coercive force and possess the temperature-dependent magnetization curve of a paramagnetic substance with a very large moment. Bean calls this superpara-magnetism. All of these kinds of behavior are observable in alloys consisting of a precipitate of ferromagnetic phase in a nonferromagnetic matrix. Fig. 1 shows a typical aging curve for the room temperature coercive force of a sample of 98 pct Cu-2 pct Co alloy

Jan 1, 1958

By Gilbert Francklyn

The requirements of coals for the manufacture of coal gas, water gas and producer gas will be considered sparately and a short description of each gasmaking process will be given. In this report the term "gas coal" is confined to coals suitable for the manufacture of city gas in horizontal, inclined or vertical retorts. The report does not refer to coke-oven practice.' Briefly, the process of manufacture consists of distilling the coal at high temperature in an externally heated retort out of contact with the air. The products of distillation, consisting of gas, tar, ammonia, etc. are collected and purified. The residue consists of coke, which is removed from the retort at the end of the carbonizing period. To supply the heat required in the process, a portion of the coke produced is converted into producer gas, which is burned under the retort settings. Qualities of Gas Coals The chief qualities that coal must possess in order to be classified as a gas coal are as follows: 1. Gas Yield.—The coal must be capable of yielding gas in sufficient volume and of a satisfactory quality. The yield depends considerably upon the temperature of distillation; a higher temperature will give a larger yield of gas, but the qualit,y of gas (now measured by the British thermal units per cubic foot) will be lower, while a lower carbonizing temperature will give less gas of higher heating value. The true measure of the yield is the number of British thermal units produced in the gas from a given quantity of coal. This number is obtained by multiplying the cubic feet of gas from 1 lb. of coal by the British thermal units per cubic foot of gas; it is called B.t.u. feet per pound. It is found that the

Jan 1, 1930

By Benjamin F. Tillson

THE past seven years, and 1937 in particular, have witnessed the return of New Jersey iron mining to a place of importance. Following the World War period, little mining was done for several reasons. The properties were operated by small merchant furnaces whose demand was not sufficiently large to warrant large-scale methods with their attendant low operating costs. Under those conditions, the ore produced could not compete with that from the Great Lakes. However, when on Nov. 1, 1.929, the Alan Wood Steel Co., of Conshohocken, Pa., leased the Scrub Oak and Washington properties at Mine Hill and Oxford respectively, they made radical changes in the mining and milling processes which greatly reduced the cost of production and pointed the way to a renewed interest in mining in New Jersey. The following factors have been advanced as influencing the reopening of New Jersey mines:

Jan 1, 1938

By AIME AIME

UNTIL recently, practically all geophysical prospecting in Australia was conducted by government departments, either by the Aerial, Geological and Geophysical Survey of Northern Australia or the New South Wales Department of Mines. At present, in addition, the Shell company is carrying out an extensive geophysical campaign in South West Queensland. The Northern Australia Survey has now been in operation for over six years, its work being carried out principally in the northern and central parts of Australia over an area of about a million square miles. At present this Survey is being brought to a conclusion but it appears certain that the geophysical section will be transferred to a Commonwealth Government department on a permanent basis. At present the officers of the Geophysical Section are preparing or have issued some 150 reports on their field work and also a special technical report on the geophysical practice of the Survey.

Jan 1, 1942

By D. R. Mitchell

FOR the second consecutive year, attendance at the Coal Division sessions far exceeded exoectations. Those in charge were continually faced with problems of finding seats and space for attending members. 115 seats were set - II~ for the annual luncheon meeting of the Division and approximately 175 members showed un. Since the hotel management would not serve more than the 115 it meant that 60 members were forced to eat elsewhere. This created hard feelings with some members. How- ever, officials of the Division were not able to obtain in advance any indication of this overflow crowd, but are suggesting to the New York Office that some means other than ticket sales be adopted to obtain an estimate of Division luncheon and dinner attendance. Members could be circularized prior to he meeting or they could be checked when registering as to the events they expect to attend. Under the inspiring leadership of Cadwallader Evans, Jr., Chairman, the Coal Division had a phenomenal growth during the year. Reporting at the luncheon meeting, Newel1 Alford stated that approximately 190 new members had been obtained. A few more years of continuing increase at this rate will make the Coal Division one of the largest Divisions in the Institute.

Jan 1, 1944

By Archer E. Wheeler

IN the copper industry, the year 1942 was one of striving for larger tonnage and increased production. The demands of the war program placed copper high in the list of strategic metals and the Government encouraged production by offering a premium of 5c. per pound for copper output in excess of the 1941 quotas. This had the effect of increasing the tempo of existing operations and also of initiating a number of projects which will eventually result in production from sources not hitherto exploited. No radically new methods of copper reduction were reported.

Jan 1, 1943

By Chas. H. Behre

MINING geology, both theoretical and practical, continued to make noteworthy progress during 1938. Mining companies generally, stimulated especially by the improvement in economic conditions during the latter part of the year, extended their workings and developed new ore bodies. Federal and state surveys expanded their search for favorable localities and actual ore bodies, with corresponding enlargement of regional knowledge. Theoretical investigations covered geochemistry of ore deposition, structural control of mineralization, and mineralogy of the ores (chiefly aided by the microscope). More geochemical work is greatly needed: ore searching is still too purely empirical, based on features that have been recognized else- where. Thus, clearer understanding of the conditions essential to transportation of metal salts is needed. Jean Verhogen has suggested that solubilities

Jan 1, 1939

By C. R. Kuzell

GEOGRAPHICAILY the industry of reducing and refining of copper continued to migrate from the .United States during 1931. While this country is losing the predominant position of its copper industry, our engineers still enjoy their pre-eminent position as leaders in the design and operation of the new plants being brought into production in the four quarters of the globe. Progress in the art, as indicated by the construction of the recently completed works, has not been revolutionary. Standard methods have been followed, augmented by novel features in flow-sheets demanded by the results of progress in the art of ore-dressing, and by reason of problems incidental to the peculiarities of the new ores being treated. Design and construction progress has likewise been orderly and without radical departure from less recent practice; new features in primary and secondary equipment being logical developments to provide for special conditions to keep abreast of improve¬ments in accessory apparatus. The new plants are being rapidly brought in without hazardous novelties and for the purpose of yielding the principal ingredient, copper, in as large a volume as it will he possible to market; the old United States procedure. In the meantime the domestic plants are shut down or operating at a very low capacity, threatened with untimely demise unless the metallurgist can extract and develop other valuable products from the ores. International agreements .and tariff protection may be a temporary reviving stimulant, but for many mines the days of profit will be numbered unless the ores can be made to yield as values the ingredients now being discarded. Invisible progress in this direction has been made during the past year, and it is to he hoped that time will prove that the outstanding progress of 1931 was in the development of processes for the ultimate recovery of by-products from copper ores, perhaps even relegating the value of the copper yield to secondary importance.

Jan 1, 1932

By Nathaniel Hen

IN the United States, in the 2 1/2 years since the rescinding of the wartime order closing gold mines, conditions have not yet returned to normal. Shortages of man power have prevented some mines from operating at all, and most of those in operation are still at reduced capacity. This fact, combined with shortages of materials, the high cost of supplies and labor, high tax rates, and a fixed price for the product have made the past years rather rough ones for gold producers. In foreign countries conditions are rather similar. In Canada several new mines are coming into production and some others are enlarging. Costs have not increased as much as in the United States and gold production is being encouraged. Recently a bonus of 20 per cent on increased production has been proposed. In South Africa, where gold mining is of major importance in the national economy the industry is also in a favored position with government; new discoveries of major importance there will markedly increase the gold output. Demand for labor is rap-

Jan 1, 1948

By Galen H. Clevenger

THE real and permanent advances which take place in any industry are for the most part slow evolutions which frequently develop and grow almost imperceptibly from clay to clay. A meritorious idea may and generally does require long and patient development and commercial application under a variety of conditions and in a number of localities before it emerges as standard and generally accepted practice. There must be not only technical perfection but also economic advantage. Thus a cross-section taken at any particular time of an industry may reveal little that is distinctly new and yet there may have been considerable progress. During the past year there has been little that is new in milling and yet there has been real progress; some problems have been solved and some of what we may term the newer developments have become more firmly, established.

Jan 1, 1930

By AIME AIME

NOTWITHSTANDING the metropolitan appearance of M. L. Haider, the present Chairman of the Petroleum Division, he is not a native New Yorker, but was born at Mandan, N. Dak., Oct. 1, 1904. He began his travels at an early stage in life and after attending the University of Southern California for two years he spent two additional years at Stanford University and was graduated in 1927. After a few months as an analytical chemist for the Portland Cement Co. he became research engineer in the natural gasoline department of the Richfield Oil Co. where he remained for approximately two years before taking a position with the Carter Oil Co. in Oklahoma. He was chief engineer for this company for three years before being trans-

Jan 1, 1945

By Rex B. McLellan, W. A. Oates

FROM a consideration of the application of the Gibbs-Duhem equation to multicomponent systems arken' derived the following equation applying to dilute solutions of a solute, 2, dissolved in a binary solution, 1-3:

Jan 1, 1969

By J. S. Aronofsky

The first step in a quantitative analysis ot the mechanism of oil displacement by water in a fractured reservoir is usually conceded to be the solution of the differential equation describing the saturation distribution of two immiscible fluids flowing in a porous medium, where the capillary pressure is taken into account. In such a system the production mechanism may consist of displacement of oil both by the flow of water due to natural or artificially imposed pressure gradients and by imbibition, which implies a flow of water not due to external pressure gradients. Owing to the presence of the two oil displacement mechanisms, the mathematical model given by the differential equation intended to describe the system may not properly represent the behavior of the physical system. In fact, in the reservoir the rate of water advance may be very slow, and in the case of a fractured reservoir with a great number of large fractures, the pressure difference determining the flow of water through the matrix may be much less than 1 lb/'psi over lengths of a few feet. In such a case, imbi-bition (the exchange between oil in the matrix and water in the fractures resulting from capillary forces) may become, with time. a significant element of the production mechanism. It occurred Lo the authors, however, that without going into a physical analysis of the process of production, it might be possible by means of simple abstract reasoning to throw some light on the variation of recovery with time under conditions occurring in a highly fractured oil reservoir with rising water table. The object of this paper is to present both the reasoning and its application to a reservoir of the highly fractured type. Specifically, the analysis given here was undertaken to try to explain the increase of recovery (as defined later) with time as observed in this reservoir, without having to assume unlikely variations in the reservoir parameters with depth. This attempt has been successful as will become clear upon comparison of the computed recoveries with the actual field data. ABSTRACT MODEL Let us consider a small volume. of porous matrix saturated with oil at time, t = 0. Let the process of oil displacement by water start at time, t = t,,. At some time, t, the process will have terminated. Then a volume of oil equal to or smaller than the original oil contained in the matrix will have been produced. The first basic assumption that describes the model and guides the forthcoming reasoning is that the oil production from the small volume. dv, is a continuous monotonic function of time and that it converges to a finite limit. Such an assumption is not inconsistent with the results of laboratory waterflood tests as well as with results of imbibition tests where this is, in fact, observed. The second basic assumption is that none of the properties which determine the rate of convergence change sufficiently during the process to affect this rate or the limit. Let it be assumed that the form of the function of time relative to production from the matrix volume. dv, is given by where V,(t) is the volume of oil produced up to that time t. R is the limit toward which the recovery converges, A is a constant giving the rate of convergence, and V,(t) is the volume of oil originally in place in the volume, dv. It should be noted that recovery at time I will be understood here to he It follows that r. tends to R as t tends to infinity. CONSTRUCTION OF RESERVOIR FROM ABSTRACT MODEL Let the reservoir consist of a series of identical blocks of porous matrix stacked vertically and separated by fractures. Let each of these blocks satisfy the conditions of our abstract model. These conditions are: (1) that recovery is a continuous mono-tonic function of time converging to finite limit, and (2) none of the properties that determine the rate of convergence change sufficiently to affect the rate or the limit. Let water be rising in fractures so that oil production from any part of the block starts when the water comes in conLact with it. TOTAL RECOVERY FROM THE RESERVOIR COMPARED TO RECOVERY FROM A SINGLE MODEL ELEMENT As stipulated in Eq. 1, in the case of the abstract model,

By L. Mair

A STUDY by J. R. Low, Jr.1 on the effect of quench aging on the Charpy-impact specimens of semikilled 1020 steel disclosed that a decrease in cooling rate from 1275°F raised the transition temperature. This was demonstrated in his investigation by controlling the cooling rate of impact specimens to duplicate that of a heavier plate and com- paring the properties with air-cooled specimens and quenched specimens. The transition temperature of the samples that had been cooled at a rate estimated to be similar to that of an air-cooled 3/4 in. plate was approximately 45ºF higher than the quenched samples. The transition temperature of the air-cooled series was between that of the slow-cooled and the quenched series. On the basis of this work, it appeared that the cooling rate of plates after rolling in a hot mill would have a bearing on the brittle fracture of the

Jan 1, 1955