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By R. D. Begley, A. W. Khair

Introduction The technique being investigated here uses a physical mine model which consists of a plexiglass room-and-pillar model 11.4 x 11.4 cm (4.5 x 4.5 in.). It is placed at the bottom of a larger plexiglass box 25.4 x 30.5cm (10 x 12 in.). The box is then filled with a model material representing geologic overburden. Sand has been selected because of its deformability under gravitational forces. The mine model is capable of creating a cavity and induces movement on the surface of the model material. This surface disturbance can be measured using a photographic technique called holographic interferometry. This paper discusses results of an investigation of the possibility of generating subsidence criteria using physical mine models and laser holographic interferometry. Problem Statement Subsidence appears to be widespread in two states - Pennsylvania and Illinois - although serious subsidence is found in localized areas of numerous other states (HRB Singer Inc., 1977). The US Bureau of Mines estimates that more than 1618 km2 (400,000 acres) of urban areas are threatened by subsidence. Pennsylvania and West Virginia contain 57% of these threatened areas, with the remainder being spread out over 16 states (Johnson and Miller, 1979). Events of subsidence have been reported in urban areas, including Pennsylvania (Gray et al., 1977) and Illinois (Mahar and Marino, 1981). One location has observed three episodes of subsidence beginning in 1950 (Bruhn et al., 1981). These subsidence events all occurred over abandoned room-and-pillar mines. Some mines have been abandoned more than 50 years (Bauer and Hunt,1981) . Available research does not offer much on the problem related to time dependent subsidence, especially those associated with the failure of remnant coal pillars. The physical modeling technique developed at West Virginia University is capable of measuring both instantaneous and time delayed subsidence. Laser Holographic Interferometry Laser holographic interferometry, or holometry, uses the interference properties of laser light to measure small movements of objects. The object requires only optical access and no surface instrumentation. This technique is closely related to photoelasticity. Both techniques rely on the uniqueness of the light reflected off or through an object in any given state of stress. The entire measurement process is done remotely without any surface instrumentation and without using a camera. The interferogram is constructed and visual observation will yield fringes on all areas that yielded or moved. The displacement represented by one fringe was determined by Wilson et al. (1977) and is given by the relationship: [d ='1(1) 2 cos 8 where d = displacement of one fringe 6 = incident angle of laser light A = wavelength of light (632.8 x 10-9 meters for Helium-Neon lasers)] In summary, holometry is capable of detecting very small movements of objects under study. It is a very sensitive process that requires laser light and vibration free experiments. Experimental Program Lab Facilities The primary components of the facilities were the laser and the optical table. The light source was 50 milli-watt, Helium-Neon laser. The optical table was a granite slab weighing nearly one ton. All experiments were performed on the optical table. It consists of a large table sitting on air cells similar to car innertubes. Six air cells were placed on top of two layers of wood and Styrofoam. Figure 1 is a schematic diagram of the vibration free table. Even with these precautions, the experiments still had to be performed at night to reduce potential traffic related vibrations. Room-and-pillar mine models consisting of three different pillar sizes were constructed out of plexiglass. The models were designed to represent three different extraction ratios. Figure 2 shows the models. The extraction ratios were determined by the tributary loading concept (Peng, 1978). These models were the primary component of a seam extraction simulator. A schematic of this simulation device is shown in Fig. 3.

Jan 1, 1986

By Robert R. Walden, LeMont West

K ENTUCKY'S first acid-grade fluorspar flotation Kmill, shown in Fig. 1, was placed in operation Aug. 1, 1952, by the Pennsylvania Salt Manufacturing Co. at Mexico, Ky. During 1951 a critical shortage of acid-grade fluorspar developed and it became necessary for the company to produce part of its fluorspar requirements. In 1951 the company purchased the Crider and Lennen metallurgical fluorspar mill and an adjacent stockpile of tailing at Mexico, Ky. The tailing, assaying about 26 pct calcium fluoride, originated from log washer and jig mill concentrators in the area. As the mill did not have a fluorspar dryer or convenient rail facilities, the company leased the Burleson concentrator at Marion, Ky., where these facilities were available. At Marion, Ky., on the Illinois Central Railroad, dry acid-grade fluorspar is transported direct to the company's Calvert City, Ky., hydrofluoric acid plant. The Mexico flotation plant was reconditioned and designed to produce acid-grade fluorspar from the jig tailing stockpile. The new plant flowsheet is shown in Fig. 2. The ore feed, old tailing, which contains 10 pct of waste rock and coarse gravel assaying approximately 8 pct CaF,, is bound together by sticky clay

Jan 1, 1955

By William H. Grady

FactoRs entering into the market value of coal are its grade, and the cost of labor, material, and capital. Reduction in these costs cannot be expected in the future, and it therefore follows that greater economy in their use must be accomplished if it is desired to hold the present markets; more tons of product per unit must be obtained in a given time from both men and material, and means devised for increasing the percentage of lump and domestic sizes. This paper is presented for the purpose of inviting discussion and stimulating thought in regard to the influence of methods of procedure and plans of mining, upon the quality of coal, the economical use of labor, material, and capital, and the cost of production. Even the better methods of the present day leave much to be desired, and a review of the reasons and necessities for their use may be of value in pointing the way to more economical mining. The writer does not attempt to discuss untried methods of mining, but rather to state clearly and concisely a summary of the results obtained under the several methods of procedure that have been adopted. In some instances a high degree of concentration has been effected, and comparisons of the results obtained with the results of lesser degrees of concentration form an interesting study. It is believed that much may be accomplished in improving the quality, and in the more economical use of labor, material, and capital, by concentration, and it is to concentration in particular that your study is invited. The writer, who has occasion to visit many mines, most of which are under different management, has been inclined to the opinion that improvement has been retarded in many ways and that mining has not as yet been entirely freed from the early-day practices which were forced upon it. Practices resulting in lack of concentration, to which reference will be made, are: The absence of robbing, necessitating the frequent interposition of barrier pillars; lack of system and of proper supervision, resulting in losses of life and coal. These practices could not well be

Jan 1, 1915

With the exception of the mentions of coal in Illinois in the period 1660-1680, already referred to, the first coal found in the United States was in the James River, Virginia, field. In 1699 a large tract of .land above the present city of Richmond was allotted for a settlement of French Huguenots by the colonial, government, near the present Manakin, about fourteen miles above Richmond. They soon found coal, tradition says it was uncovered by a hunter pulling out a small tree in a. steel) bank near a stream, and Colonel William Byrd, F.R.S., the most prominent man of his day in the colony, wrote to the Colonial Council of Virginia, May 10 and 11, 1701: "The 10th of May, last., I with Coll. Randolph, Capt. Epes, Capt. Webb, &c., went up to the new settlements of ye French Refugees at ye Manaken Town.... We went tip to ye Cole, w'ch is not above a mile and a half from their settlement on the great upper Creeke, w'ch, riseing very high in great Raines hath washed away the Banks that the Coal lyes bare, otherwise it's very deep in the Earth, the land being very high, and near the surface is plenty of Slate.", Some of the Frenchmen were evidently familiar with the use of coal, as on May 22, 1702, "David Menestrier a black smith and one of ye french Refugees Inhabiting at Luciana Petitioning his Excellency that he may have leave to use ye coal mines lately discovered there for his forge his Excellency by and with ye advice of ye Council loth hereby give Leave to ye said David Menestrier to take what coales he shall want. out of ye said Coal mine for ye use of his forge according to ye Prayer of ye said Petition."2 There was some uncertainty about the grant of these lands to the Huguenots which caused the request for leave to use this coal, as a Virginia patent in its usual form allowed the owner to mine all minerals excepting gold and silver, which were subject to royalties for the Crown. After the visit to the coal above mentioned, "Wm. Byrd, understanding the land had not been granted to the French, took out a patent for 344 acres, including the same, (the coal) which patent was dated October 20, 1704".3

Jan 1, 1942

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of April, 1913: BARNES, BLAKESLEE, Min. Engr Burrwood, La. BOYLSTON, HERBERT M., Cons. Met. Engr 26 Abbot Bldg., Cambridge, Mass. BUEHLER, HENRY A., State Geol Rolla, Mo. CASTO, WILLIAM H., JR., Mining Bonanza, Idaho. COHEN, MAXWELL B., Mill Operator Miami, Ariz. EVANS, MILTON R., Shop Draftsman 92 Division St., Kingston, Pa. HARPER, WALTER S., Asst. Treas 42 Broadway, New York, N. Y. JAMES. JAMES S.. Min. Engr Telluride. Colo.

Jan 5, 1913

By J. P. Smith

Permian salt measures carry extensive lenses of soluble potash salts in north central Germany. Potash deposits of Oligocene age are found in the Upper Rhine Graben of Alsace (France), and in the Catalonian Basin of Spain. These deposits are found in a wide range of structural settings. Reserves are large, and the production of potash salts is an important phase in the economy of each of these countries.

Jan 1, 1950

NEW- MEMBERS The following list comprises the names of those persons who became members during the period Feb. 10, 1917 to Mar. 10, 1917. ANDERSON, .LAWRENCE W., Min. Engr., Boston Mine, Utah Copper Co. Bingham, Utah. AUSTIN, JOHN W., Assayer, Magma Copper Co., P. 0. Box 101, Superior, Ariz. BARNARD, C. W., Treas. and Resident Mgr., Arizona Asbestos Assn., Globe, Ariz. BIERMAN, A. C : Geol., Producers Oil Co., Box 75, Houston, Tex. BOCHERT, W. C., Prof. of Mining, South Dakota State School of Mines, Rapid City, So. Dak. BROOKS, FLOYD R., Shift Boss, Mond Nickel Co., Ltd., Worthington, Ont., Can. BROWN, CECIL J., Draftsman &,Surveyor, Wallaroo SC Moonta Min. & Smelt. Co., Wallaroo, South Australia. BURRAGE, ALBERT C., Vice-Pres., Chile Copper Co., 85 Amos Bldg.; Boston, Mass. BURGESS, JOHN ALBERT Genl. Supt., United Eastern Min. Co., Oatman, Ariz. CARLOCK, JOHN BRUCE, Supt., O'Neall Oil Process Co., - 608 Haas Bldg., Los Angeles, Cal. CARPENTER, BYRON H., Min. Engr., . . Willoughby, Ohio.

Jan 4, 1917

Under the joint auspices of the Illuminating Engineering Society and the University of Pennsylvania there will be given about 20 lectures covering the general principles of illumination and the aspects of lighting practice. They will be held at the University of Pennsylvania in Philadelphia, from Sept. 21 to 28, 1916, inclusive. The subject of illumination of mines will be included in this series, which will be delivered by men selected on account of their qualifications to deal authoritatively with the several phases of the subject. In connection with the lectures there will be an exhibition of the latest developments in illuminating appliances, including lamps, accessories, photometers, together with novel applications of light. There will also be an inspection tour which will include visits to manufacturing establishments, laboratories, lighting companies and notable lighting installations. For further particulars apply to the Illuminating Engineering Society, 29 West 39th Street, New York City.

Jan 6, 1916

By J. F. Myers, F. M. Lewis

The paper reports the development of a large, slow speed ball mill closed circuited with a hydroscillator. This increased grinding efficiency 28 pct over conventional units.

Jan 1, 1950

By Kalervo Rankama

UNTIL a few years ago, geological mapping, the study of ore boulders, and different geophysical methods were the principal means used in the systematic search for mineral deposits covered by a layer of disintegration products or soil. These methods have been developed to a high stage of perfection as far as the geometrical definition of the conductor is considered. Use of geophysical methods in prospecting is based on the fact that an ore body differs from the country rock not only geologically but also in its physical properties. The general drawbacks and complications included in the use of geophysical methods are well known to everyone who has been using them, so need not be entered into here in detail. One of the more important ones is the fact that geophysical methods are unable to furnish information concerning the chemical composition of the ore bodies responsible for the indications. Further, the ores of many metals, such as silver, gold, beryllium, zinc, mercury, tin, lead, vanadium, antimony, chromium. molybdenum, tungsten, manganese, cobalt, nickel, and the platinum metals cannot be directly located by known geophysical methods, owing to lack of physical characteristics suitable for distinguishing them from the country rock. Thus it is quite natural that efforts have been made to develop direct methods for prospecting and locating ore bodies of the elements named. Known as chemical, biogeo-chemical, and geobotanical methods of prospecting, these have been much improved during recent years. A brief review of these methods and of some results obtained with them will be presented in the following, on the basis of available information and my own experience.

Jan 1, 1947

Bailey, Lewis Newton, Master Engineer, Senior Grade, 4th Regiment, U. S. Engineers, Headquarters Company, died of pneumonia at Camp Merritt, N. J., on April 30, 1918. Baird, Louis, Lieut., Royal Field Artillery, British Army, died on the battlefield in 1915. Cobeldick, William Morley, Royal Engineers, died from gas poisoning on October 7, 1915. Dougall, Ralph, killed in action. Evans, Alfred Winter, Lieut.-Col., New Zealand Rifle Brigade, D. S. 0., D. C. M., killed in action on October 12, 1917. Gorman, Thomas C., Lieut., Canadian Engineers, killed in France, Mar. 18, 1918. Hague, William, 1st Lieut., Engineer Officers' Reserve Corps, died in active service. Hall, William T., Capt., Royal Flying Corps, killed in action. Heine, Bernhardt E., Lieut., Aviation Service, killed at Fort Sill, Okla., Aug. 10, 1918. Irving, John Duer, Capt., 11th Engineers, A. E. F., died while on active service in France on July 26, 1918.

Jan 9, 1918

By Walter W. Bradley

FOR a number of years up to the economic setback of the 1929-1931 period, the greatest proportional advances in the mineral industries in California were made among the substances in the nonmetallic groupings, particularly among the so-called industrial minerals and the salines. During the past year or two, although these have not regained the stride that marked their progress in the preceding decade, we can still record, -some new developments. California produces annually between 55 and' 60 different minerals on a commercial scale. Of these, some 40 to 45 comprise the "structural," "industrial," and "salines" materials as grouped in the reports of the State's Division of Mines. Barite-The barite deposits of California were described in Report

Jan 1, 1935

By Raymond D. Sloan

Development and exploration in Oklahoma showed a definite increase in 1941 over 1940 in production, wildcat activity and total well completions. Geological and geophysical work continued and possibly increased slightly in amount. Oklahoma retained third place in the ranking of oil-producing states of the nation, topped only by Texas and California, and followed by Illinois in fourth position. Production averaged 416,800 bbl. daily, a 1.7 per cent increase, as compared with 409,900 bbl. daily for the year 1940. Maintenance of the state's relatively stable producing rate resulted from the discovery of numerous small pools, the recombing of old areas, the establishment of new producing horizons, and the drilling of an increased number of marginal wells. The market for the Mid-Continent crude was strengthened materially to meet the increased demand. Coincident with a deeline in production in Illinois, shipment of Oklahoma-Kansas crude to the eastern points averaged 453,000 bbl. per day, an increase of 49.4 per cent as compared with 1940. The movement south amounted to an average of 42,000 bbl. per day, a loss of 41.7 per cent. Secondary-recovery programs in Oklahoma were given more consideration, operators realizing that in the future many pools would necessarily have to resort to this type of operation. Five permits for water-flooding were issued by the Corporation Commission during the year. These projects were in Rogers, Wagoner and Nowata Counties, in the shallow northeastern area, which has relatively extensive development of this type in the Bartles-ville sand at from 600 to 1000 ft. in depth. Gas repressuring of an individual lease in the 35-year old Glenn pool, Creek County, proved relatively successful, and after a year's operation was extended to cover a much larger area, with several operators participating. More of this type of work is expected in the future; however, it was given an initial setback when the legislative proposal authorizing secondary recovery in the Wilcox zone of Oklahoma's largest pool, the Oklahoma City pool, was pigeonholed by the committee. A continuation of the low discovery rates within the state would possibly lead to a revival of interest in the project. Many pools formerly classified as prorated areas were removed from this classification and transferred into the group of settled production. At the close of the year the issuance of the Federal Conservation Order M-68 and the interrelated Preference Rating Order P-98 caused a sharp decline in drilling operations, which is expected to continue until such operations are stabilized at a lower rate. The ultimate effect of these two orders on discoveries, production and reserves is a matter of speculation and conjecture. During the year, 2110 new wells were drilled, an increase of approximately 18 per cent as compared with the previous year. Of the total, 1235 were oil wells with a combined initial potential of 342,754 bbl. daily, 178 were gas wells with a total

Jan 1, 1942

By Raymond D. Sloan

Development and exploration in Oklahoma showed a definite increase in 1941 over 1940 in production, wildcat activity and total well completions. Geological and geophysical work continued and possibly increased slightly in amount. Oklahoma retained third place in the ranking of oil-producing states of the nation, topped only by Texas and California, and followed by Illinois in fourth position. Production averaged 416,800 bbl. daily, a 1.7 per cent increase, as compared with 409,900 bbl. daily for the year 1940. Maintenance of the state's relatively stable producing rate resulted from the discovery of numerous small pools, the recombing of old areas, the establishment of new producing horizons, and the drilling of an increased number of marginal wells. The market for the Mid-Continent crude was strengthened materially to meet the increased demand. Coincident with a deeline in production in Illinois, shipment of Oklahoma-Kansas crude to the eastern points averaged 453,000 bbl. per day, an increase of 49.4 per cent as compared with 1940. The movement south amounted to an average of 42,000 bbl. per day, a loss of 41.7 per cent. Secondary-recovery programs in Oklahoma were given more consideration, operators realizing that in the future many pools would necessarily have to resort to this type of operation. Five permits for water-flooding were issued by the Corporation Commission during the year. These projects were in Rogers, Wagoner and Nowata Counties, in the shallow northeastern area, which has relatively extensive development of this type in the Bartles-ville sand at from 600 to 1000 ft. in depth. Gas repressuring of an individual lease in the 35-year old Glenn pool, Creek County, proved relatively successful, and after a year's operation was extended to cover a much larger area, with several operators participating. More of this type of work is expected in the future; however, it was given an initial setback when the legislative proposal authorizing secondary recovery in the Wilcox zone of Oklahoma's largest pool, the Oklahoma City pool, was pigeonholed by the committee. A continuation of the low discovery rates within the state would possibly lead to a revival of interest in the project. Many pools formerly classified as prorated areas were removed from this classification and transferred into the group of settled production. At the close of the year the issuance of the Federal Conservation Order M-68 and the interrelated Preference Rating Order P-98 caused a sharp decline in drilling operations, which is expected to continue until such operations are stabilized at a lower rate. The ultimate effect of these two orders on discoveries, production and reserves is a matter of speculation and conjecture. During the year, 2110 new wells were drilled, an increase of approximately 18 per cent as compared with the previous year. Of the total, 1235 were oil wells with a combined initial potential of 342,754 bbl. daily, 178 were gas wells with a total

Jan 1, 1942

On the following pages are abstracts of papers published by the Institute during the year 1935 as TECHNICAL PUBLICATIONS and CONTRIBUTIONS, papers in bound volumes appearing for the first time, and papers in MINING AND METALLURGY. For abstracts of papers that appeared in bound volumes in 1935 but that were published as TECHNICAL PUBLICATIONS in 1934, see the YEAR BOOS dated January, 1935.. Many of the TECHNICAL PUBLICATIONS have been reprinted in bound volumes. Information regarding this disposition, and number of pages in each paper, may be found in the list beginning on page 64. Volume numbers are given as listed at the beginning of the index, page 71. The abstracts are grouped as follows: [Page Metal Mining 17 Uses of Metals 23 Milling and Concentration 23 Iron and Steel Division 26 Nonferrous Metallurgy (Reduction of Ores)...: 34 Institute of Metals Division (Founding and Metallography of Nonferrous Alloys) 36 Page Coal Division 43 Petroleum Division 50 Industrial Minerals Division (Nonmetallics) 57 Mining Geology 60 Mineral Industry Education Division 62 Geophysical Prospecting 62]

Jan 1, 1936

By James K. Richardson

Today, the enigma of the "missing man" in the metal mining industry equals, and frequently surpasses in objective importance, the problems of ore development, drilling, sampling, pumping, milling techniques, geophysical prospecting, or any one of a hundred highly technical subjects. Unfortunately, as engineers, we have confined our attentions, in the main, to the scientific phases of mineral technology, relegating our man power problems to the background. But what good has all our scientific study and preparation been if we can't get the ore mined, milled, or smelted? What has happened to our labor supply? Where is the good old miner who could timber, drill a round, lay track, or do any job underground?

Jan 1, 1949

Aamot, Olav Crone, Chem. Engr., Norsk Elektrokemisk, Kongensgt. 18, Olso. Norway. '29 Abadilla.-Quirico A., Dir., Bureau of Mines Manila, P. I. '38 Abbott, Clarence E., V.P., Charge of Raw Materials, Tennessee Coal, Iron & R.R. Co., 1212 Brown-Marx Bldg., Birmingham, Ala. '04 Abel, Raymond L., Prof., Dept. of Pet. Refin., Univ. of Pittsburgh Pittsburgh, Pa. '29 Abel. Walter D., Cons. Engr 1839 Holmby Ave., W. Los Angeles. Calif. '32 Abele, Louis T R. F. D. 5. Susquehanna Trail, N., York. Pa. '31 Abell, Leo M., Ore Dressing Investigator, School of Mines Adelaide, S. Australia. '31 Abenius. Hakan V., Mine Supt., Bolidens Gruvaktiebolag Boliden, Sweden. '37 Aborn, Robert H., Asst Met., Research Lab., U. S. Steel Corp. Lincoln Highway, Kearny, N. J. '19 Abraham, W. E. V., East India United Service-Club, 16 St. James' Sq., London, S. W. 1, England. '28 Abrams. Charles Jackson 1624 17th St., Denver, Colo. '36 Abstein, Henry T., Engr. & Mgr., Profile-Tamarack Mines Co Yellow Pine, Idaho. '27

Jan 1, 1938

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.'," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".'"', '" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"' have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.' The final expression presented by Starling and Ellingto'n is: i'. (micropoise) -- /t,, exp rX(7') p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) ' ' ' X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay's method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967