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By Forest Mintz

Many oil and gas producers find it advantageous to borrow against the value of their hydrocarbon re- serves. This paper considers the requirements for a reserve based loan and the calculations that a bank would perform to arrive at a loan amount. Three of the most common loan structures, i.e. a term loan, a production payment, and a revolving credit/term loan will be discussed. A typical outline for each type of loan is presented. Finally, a comparison of major considerations in the three financing techniques is shown.

Jan 1, 1982

By Lester F. Engle

Books have been written, complex charts drawn, great batches of punched cards handled by ever increasing numbers of computers, and innumerable meetings held-all for the purpose of making effective the ultimate objective of new, revised or improved process facilities. It is to the credit of management, engineers, and others that in the vast majority of cases, the outcome of their work has been technically sound and economically rewarding. There is a way, however, to insure even better results.

Jan 5, 1966

By R. B. Sudderth, C. R. Merigold

Greater, emphasis is being placed on recovering nickel from laterite ores by ammonia leaching techniques. New methods are required for lower cost, non-polluting techniques to separate more efficiently the metals of interest. Liquid ion exchange techniques meet these requirements with the added advantage of producing salable electrowon nickel cathodes at the plantsite. A complete solvent extraction- electrowinning process is described, including preliminary engineering and cost data for a typical plant producing 50 million pounds of nickel per year.

Jan 1, 1973

By F. W. Jessen, H. Kazemi

A washing technique has been developed to form a spherical cavity in massive salt. The technique is, basically, a process of controlling the fluid motion in the cavity, the concentration distribution of brine, the rate of dissolution at the walls of the cavity, and the particular settings of the wash pipe, or pipes (inlet and outlet pipe) employed. For a particular arrangement of tubing and casing, fresh water enters from the casing annulus at a position above the bottom of the tubing, and the dissolved material leaves the cavity through the tubing near the bottom of the projected hole. The initial configuration of the cavity is cylindrical, representing the drilled hole situated at the axis of the projected cavity. As washing progresses the original hole is enlarged radially (any direction perpendicular to the axis of the hole). An inert fluid (generally a hydrocarbon, natural gas, or air) which serves as a blanket is injected through the annular space between the original hole and the casing. The controlled downward motion of this blanket maintains the upper edge of the brine region that is expanding on the surface of the projected sphere. A large spherical glass container and a radial model were used to investigate the flow patterns and the concentration distribution of brine occurring during the progress of solution of the salt. Aluminum flakes and dye were injected and flow patterns were observed and recorded on motion picture film. Based on the results of these model studies and other work carried out in this laboratory, the controlled washing technique was formulated. INTRODUCTION Underground cavities leached in salt beds and salt domes have been used extensively for storing hydrocarbons. Little attention has been focused on the shape of the cavities as long as large volumes were obtained and the cavities were structurally stable. The general process involves circulating fresh water and removing brine. Two distinctly different circulating systems can be employed, each of which yields characteristically different shapes. By far the most generally accepted method of washing storage caverns in salt domes is the direct circulation system. Water is introduced through the innermost pipe of a concentric pipe system, and brine is withdrawn through the annulus. In the reverse-circulation method, water enters through the annulus and is discharged through the smallesc tubing string. The size of the operation, and hence the size of tubing and casing used, depends on such factors as cavity volume, length of hole, availability of water, disposal of brine and power requirements. Underground caverns are from 100 to 1,000 ft or more in length, and when completed vary from 40 to 100 ft in diameter, providing storage of 100,000 bbl or more. The volumes of water required per volume of salt removed vary from 6 to 7 for the reverse circulation method to 10 to 11 for the direct circulation method. Up to 80,000 BWPD are often circulated. In the direct circulation method, because water enters near the bottom of the projected cavity, solution of salt is greatest at this point, particularly in view of the fact that when the washing is begun turbulent flow undoubtedly exists in the immediate vicinity of the discharge of the inlet water. As the diameter of the hole increases, flow rates also are increased, so perhaps the condition of fluid turbulence is maintained for some time. During the later stages of leaching, when capacity of equipment may be the limiting factor in maintaining flow rates, there may still exist some turbulence adjacent to the point of influx; however, for the most part laminar flow conditions prevail. There appears, therefore, rather good evidence to indicate that the state of fluid motion is responsible for the typically shaped cavity which results from such washing — namely a cylindrical form, generally somewhat larger at the bottom than at the top. Depending on the number of so-called stages which might be employed, the walls or surfaces of the salt diminish rather uniformly from bottom to

Jan 1, 1965

By G. S. Rice

IT is evident from Professor Louis' remarks that he holds a different opinion on certain phenomena connected with a specific type of surface subsidence from mining than is held by many engineers in the United States. The question which appears to be at issue is whether or not the line or plane of "draw" produced in ground movement resulting from extraction of pillars may, under certain conditions, be vertical or even inclined toward the workings rather than inclined for- ward over the unworked mineral, as it is universally agreed occurs in mining by the longwall advancing method. In discussing this case it is well to take the simplest condition, such as specified by Professor Louis, of a flat bed, whether it be coal, iron or other mineral, where the overburden is stratified rock and where there is no overlying quicksand. Professor Louis says in effect that his experience is that the ultimate angle of draw is always positive and inclined 5" to 15" from the perpendicular over the unwrought mineral. My experience under Illinois coal-mining conditions is that .'where longwall advancing is used the draw is always positive as Professor Louis describes it, but that in extracting of panels by withdrawal of pillars, the ground movement is manifested, after the first roof' beam break, by the forming of an unstable dome over the goave. Then subsequently, by the falling of individual slabs from the under side, the dome gets larger and higher until it breaks through to the surface of the rock., Up to this time, arch stresses buttress the rocks above the solid coal or mineral. When, however, after. the dome breaks through and the central hole - #enlarges so the arch is no longer sufficiently supported -the stratified rocks cantilever out .from over the solid unworked mineral and tend to break off in masses triangular in vertical cross-section, until the broken loose material, sliding down against the solid rock, .has such a thrust that it balances the tendency ,for the solid stratified rock to break away and slide toward the excavation.

Jan 1, 1929

By Hal M. Lewers

IN the past few years and especially since the beginning of World War No. 2, gold has attained a new, important. and critical place in the international scene, and in world affairs. In the past, as far back as history records, most wars have been waged for the purpose of acquiring it from someone else by conquest. But now, the most titanic struggle of all time is being waged with the avowed purpose of not only destroying it, but of destroying all that it stands for and represents. A tradition dating back to ancient Rome, affirms that battles are fought by men with weapons, but wars arc eventually won by gold. The validity of that tradition is now being subjected to its major test. Hitler has proclaimed that in his new world order, the work dollar or reichsmark, a beautifully engraved paper currency representing only a theory of value, based on unit of work and production, will become the supreme medium of world exchange, and that gold eventually will he valueless and obsolete.

Jan 1, 1942

Jan 1, 1882

Henry C. Carlisle: This is a husband-and-wife act, in which Mary Carlisle is going to listen, and break in as often as she feels like it. I am going to describe my career as a mining engineer. We are at Nantucket, in the 75 Main St. house; The year is 1959. Q: This is something the boys and I have wanted you to do for a long time. Carlisle: After leaving Columbia in 1910, I arrived at Ray, Ariz., January 1, 1911, and rustled a job from Louis Cates, Ralph Nowland and Sprott Boyd, who were running the Ray mine. I went to work as a surveyor's helper, made $90 a month, and paid $35 a month board. I lived in a dormitory where about 25 other engineers, graduates from different colleges, were living. It was very social and you made a lot of young friends early in the game. I did not think much of the idea of being a surveyor, or even a surveyors, helper; the higher-up surveyors only got $125 a month, and had been there quite a long time. So, I asked to be changed to underground sampling, where I would see the mine faces every day and learn more about mining. In about three months, I became an underground sampler and remained at this for a year, but in three months I was promoted to head sampler, with six people under me.

Jan 10, 1963

By C. Scala, F. Bernstein

General expressions are derived relating the streaming potential to the electrochemical potential of a permeable junction separating two electrolytic solutions. By the methods of irreversible thermodynamics, these potentials are related to the flux of mobile species arising from differences in pressure and chemical composition. The flux is conveniently expressed as a transference number, the equivalents of a mobile species transferred through the junction per faraday of electricity. At constant pressure, the flux equation gives the electrochemical potential across the permeable junction. The streaming potential across the junction is obtained by imposing the condition of constant chemical composition. The familiar expression for the borehole SP is shown to be a particular solution of the general flux equation. The derived exprersions were verified in experiments with seven shale samples. Both the theory and experimental data provide additional proof of the presence and magniturle of the streaming potential in shales. INTRODUCTION In the interpretation of electric logs, there has been much concern over the correction to be made to the recorded SP for an electrokinetic or streaming potential originating from the difference in pressure between the mud column and the formation. It was long recognized by M. R. J. Wyllie that such an electrokinetic potential source mas in the mud cake opposite permeable sands.' More recently, M. Gondouin and C. Scala2 showed an additional but opposing electrokinetic source of potential to be in shale beds. Their work was supported by the very extensive and excellent work of Hill and Anderson.3 n the present contribution, the general relationships between the electrochemical potential and the corresponding streaming or electrokinetic potential are examined and clarified. A notable advance towards understanding the relation between the various sources of electrical potential in a borehole has been the application of the now common methods of irreversible thermodynamics to describe the passage of ions and water through charged electrolyte junctions such as in shales.' The advantages of these methods are twofold. Unlike classical thermodynamics, they can be applied to non-equilibrium sys- tems, i.e., systems in which flow takes place, provided the flow processes have reached a steady state. They also permit conventional thermodynamic properties to be related to the steady-state dynamic properties. These methods arc used here specifically to derive expressions relating the potential behavior of shales in terms of ion and water transport. Experimental verification of the expression for the shale streaming potential is given which in turn offers theoretical support to the existence of a streaming potential in shales.' Importantly, the relative contribution of transport parameters to the SP is clarified. The theoretical treatment is essentially that of Lori-mer, Boterenbrood and Hermans3 ut has been extended to derive the general expression for the SP.

By C. R. Breck

THERE has been a running discussion over the past several years with respect to the life and adequacy of our natural gas reserves. Some of the experts agree on one phase of the subject at least-that eventually it will be necessary to augment deliveries of natural gas in the northern markets by the development of a more or less comparable synthetic gas made from coal. The purpose of this paper is to point out: 1. It may be later than a good many people think-the demand for addi¬tional domestic and commercial pipeline gas in at least one section of the North will probably be felt rather keenly before an adequate synthetic pipe¬line-gas project, developed on economic lines, could be completed, even if initiated in the near future. 2. The evidence is considerable that such a project would be technically sound and economically self-supporting, although the margin of profit at first might be so small and the magnitude of an economic enterprise so great -that financing would be impossible without Government aid in some form or other. The part of the country referred to is the heavily populated section in the northeast of the United States. To simplify an examination of the situa¬tion, let us take the potential marketing areas within range to the north and east of the three pipelines: 1. Tennessee Gas Transmission Co. as it enters Erie County, New York state. 2. Texas Eastern Transmission Corporation just before the tap that sup¬plies the general Philadelphia area. 3. Transcontinental Gas Pipe Line Corporation as it enters the state of New Jersey. The sources of gas for these three pipelines are in Texas and Louisiana. The ultimate maximum combined capacity of the three lines at the points stated is approximately 1,200,000,000 cu ft per 24 hr at the maximum load factor probable of attainment in normal operation. The areas supplied by the three lines north and east of the points stated, or assumed as eventual markets, are: 1. Central New York state, from Buffalo to Albany (both inclusive).

Jan 1, 1953

By R. W. Raymond

In connection with the paper of Mr. Locke on Gilsonite or Uintahite (Trans., xvi., 162) read at the Salt Lake session of the Utah and Montana meeting, in July, 1887, the following data may be of interest and value. In December, 1887, I received from Mr. William Wagner, Seeretary of the Denver & Rio Grande Railway Co., a box of specimens of an asphaltic mineral from Utah. In the course of the correspondence which followed, I learned that the box had been forwarded by Mr. J. A. McMurtrie, of the firm of McMurtrie & Streeter, railroad contractors, Denver, Col. Mr. McMurtrie was, in 1883, chief engineer of the Denver $ Rio Grande Railway, and the mineral mas first brought to his attention in that year by Mr. Thomas H. Wigglesworth, who was then employed in making preliminary reconnaissances for wagon-roads to be used in constructing the Utah extension (now the Denver, Rio Grande $ Western) of the railway. Mr. Wigglesworth, I understand, was subsequently chief engineer of the Colorado & Utah Midland, and is now again employed by the Rio Grande. He writes substantially as follows concerning this mineral:

Jan 1, 1889

By Mrs. V. J. DeCarlo, G. P. Salvo, H. W. Schadler, L. M. Osika

The lattice parameter of the inlerrnetallic compound Nb3Sn has been measured as a function of temperature from 80° to 1290°K. The results are compared with published data on the thermal ex- ThE recent interest in the intermetallic compound, Nb3Sn, as an engineering material for the production of superconducting devices has necessitated that certain engineering data be obtained. Because of the difficulty encountered in producing bulk pansion of niobium and indicate that the compound when made by diffusion of tin into niobium at 1000°C, would be subjected to a tensile strain of about 0.1 pct when cooled to room temperature. material which is single phase, the coefficient of thermal expansion has not been measured by dilata-tional methods. Therefore the lattice parameters of fine-grained samples of Nb3Sn produced on the surface of a niobium sheet by heating in molten tin at 950°C have been obtained as a function of temperature. The results are compared with published data on niobium2 and Nb3Sn3 and with lattice-parameter measurements made on small single crystals of Nb3Sn.

Jan 1, 1964

By Albert F. J. Bordeaux

Discussion of the paper of Albert F. J. Bordeaux (Bi-Monthly Bulletin, No. 23, September, 190S, pp. 629 to 640). A. H. BROMLY, Zihuatanejo, Guerrero, Mexico (communication to the Secretary*) :-The following criticism of what "is offered as a summary which may be found useful by mining engineers," is not dictated by any captious spirit, but in the interest of historical and scientific accuracy. The States of Queretaro and Oaxaca have produced sufficient silver to warrant more extended notice. Referring to Pachuca, State of Hidalgo, the somewhat loose and. inexact statement is made that "the ore-deposit is an andesite, intermixed with quartz-veins, rich from the surface." A better description would be,-the ore-deposits consist of quartz-veins in andesite. It is notable that many of the rich shoots worked in recent days did not come to surface. In consequence, Pachuca, is often quoted by the ill-informed as a camp in which values improve with depth, the truth being that the veins carry shoots, or clavos, some of which were exposed at surface and some not. The name of " electric plow," applied to the mechanical stirrer of recent use, is certainly not to be recommended. The stirrer, or agitator, consists essentially of a traversing gang-plow, operated by power through shafting, drums, and wire-rope. The fact that in certain plants the motive-power used is electricity does not make it an electric plow. Such a name suggests a machine of which the motor is an essential and integral part; which is not so in this case. A lathe in a factory driven by water-power is not called a hydraulic lathe. My experience agrees with Dr. Raymond's note as to azulaque, which in sortie districts is also applied to blue copper carbonate. The El Oro, Esperanza, and Mexico mines should be allocated to the State of Mexico; the Dos Estrellas being in Michoacan, as stated. The El Oro quartz certainly does not appeal to me

May 1, 1909

By J. H. Moran, E. E. Finklea

The pressure build-up technique is a recognized method of determining permeability from conventional drillstem tests. In this paper an effort is made to extend such techniques to the interpretation of data obtained from the wireline formation tester. Such a study is necessary because of the differences, for this case, in the magnitude of the flow parameters (rate of flow, amount of recovered fluids) and in the flow geometry (flow through a perforation vs flow across the face of the wellbore, etc.) involved in the solution of the equations of flow for compressible fluids. The perforation is replaced by a spherical hole, and the effect of the borehole is neglected, so that the flow can be considered to be radial in a spherical co-ordinate system. Arguments are presented to justify this idealization. Assuming single-phase flow, general relations between pressure and flow rate are developed for a homogeneous medium. The study is then extended to permeable beds of finite thickness. It is shown that the early stages of pressure build-up tend towards spherical flow, while the later stages tend towards cylindrical flow. The thinner the bed, the more quickly flow approaches the cylindrical model. The prevalence of thin beds in practical work makes this analysis quite important. Cases involving permeability anisotropy are treated. INTRODUCTION From wireline formation tester operation, two types of data are obtained: (1) the nature and amount of recovered fluids, and (2) the pressure history recorded during the test. A number of papers have been written dealing with the interpretation of formation production on the basis of the recovered fluids.'.' In general, the methods described have been quite accurate for both high- and low-permeability formations. The present paper will deal with an analysis of the pressures observed. An analysis of the pressure build-up curves obtained in hard-rock country has already been attempted on the basis of the formula proposed by Hor-ner. Although this approach has met with success in many instances, some questions have been raised as to its validity. It is the aim of the present study to place the analysis of pressure build-up in the formation tester on a firmer basis, from which more detailed methods of interpretation can evolve. Because of the great differences between the operation of the wireline formation tester and the conventional drillstem test, modifications are necessary in the interpretation. The major difference relates to the flow geometry. Once the flow geometry has been established other features such as multiphase flow, skin effect, afterflow, etc., well described in the literature, can be introduced. It will be assumed that the mechanical operation of the formation tester is already known to the reader.6 t will suffice here merely to state that the tester provides the means for taking a relatively small sample of the fluid immediately adjacent to the borehole, and for recording the subsequent pressure response. In comparison with conventional drillstem tests, the time required for a satisfactory pressure build-up response is much shorter, because of the relatively small quantity of fluid withdrawn by the wireline tester. This feature is highly desirable in the case of low-permeability formations. For an analysis of the pressure response within the formation, three simple flow geometries are considered— linear, cylindrical and spherical. The spherical and cylindrical flow geometries are most pertinent to the formation tester; therefore, they will receive the major emphasis. Since the configuration of the borehole and the perforation made by the tester complicate the flow geometry, it is necessary to allow for them in the drawdown response. However, because of the volume of formations contributing to the pressure-response, the details of the perforation shape are unimportant in the build-up period. Since relatively small amounts of fluid are withdrawn from the formation, in contrast to a conventional drill-stem test, a study of the "depth of investigation" and the significance of drawdown as well as build-up data will be included. Because the "depth of investigation" will be shown to be rather large, the effect on the build-up curves of the finite thickness of the permeable bed is considered. It is this consideration that leads to the importance of cylindrical flow geometry. Also included is a discussion of permeability anisotropy and its effect on the interpretation of the tester results. The pressure curves recorded by the formation tester will follow two general patterns, depending upon whether the formation is of high or low permeability. Fig. I (a and b) schematically illustrates these two responses. In Fig. 1(a), the high pressure recorded during fill-up of the tool is essentially the pressure differential across the choke in the system. In Fig. l(b), the flow rate is

By T. E. SCHTVARZ

THE publication of the report by Mr. F. L. Ransome was welcomed by many engineers who had mined in the heart of the Sail Juan country, braved its long and snowy winters, climbed its lofty peaks, run the gauntlet of its snow-slides, and studied its problems of geology, while making dividends for their English or American clients. This report helps one to understand why the bonanzas occurred, and why the inevitable borrasca presents itself where least expected. The Red Mountain district of Ouray county, a very productive section from 1884 to 1893, occupies considerable space in the report mentioned.. The character of the ore-occurrence, being distinctive and presenting many features not existing elsewhere, has been deserving of special study. It is to be regretted that Mr. Ransome was .unable to observe the conditions underground, as all the principal properties, many of which I opened and developed, were closed at the time of his investigation: It has been my privilege to have contributed a few brief papers recording my observations in developing these properties ; and it is the object of the present paper to present certain sections of the Yankee Girl mine, which throw additional light on the geology of the section and make the available data more complete. The main Yankee Girl chimney or " stock" was the most productive for the first 500 ft. in depth of any chimney in the district.

Mar 1, 1905

By T. L. Joseph

S. T. Killian (Johnstown, Pa.)—This is one of the finest papers I have read. Tying in stoichiometric calculations with furnace performance and practice is a step which had to be taken sooner or later. The noteworthy difference between Dr. Joseph's type of calculations and regular blast furnace calculations is that the Ib mol system is used as a basis. With the Ib mol system, weights, volumes, and chemical reactions can all be expressed in the same equation. In the paper, wind, ore, flux, and fuel are all expressed as lb or lb mols. Probably Dr. Joseph does not realize it, but the vague word coke appears only twice in the entire paper. Lb of C and Ib mols of C are followed through reactions but the word coke appears only as 1560 lb coke per ton of pig and 1700 lb of coke per ton of iron. Obviously in order to understand furnace reactions, the coke should be expressed as lb or lb mols of C. Furnaces can also be compared more easily. In some respects the paper is too thorough and too complete. The effects of the metalloids reduced into the iron upon the top gases represents a difference of less than 3 pct of the CO formed in the bosh. Due to the completeness of the calculations in relation to the CO/CO2 ratio, this was included and was necessary. However, the exclusion might have enabled more furnace men to follow the lb mol system of calculations through the blast furnace to a better degree. By considering only irons of similar analysis, this part of the calculations might have been omitted. However, if this had been done, total rewriting of the paper later would have been necessary in order to make the work complete as it is now. It also would not have been nearly as authoritative. In the paper, there appears the reaction: H2O + CO ? CO2 + H2 [I] Dr. Joseph states that he did not take this reaction into consideration in any calculations pertaining directly to the paper. The piobable reason- for this is that although it contains all the main reacting top gases except N2, it is rather inflexible since it is monomolecular in relation to each of the reacting gases and does not tie in with the gasification of C. Actually the reactions: H2O + C ? CO + H2 [2] 2H2O + C ? CO2 + H2 [31 and the solution loss reaction: CO2 + c ? 2c0 [41 tend to assume an equilibrium through the reaction: H2O + CO ? CO2 + H2 [I] which should be considered a balancing or equilibrium reaction. Reactions 2, 3 and 4 permit furnace conditions to balance with the CO/CO2 ratio and H2 formation. They tie in with the solution loss. Reaction 1 unites them chemically. Probably the best calculation to make at this time would be to try to find the relative importance of the CO2 from the flux and the H2 in the dilution on an actual furnace gas analysis. For this purpose the Dob-scha-Carnegie-Illinois paper—"Effect of Sized and Sintered Mesabi Iron Ores On Blast Furnace Performance" is chosen. This paper was presented before the blast furnace section of the AIME in 1948. This represents the best large scale furnace operation available to me. Unfortunately the changes were brought about by beneficiation of the burden and not by changes on one burden. In choosing the basis for the calculation in relation to the furnace, 100 mols of dry top sgas is chosen. This leaves something to be desired inasmuch as the nitrogen basis is changing but I believe it will be better understood than any other type and it is the easiest to use.

Jan 1, 1952

By J. Leslie Goodier

The International Law of the Continental Shelf, so far ratified by 35 nations, extends the national boundary of any coastal nation to the edge of the continental shelf, this normally being at a continuous water depth of 200 m. The Law further extends this boundary to include the floor of the deep ocean to any depth that can be mined by advanced mining technology. In effect, proof of mining can constitute proof of ownership of the subaqueous land and the minerals on or below the sea floor. Irrespective of the fact that present technology is too limited to permit mineral exploitation in the high seas-and the law regarding the right to mine appears hazy-the U. S. Treasury Department's Bureau of Customs, has a ruling that would further deter mining operations on the high seas. This law contends that minerals mined on the continental shelf of the United States are actually mined within the continental United States and are free of tariff, but mined products or other articles obtained from the ocean or the sea floor beyond the continental shelf, if brought into this nation, must be considered as imported and are subject to such customs duties as are applicable under the tariff schedules of the United States.

Jan 7, 1968

By AIME AIME

EDWIN W. KEMMERER, professor of international finance at Princeton, in a speech before a banking conference at Urbana, Ill., on Nov. 26, stated that the increase in the store of gold held by the United States is not so alarming as it appears on the surface. Excerpts from his address, as reported by The New York Times, follow: "It is significant . . . that the value of gold as expressed in its purchasing power in the United States during the last half-dozen years has been higher than at any other equivalent period since our records began 140 years ago. Our so-called 59-cent dollar today buys about 25 per cent more goods at wholesale than did our old dollar in the prosperous year 1926, and an ounce of gold will now buy considerably more than twice what it did then. This present high value of gold is one reason for its recent large production.

Jan 1, 1941

By S. W. Churchill

A digital computer was used to obtain an exact numerical solution for the transient behavior of the insulation and earth adjacent to an isothermal, submerged flat surface for a single set of parametric values. Comparison of the computed results with analytical solutions for limiting conditions revealed that a complete and general solution for all parametric values could be constructed from these limiting solutions. Complete and general solutions for insulated spheres and cylinders can also be constructed from limiting solutions. The procedure is illustrated in part for an insulated spherical tank. The heat flow was found to fall rapidly to a pseudo-steady state; after some time, it then decreased slowly to zero for a flat plate and cylinder, and to a low steady-state rate for a sphere. The accumulative heat flow during the initial falling-rate period may be a significant fraction of the heat flow during the entire first year. INTRODUCTION Underground storage of liquefied natural gas and liquefied petroleum gas has received considerable recent attention. The rate of heat flow from the earth to the storage cavity and the resulting temperature field in the earth are important factors in the technical and economic evaluation of such storage facilities. The objective of this paper is to indicate how complete solutions can be developed for the transient flux and temperature field for various geometrical configurations. The representative properties and dimensions, and the resulting parameters utilized in the illustrative results, are indicated in Table 1. The results presented herein are for dry earth. The effect of the latent heat of solidification of water in the soiI will be described in a subsequent paper. The temperature field in the insulation and earth is determined by energy balances, boundary conditions and initial conditions. The physical problem can be described mathematically with virtually no idealizations insofar as physical properties are known. It appears possible to solve the equations by numerical integration on a high-speed digital computer for any geometrical configuration and conditions. For complex situations, however, the computations are expensive and the results are highly specific. Analytical solutions have been developed for a few simple but important geometrical configurations and conditions, including one-dimensional heat transfer from (or to) earth at an initially uniform temperature to (or from) flat plates, spheres and circular cylinders. The solution for an insulated flat plate has also been derived but is in the form of a slowly converging series involving taklated functions. It was planned to use a computing machine to evaluate this series for a number of representative conditions. However, upon examination of the results of preliminary computations it was discovered that a complete, general and accurate solution could be developed by interpolation between several much simpler solutions for limiting conditions. This technique then was used to develop a a complete solution for an insulated sphere. The equations presented herein are derived in Carslaw and Jaegerl and other books on applied mathematics, or they are simple extensions of these previous results. Hence, all derivations are omitted. Emphasis is instead placed on the results and their

SME Membership Directory Listings of record March 31, 1072 SOCIETY OF MINING ENGINEERS OF AIME

Jan 7, 1972