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By K. P. Fournier

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus:

Jan 1, 1966

By Ernest F. Burchard

A reconnaissance of the chrome and manganesel ore deposits of Cuba was made in the spring of 1918 by Albert Burch, representative of the U. S. Bureau of Mines, and the writer, representing the U. S. Geological Survey. The object of the study was to obtain authentic information for use of the United States Government as to the location, character, size, and availability of the Cuban deposits of the ores of these important steel-alloy metals. The Cuban Government courteously detailed Sr. E. I. Montoulieu, a mining engineer connected with the Treasury Department, to act as escort and associate throughout the work on the Island. Mr. George A. Wright, of Baracoa, Cuba, a minirng engineer especially familiar with the chromite deposits of Oriente Province, was a member of the party from Feb. 25 to Mar. 20. It was possible to visit most of the chrome-ore deposits that seemed to be of promise, but there was not sufficient time to visit all that were brought to our attention, some of which may have merit. Furthermore, no attempt was made to examine the extensive chromiferous iron-ore deposits of the Mayari, Moa, and Cubitas districts, as these deposits cannot be regarded as sources of chromium except indirectly. At the close of the field work the essential data concerning the quantity and quality of ore probably available for shipment during 1918 and 1919, in the event of the continuation of the European war, and of the tonnage of ore in reserve, were furnished to such Government bureaus as were interested, including the Shipping Board and the War lndustries Board, and as soon as chemical analyses of the chrome ores could be obtained, a press bulletin on the subject was published by the Geological Survey. In the present paper the engineering data and tonnage estimates contained in the unpublished notes of Mr. Burch have been freely used, and their helpfulness is hereby gratefully acknowledged. Many thanks are due Senor Montoulieu and Mr. Wright for their valuable work in the field; to the officials of the Spanish American Iron Co. and of the various other companies; and to individuals holding chromite claims, for courteously facilitating the work of the party.

Jan 1, 1920

By AIME AIME

AMONG the recent mining and metallurgical developments in England great interest has been shown in the development of an iron-ore field covering 26,0.00 acres in Northamptonshire, containing 500,¬000,000 long tons of ore; and the erection at Corby, by Stewarts & Lloyds, of a modern basic bessemer steel plant and tube works. The entire project was planned to cost about £3,300,000. Many improvements have been made in the varied equipment that is being installed, some of which has set mew records for massiveness. There is, for instance, a new roll crusher, which has been manufactured by Hadfields, Limited, of Sheffield, the largest ever built in England, and weighing 130 tons. This machine, shown in Fig. 1, as erected at the Hadfields shops, is primarily designed to take blocks of iron ore as they come from the steam shovel. The maximum size is 54 by 48 by 36 in., hut occasional pieces slightly larger than this may be accommodated. The capacity is upwards of 500 tons per hour, the product passing to a secon-

Jan 1, 1934

By Thomas H. Sheldon

IN the zeal for opening up new ore-bodies, or for. extracting the ore from attractive bodies gal ready opened up, we very often lose sight of the fact, that, after all, the operation of a mine is a business proposition, pure and simple; and for the best working-results should be treated upon a strict business basis. Of course, in every mine of consequence a record is kept of expenditures and receipts, and such glittering generalities as "gross receipts," " net receipts," " mining expenses," .and " per cent. profit," can be told to the cent; but does this . record show economy of management, either as compared with the same record of other months, or as compared to the record of other mines of the' same class ? Moreover, if such a record shows that the cost of mining is high, does it in any way en¬able the manager to put his finger on the leakage? Does it necessarily follow that a mine which makes a profit of, say, 40 per cent on 25-dollar ore, is doing less economical mining than one which saves 60 per cent on 80-dollar ore ? Of course the figures in the latter case look the more attractive, but when it comes to a point of saving everything which can be saved, and of cutting down expenses to the lowest possible cost of operation, the former mine is doubtless on the most firm and economical financial basis. But as the relative merits of the system of mining in the two cases, nothing could be decided without a basis of detailed comparison ; if one system is more economical than the other, why is it so, and wherein does the advantage lie ? This can be shown only by keeping accurately the cost of each mining operation. And no matter how dissimilar two mines may be in character and operation, yet there are a few general heads common to all mining operations. In the first place, it is necessary to break the ore from the solid ground ;

Nov 1, 1905

With a total value to date of well over $200,000.000.00 for its ore production, the Tintic mining district, which is about 100 miles southwest of Salt Lake City, ranks as one of the three main ore producing areas of Utah. In it are located the biggest silver mines of the country, silver having been the chief metal produced in the camp since its start. Tintic's silver production to date has a total value of over $1 00,000,000, approximately half of the value of the camp's ore production, the balance being roughly divided among lead, gold and copper. Discovery of the camp was made in the late sixties. Lack of transportation and ore reduction facilities delayed extensive development of the area for nearly a decade. In recent years Tintic's ore production has ranged from 350,000 to 400,000 tons annually. In 1924 the camp produced one-eighth of the silver produced in the nation with an output of 7,729,700 ounces. Its lead production was 77,765,000 pounds and its gold production 26,285 ounces.

Jan 1, 1925

By Renato G. Bautista, David C. Lindholm

The results of scale-up studies on a continuous, multistage horizontal mixer-settler extractor are presented. The chemical and mechanical system involves the separation of lanthanum from a mixture of rare earth chlorides using di(2-ethylhexyl) phosphoric acid as the solvent and dilute HCl as a scrub solution in a bench scale extractor. Each stage has a hold-up of 2.6 l. A single stage unit is utilized for scale- up studies. Results are obtained on four sizes of geometrically similar units, the largest being six times the volume of the original bench size. A unit operations technique is chosen so that mixing and settling can be examined independently. Variables examined include type of continuous phase, flow rate of inlet streams, and power input to the mixer. Inlet flow-rate ratios are kept constant for all tests. TWO potential methods of unbaffled pump-mixer scale-up are explored; the maintenance of constant impeller tip speed and constant power input. For the settler, the previously successful method of basing design on constant flow-rate per unit cross- sectional area is used.

Jan 1, 1977

THE shipments of high-grade manganese ore, con-taining 35 per cent or more of manganese, from the mines in the United States in 1926 were slightly less than half as large as similar shipments in 1925, accord-ing to the United States Bureau of Mines, Department of Commerce. The shipments in 1926 by 45 producers amounted to 46,258 long tons as compared with 98,324 long tons by 42 producers in 1925. This decrease was due to the falling off of the shipments from Montana. The domestic production of metallurgical ore in 1926 was 26,530 tons; that of chemical ore, 19,728 tons. Montana was the largest shipper with 5713 tons of metallurgical ore and 17,904 tons of chemical ore. The largest individual shipper of metallurgical ore was the Crescent Mine in the Olympic Mountain Region, Clallam Co., Washington, from which the shipments for the year were 3162 tons. The mine was operated by lessees and reverted to the owners in July, and thereafter to the close of the year no .ore was shipped.

Jan 6, 1927

By Gordon E. Frantti

Under the auspices of the Geophysical Committee of Michigan College of Mining and Technology, an investigation was made in Michigan's Upper Peninsula to obtain geophysical data related to the regional subsurface geology in the area covered by Paleozoic sediments. The area surveyed includes that portion of the Upper Peninsula which lies between R18W to R26W and T41N and T49N, covering approximately 1300 square miles. On the index map, Fig. 1, it is represented by the cross-hatched zone west of Munising. Four of the five sites of detailed investigation are indicated by the letters A, B, C, and D. A detailed gravity and magnetic survey had previously been conducted by J. G. Wilson near Perkins, 8 miles north of Rapid River, on a local anomalous area. Results of his work, which showed a large positive magnetic anomaly associated with a gravity anomaly, aroused interest in the possible economic significance of the formations underlying the Paleozoic sediments in this part of the Upper Peninsula.

Jan 1, 1956

By Sherwin F. Kelly

THE present lull in engineering activities presents an advantageous moment for inquiring into the position now occupied by geophysics in its various fields of application. The recent over-expansion in all lines of work resulted in an uncritical employment of these methods of exploration which was bound to have its harmful reaction. The pendulum has now swung back, producing a decidedly hypercritical attitude toward the new science that had been recently welcomed so joyfully as the panacea for prospecting troubles. The severe retrenchment in exploration has forced upon us a period of waiting and, it is to be hoped, of profitable contemplation. This can well be employed in trying to pass a reasoned judgment on what position geophysics should occupy in the new geological exploration programs that will inevitably ac- company the looked-for industrial recovery.

Jan 1, 1931

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members) Member, Graduate Colorado School of Mines. Four years' experience in West and Northwest. Two years with American Smelting and Refining Co. Wishes to join field party on geological work, mining or areal, where opportunity will be given to be of direct assistance to chief of party in solution of field problems. Age, 26. Unmarried. At liberty June 1. No. 342. Member, technical graduate, aged 30, with' 7 years' experience in concentrating and mining, desires a position of authority with reliable company. At present employed. No. 343. Member. Ambitious, energetic, tactful engineer, college graduate, married, aged 30, desires location with a large coal mining organization. Seven years with present employers -n middle west; has had broad experience in the past eight years on examination, development and construction; successful record in handling men. Position must carry responsible work and a future. Will go anywhere for proper opportunity. Exceptional references as to reliability, character and capacity for work. No. 344.

Jan 3, 1917

By William E. Ford, Edward Salisbury Dana

URANINITE. Cleveite. Broggerite. Nivenite. Pitchblende. Isometric. In octahedrons (o), also with dodecahedra1 faces (d) ; less often in cubes with o and d. Crystals rare. Usually massive and botryoidal; also in grains; structure sometimes columnar, or curved lamellar. Fracture conchoidal to uneven. Brittle. H. = 5'5. G. = 9'0 to 9'7 of crystals; of massive altered forms from 6'4 upwards. Luster submetallic, to greasy or pitch-like, and dull. Color grayish, greenish, brownish, velvet- black. Streak brownish black, grayish, olive-green, a little shining. Opaque. Comp. -A uranate of uranyl, lead, usually thorium (or zirconium), often the metals of the lanthanum and yttrium groups; also containing the gases nitrogen, helium and argon, in varying amounts up to 2'6 p. c. Calcium and water (essential?) are present in small quantities; iron also, but only as an impurity. The relation between the bases varies widely and no definite for- mula can be given. Radium was first discovered in this mineral and it has been shown that it and the helium present are products of the breaking down of the uranium.

Jan 1, 1922

By A. G. Allten

EXAMINATION by metallographic and X-ray diffraction means of an austenitic steel containing 0.06 pct C, 1.26 pct Mn, 0.38 pct Si, 21.15 pct Ni, 18.72 pct Cr, 3.07 pet W, and 9.14 pet Mo indicated that a - phase, which had not been reported in the literature, existed in this steel. Both the s and car-bides of the M6 C type were present in the as-forged steel. The carbides dissolved completely in the aus-tenite at approximately 2200°F (1205°C). The s, however, was present at all temperatures up to the solidus temperature of the steel at approximately 2375°F (1300°C). Ferrite was not found in any condition of the steel. The faintness of some of the s lines in X-ray patterns obtained from samples of the steel made it desirable to isolate the s prior to verification of its entire pattern. It was found that the s phase could be separated from samples of the steel which had been water quenched from 2250°F (1230°C) by dis-

Jan 1, 1955

By D. A. Elgillani, M. C. Fuerstenau, J. D. Miller

Adsorption of lead and ferric iron on quartz and alumina is presented as a function of pH. Only the hydrolyzed species of these metal ions, FeOH++ and PbOH+, adsorb significantly on each of these minerals. Zeta potentials of quartz were measured as a function of pH in the presence of various additions of aluminum, lead, and magnesium salts. Sign reversal occurs at the pH values where significant concentrations of hydroxy complexes are formed. Models of adsorption are presented in the absence and presence of collector. The mechanism of adsorption of metal and collector species in the activation of nonmetallic minerals is still the center of considerable discussion in spite of the extensive study given this system. Until recently, the view was widely held that hydrated metal ions were responsible for this phenomenon. This fact is surprising, since it had been shown that the pH range in which flotation is effected corresponds to that in which metal ion hydrolysis occurs.' Additional support of this concept was pro vided by the work of Wolstenholme and Schulman in another system.' Later work has shown that hydroxy complexes of metal ions are the active species. These studies have also indicated that basic aqueous complexes of metal-collector may be necessary for flotation.3-7 Depending on the molecular weight of the collector, formation of these complexes may occur before or after precipitation of the metal-collector salt has occurred. Ion pair formation can occur when low molecular weight collectors are involved because relatively high concentrations of metal hydroxy complex and collector can be present in solution before precipitation occurs. This is not the case when high molecular weight collectors are used. A model of aqueous complex adsorption has been presented6,7 in which it has been assumed that adsorption occurs by the formation of water from adsorbed hydroxyl and hydrogen of the hydroxyl contained in the complex. Other authors8 have suggested that hy-droxy complexes are involved in these systems but that collector adsorption occurs by replacement of the hydroxyl of the adsorbed metal hydroxy complex with a fatty acid anion. All of these investigations have involved mineral surfaces that were negatively charged so that it is not possible to state with certainty whether hydrated metal ions or hydroxy complexes are the active species in this system. Use of a positively charged mineral should be helpful, however, since the hydrated metal ion will be repelled from this surface. On the other hand, if the hydroxy complex adsorbs by splitting out water, surface charge should have no effect because of the free energy decrease that the system will experience when water is formed. In this regard, sapphire is well-suited for study, since its surface is positively charged until approximately pH 9. Electrokinetic studies of quartz in the presence of various metal ions should also be useful in establishing the mechanisms of adsorption in these systems. That is, if the hydroxy complexes adsorb by water formation, drastic changes in the zeta potential should occur in the pH range in which hydrolysis occurs. In this view, adsorption of ions of widely different hydrolysis characteristics on both sapphire and quartz was measured. In addition, zeta potentials of quartz were measured as a function of pH in the presence of various metal ions and compared with flotation responses obtained under similar conditions. Experimental Materials and Techniques Reagent-grade aluminum, ferric and magnesium chlorides, and lead nitrate were used in this investigation. Adjustments in pH were made with reagent-grade HCl or KOH. Conductivity water, made by passing distilled water through an ion exchange column, was used in all of the experiments.

Jan 1, 1971

By C. Feng, C. Elbaum

Knoop hardness measurements were carried out on large grains of iodide titanium containing different amounts of oxygen. For each oxygen content the hardness is recorded ainingas a function of the crystal orientation and of the angle 4 between the indenter diagonal and the projection of the C (hexad) axis in the surface. The results can be expressed by the following relation; hardness = n-k cos 2ø, where n and k are constants for a given oxygen content and crystal surface orientation. A NISOTROPY of hardness is a well-known phe-nomenon and has been reported for many metals.1-3 At the present time, however, such information is not available in the literature for titanium. Consequently, a systematic study of the simultaneous effects of oxygen content and crystallographic orientation on the hardness of titanium was undertaken in this laboratory. Evaluations of oxygen content in titanium are frequently carried out through hardness tests. Although such procedures may be justified in small grain specimens, the results of the present investigation indicate that the anisotropy of hardness should be taken into account in the case of coarsegrained specimens as well as in the case of pronounced preferred orientation. Materials and Experimental Procedures Iodide titanium, 99.99 pet pure and containing of the order of 0.002 wt pet O, was used throughout this investigation. The metal was arc melted in an argon atmosphere and cold rolled into strips 1/16 in. thick. These strips were subsequently recrystal-lized and strain annealed in vacuum (10" mm Hg or better) at 850°C in order to produce crystals varying in diameter from 10 to 25 mm. Oxygen was introduced into selected large crystals by heating at 700°C in an atmosphere of pure oxygen under an observed pressure of approximately 50 mm Hg. Each sample was subsequently annealed in vacuum at 850°C for 100 hr, in order to homogenize the oxygen content throughout the specimen. It was found that longer annealing was not necessary, for no change of surface hardness in a given direction was detected after prolonged annealing. The oxygen content was determined by the difference in weight of the specimens before and after the oxidation-annealing cycle. The accuracy of oxygen determination is within ±0.1 mg in samples weighing 0.5 to 1 g. A vacuum fusion analysis of oxygen was performed on several samples and gave results in good agreement with the ones obtained by the weight change. It should be emphasized that expected weight losses through evaporation of the metal in vacuum at 850°C' are many orders of magnitude lower than the precision of these measurements. Following the annealing treatment, both oxidized and unoxidized crystals were carefully polished. All detectable traces of surface cold working were removed by repeated polishing and etching. Laue back reflection X-ray patterns were taken for each crystal for the purpose of determining the orientation and ascertaining the absence of substructures detectable by this method. Hardness measurements, using a 1 kg load, were subsequently carried out on a Tukon hardness tester equipped with a Knoop indenter. The Knoop indenter was used throughout this work because indentations obtained by means of a Vickers indenter are considerably distorted due to the anisotropy of the elastic constants in titanium. Such distortions are much less pronounced in the case of Knoop indentations, although for some orientations a cer-

Jan 1, 1959

By R. E. Gilchrist, R. F. Nielsen

When a gas is displaced by mother in a porous medium, and there is a relative immobile liquid present. there is a transition zone in which the gas composition varies from essentially that of the original gas to that of the injected gas. The change in extent of this zone with time may be governed by a mixing process in the direction of flow and by the rate of establishment of gas-liquid equilibrium, if the gases are appreciably soluble in the liquid. The relative importance of these two factors in deterri~ining the growth of the transition zone is discussed, with appropriate equations and experimental data. INTRODUCTION The various solution methods of oil recovery involve a transfer of the components of a mixture, whether within a single phase or between a liquid and gas. The similarity of a natural porous medium to systems used in separation and chromatographic processes makes it seem reasonable that certain concepts used by chemical engineers in "mass transfer" might be applicable to petroleum reservoirs. One approach, the HETP (height equivalent to a theoretical plate), involves a distance or length of time over which equilibrium might be con. sidered as established. Another approach involves direct use of a rate of mixing or rate of establishment of equilibrium. The latter approach has been preferred in relation to production problems. DISCUSSION AND PROCEDURE When a gas or liquid in a porous medium is displaced by one of different composition but miscible with it there will be set up a transition zone in which the composition varies from cssentially that of the original fluid to essentially that of the injected fluid. If the fluid being displaced is a gas, and there is a relatively immobile liquid present, the transition zone may be

By George Burrell

J. S. HALDANE, M. D., F. R. S., Oxford, England (communication to the Secretary?).-The valuable paper of Messrs. Burrell and Gauger is of special interest to me as, through the courtesy of the management, I had an opportunity of visiting the Portland mine, Cripple Creek, in 1911, in connection with the investigations on acclimatization to high altitudes, carried out on Pike's Peak, near Cripple Creek, by Professors Yandell, Henderson and Schneider, Dr. Douglas and myself.1 The analyses of one or two samples of the vitiated air were entirely confirmatory of those of the authors. A fatal accident owing to two men being lowered down a shaft filled with the gas had occurred in a neighboring mine just before our visit.

Jan 12, 1916

By J. D. Rice, S. C. Pitzer, C. E. Thomas

Interpretation of pressure build-up data obtained in the conventional manner has often been difficult because of the deviation from theoretical behavior. Major causes of this deviation have been attributed to damage and afterflow, and to fluid redistribution in the wellbore which, in extreme cases, can result in a pressure hump in the early portion of the build-up curve. Theoretical investigations show that bottom-hole pressure is definitely influenced by phase redistribution in the tubing column during surface shut-in tests, and that the magnitude of the effect is sensitive to the producing gas-oil ratio and stabilized rate of flow in the well. For field experiments a wire-line tubing packer, which can be run in the tubing against a stabilized flow rate, was developed for bottom-hole shut-in tests. By use of this bottom-hole .shut-in method, pressure humps previously observed in surface shut-in tests were completely eliminated and the effects of afterflow minimized. Analog and digital computer studies have been made to obtain theoretical curves for comparison with field curves, and remarkable agreement between the results of bottom-hole shut-in tests and theoretical curves has been obtained. INTRODUCTION Pressure build-up data from shut-in wells have been used by the petroleum industry to determine the permeability of the formation, to estimate wellbore damage, to evaluate the static reservoir pressure and to speculate reservoir volume. Calculation of these factors is based on methods of analysis developed for theoretical systems whose build-up curves have a charac- teristic shape when the wells are shut-in at the sand faCe.1,2,3,5,8,10 However, field curves obtained by conventional surface shut-in methods do not always exhibit this characteristic. Such factors as stratification, rock heterogeneities and irregular reservoir geometry can cause the character of a build-up curve to deviate from that predicted by theory for a simple system. In addition, all field build-up data are affected by the methods utilized in obtaining the measurements. Conventional surface shut-in techniques allow two effects to occur which contribute directly to the manner in which pressure builds up at the sand face. The first, afterflow, has been recognized for some time and methods are available for estimating the magnitude of its effect and for correcting its influence.' The second, phase segregation in the tubing column after shut-in, has been reported only recently and appears to exert a considerable influence on the character of field build-up curves.!' In extreme cases, phase segregation can produce "pressure humps" in the early portion of the build-up curve. Such curves have been considered anomalous and have defied analysis. It is the purpose of this paper to discuss the effect of phase segregation in the tubing string during build-up and to present a bottom-hole shut-in technique for obtaining field build-up data which minimizes the influence of afterflow and eliminates phase segregation effects. It will be shown that reliable reservoir information can be calculated from build-up measurements obtained using this method, even though conventional surface shut-in tests on the same wells yield anomalous data. DISCUSSION OF PHASE REDISTRIBUTION EFFECTS Some of the effects of phase redistribution on pressure build-up curves have been described previously by Matthews and Stegemeier" who have presented evidence that phase segregation is responsible for the pres-

By J. W. Givens, P. B. Crawford

A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. INTRODUCTION One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of water-flooding or gas cycling programs.1-5 However, there arc few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures.6,7 It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee8 it has been widely used to study numerous types of fluid displacement problems. The potentio- metric model can be used for fluid displacement studies when the following assumptions are valid: (a) steady-state conditions exist; (b) the mobilicy ratio is one; and (c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN — ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattem with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattem expressed as a per cent. The cross-hatched areas of this

Jan 1, 1967

By William R. Rumbold

THE Kinta valley in the State of Perak, one of the largest of the Federated Malay States, is probably at the present time the richest alluvial tin-district in the world, Perak producing from 20,000 to 25,000 tons of tin annually, and the Kiuta valley being the chief producer. The valley runs approximately north and south, and is 30 miles long by 12 wide. It is very flat, the mountain-ranges on either side rising abruptly from the plain, that on the east being the great Central range of the peninsula, and that on the west a subsidiary range marked " Kledang " on the map, Fig. 1. The valley is drained by the Kinta river, which rises in the eastern mountain range and flows south to join the Perak river, being joined by numerous streams from both mountain-ranges. The rain-fall is heavy, averaging annually about 90 in. The whole country is covered with dense jungle, except where it has been cleared for mining-operations and a small amount of cultivation. Mining villages are scattered throughout the valley, the chief towns being Kampar, Batu Gajah, Lahat and Ipoh, the latter being the center of the mining-operations. An ideal section of the main geological features of the Kinta valley is given in Fig. 2. The valley is composed of a highly crystalline limestone, usually white in color, sometimes gray; in fact, it may be called marble. It is always highly inclined and often contorted, and in some places is interbedded with shale. On the east side of the valley, near its contact with the granite, it forms a remarkable series of limestone cliffs, which rise in some cases as high as 2,000 ft. above the level of the limestone in the valley. It is non-fossiliferous, and its geo-

Sep 1, 1906

By K. Leutwyler

The key to realistic casing stress analysis in thermal recovery installations is accurate knowledge of the temperatures involved. Much information leading to prediction of heat losses from tubing string to wellbore has been published. This .same information permits calculation of casing temperature under certain conditions. This paper reviews the basis for most of the published work, the line source solution to the diflusivity equation and examines some of its application criteria in the light of unsteady-state conditions. An alternate finite differences method is presented for correlation, and experimental data pertaining to the heat transfer mechanism in the annulus is reported. In the light of the information presented in the paper, it appears that the assumption of a line source for the tubing-wellbore system is valid even for reasonably short periods of heat flow, .such as "steam soak" operations. The empirically modified equation presented earlier matches computer derived results of the finite differences approach lor periods as short as 50 hours. Previously predicted cas ing temperatures and the associated stress levels are thus verified based on these correlative computations and the reported experimental information. Fall out from the computer output resulting in some studies of the influence of insulating cement properties on casing temperature, and experimentally studied effects of nitrogen placed in the annulus at various pressures., are described. INTRODUCTION Generally speaking, predictions of average casing temperatures have been based on an idealized model involving a centralized tubing string at uniform constant temperature radiating energy towards the casing under steady-state conditions.'. ' Heat is transferred away from the casing to the formation by unsteady-state conduction across thermal barriers consisting of cement and the mud sheath. Heat balances written on the casing permit prediction of instantaneous casing temperatures. During early periods of injection, casing temperature varies appreciably as a function of time; however, for long injection times this variation decays as heat flow from the wellbore to the formation stabilizes, and it becomes virtually negligible as conditions surrounding the wellbore become quasi-steady-state (Fig. 1). Carslaw and Jaeger -escribe a solution to the diffusivity equation for a line source (Fig. 2). A constant supply of heat is introduced into the medium from the line placed into the origin of the x-y coordinate system and parallel to the z-axis. Heat spreads outward in the infinite cylindrical solid and the temperature increase on a line going through point (x, y) parallel to the z-axis at a distance r can be predicted by: The following criterion must be considered: the Carslaw and Jaeger equation is obtained on the basis of a large

Jan 1, 1967