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By K. E. Brown, G. H. Fancher

An 8,000-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 3/8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 B/D at various gas-liquid ratios from 105 to 9,433 scf/bbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gas-liquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scf/bbl. These deviations me believed to be mainly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.l As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gas-liquid ratios and flow rates. Definite changing flow patterns do not allow any one correlation to be accurate for all ranges of flow. INTRODUCTION The ability to analytically predict the pressure at any point in a flow string is essential in determining optimum production string dimensions and in the design of gas-lift installations. This information is also invaluable in predicting bottom-hole pressures in flowing wells. Although this problem is not new to industry, it has by no means been solved completely for all types of flow conditions. Versluys,2 Uren, et al, 3 Gosline,4 May,5 and Moore, et al,6,7 were all early investigators of multiphase flow through vertical conduits. However, all of these investigations and proposed methods were very limited as to their range of application. Likewise, many are extremely complicated and therefore not very useful in the field. Only in the last decade have any significant methods been proposed which are generally applicable. The most widely accepted procedure in industry at the present time is a semi-empirical method developed from an energy balance, proposed by Poettmann and Carpenter8 in 1952. Their correlation is based on actual pressure measurements from field wells. Accurate predictions from this correlation are limited to high flow rates and low gas-liquid ratios. Although this method will be discussed in detail later, it should be pointed out that two important parameters, namely the gas-liquid ratio and the viscosity, were omitted in their correlation. The viscosity was justifiably omitted since their data was in the highly turbulent flow region for both phases, and most wells fall in this category. The gas-liquid ratio was incorporated to some extent in the gas-density term. In 1954, Gilbert9 presented numerous pressure gradient curves obtained from field data for various flow rates and gas-liquid ratios for the determination of optimum flow strings. However, no method is presented for predicting pressure gradients except by comparison to these curves. Baxendell, et al,10 proposed a method based on Poettmann and Carpenter's procedure

By Henry J. Sandri

The use of economic models for forecasting purposes is an inexact yet necessary tool for mineral decision making. One method not commonly used is cyclical analysis because of its "non-scientific approach". However, under certain circumstances a modified cyclical approach can provide useful insight to mining companies. The current paper discusses mineral modeling, the type of economic models and the use of cyclical forecasting for mining firms (not speculators) involved in precious metals.

Jan 1, 1984

By G. Y. Chin, W. L. Mammel

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of' virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law'), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.' Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor's original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*'8 showed that Taylor's least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen' obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

By B. E. Field

Cobalt is a silvery white metal with a slight bluish cast. It strongly resembles nickel in its appearance and properties, notably its resistance to corrosion, although its alloys with other metals differ decidedly in their properties from those of nickel. The name "cobalt" was derived from the German Kobold, meaning goblin, and this came to be applied to the cobalt minerals which, although they resembled ores, did not readily yield metal when smelted by the primitive processes available in the Middle Ages. Cobalt minerals were used as pigments by potters and glass workers before the Christian era. Cobalt blue glass was found in the tombs of the Egyptians and in the ruins of Troy, and many colors used by the ancient Greeks and Romans contained cobalt. The ancients were entirely unaware that the colors they used were caused by cobalt and the metal itself was not isolated until about the middle of the eighteenth century, by Brandt, although the preparation of cobalt compounds had been carried on in a small way ever since the opening of the silver-cobalt deposits at Schneeberg, Germany, in 1470.

Jan 1, 1935

By Junichi Sato, Takash Suzuki, Tatsuo Imamura, Mamoru Hojo

INTRODUCTION Hitachi Refinery of Nippon Mining Co., Ltd. was constructed in 1911. The refinery began early to recover by-product metals and to manufacture copper products. Today, the refinery recovers gold, silver, selenium, platinum and palladium as by-products of the copper refining process and manufactures copper powder, copper foil, wire bars and chemicals for plating. In 1969, the capacity of the Hitachi Refinery reached 6,000 tons/month. (T/M). Because, at that time, the forecast was for the demand for copper in Japan to increase, planning for the expansion of the Hitachi and Saganoseki refineries was begun. A new 10,000 T/M capacity tank house, a new electrolyte purification plant and a enlarged anode slime treatment plant were planned for the Hitachi Refinery. Construction at the Hitachi Refinery began in December, 1970, and was completed in April, 1974. The development of new machines and processes has resulted in an efficient refinery with a production capacity of 16,000 TIM. This paper is a report on the new anode slime treatment plant at the Hitachi Refinery, and especially on the copper removal process in that plant, the Ferric Leaching Process.

Jan 1, 1976

By Mark David Rankin

This paper represents a general assessment of the primary factors driving the market for mobile offshore drilling rigs and the utility of those factors as choice variables for the offshore drilling program planner.

Jan 1, 1982

By W. Scott Dunbar

INTRODUCTION Methods of linking boundary integral (BI) solutions with finite element (FE) solutions have been well described theoretically in other publications (e.g., Zienkiewicz, et al., 1977). The purpose of this paper is to point out some practical aspects of implementing these linkage algorithms for rock mechanics applications and to describe an alternative linkage algorithm. A not so obvious motivation for using FE-BI linkages is illustrated in Figure 1. The cost of modeling the excavation of the crusher station by the BI method can equal or exceed the cost of an equivalent FE model. This is due to the large surface area which must be modeled by the BI method. In such cases, a more economical approach might be to model the region immediately adjacent to the crusher station by finite elements and link the solution at the periphery of the FE model with a solution for the exterior region. Further economies can be realized if some flexibility in the type of exterior solution is possible. For example, it would be desirable to use a coarse discretization of the FE-BI interface for a BI solution, which would be less demanding of computer storage and time, or to use an analytical solution for the exterior region. The alternative linkage algorithm to be discussed allows such flexibility. BOUNDARY INTEGRAL METHODS There are basically two formulations of BI methods: the direct and the indirect. FE-BI linkage algorithms depend on which formulation is used. The purpose of this section is to briefly describe each method.

Jan 1, 1982

By R. E. Frounfelker, W. M. Hirthe

INVESTIGATORS in the areas of plasticity, crystal growth, and stress analysis have a need for crys-tallographic data such as the interplanar angles. This information is utilized in the form of a stereo-graphic projection from which orientation determinations can be made. Calculations of mechanical properties, such as the critical resolved shear stress, require values for the angles between directions as well as the interplanar angles. Only a limited amount of this data is available for tetragonal crystals. The equations for these angles are relatively simple but because of the large numbers of angles involved and the infinite number of structures that could be investigated, it was decided to program these calculations on a high speed digital computer. The angle, 8, between two crystal planes (h1 k1 l1)

Jan 1, 1962

By J. J. Knoerzer

A full-scale operational test was conducted on the Coaltek preheating and pipeline charging system at the Semet-Solvay Div. of Allied Chemical at Ironton, Ohio, for the purpose of determining whether a high-quality blast furnace coke could be made from blends containing at least 75% Illinois No. 6 Coal and at the same time reduce air pollution during the charging of the ovens. The coke produced had similar physical characteristics as compared to our conventional wet-charged coke, with the exception of smaller size for the preheat coke. Air pollution during charging was con- trolled and there were no serious operating problems. The coking time was reduced 25% from our normal 17 hr for wet charging to 12.8 hr for preheated charges. The blast furnace performance with preheat coke was satisfactory.

Jan 1, 1976

By T. W. Guy

THE increased moisture due to water¬spraying for coal dust control is of interest even for mines from which the coal is to be wet-washed before screening, because in many cases wet coal dust materially decreases the loading efficiency of men an equipment at the faces. It also causes serious increase in the normal wear and deterioration of all equipment with which it comes in contact. It is important to the consumer if it increases his as-receive moisture. No attempt will be made in this paper t cover the entire subject of water-spraying of coal for dust control. It will be confine to discussion and data on (r) percentages c dust in bituminous coals, (2) moisture increases due to spraying for dust control in mines or plants by methods which have proven satisfactory for periods of one to five or more years, and (3) a few suggestions for research. SIZE AND PERCENTAGE OF COAL DUST The U. S. Bureau of Mines1 classifies a coal dust all bituminous coal passing 20-mesh sieve (0.0328 in. square opening; The percentage of such dust to be found is ROM coal, of course, varies widely wit. the characteristics of the seam, and with the methods used in the mining and in the preparation of the coal. ROM screen analyses of 12 U. S. coals selected at random from personal files given in Table I show: A few other screen analyses examined indicating 40 pct or more of 2o-mesh X o dust in 3/8 in. X o-sizes were not included because of uncertainty that they were representative. The number of results in Table I is not sufficient to give a reliable estimate of the average, or of the range to be expected, but it indicates that in every case the coal dust is a relatively large percentage of the total ROM coal, and, of course, a progressively larger percentage of resultants as the larger sizes are separated for marketing.

Jan 1, 1948

TO THE BOARD OF DIRECTORS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-The following report covers briefly some of the more important activities of the Institute during the year 1923. In my report for the year 1922, I drew attention to the falling off in membership of the Institute due to the depressed condition of the mining industry in several lines and the inability of many of our members to find profitable employment in mining or its associated branches. A number who were unemployed during 1922 established connections during 1923, but a still greater number have been forced to resign or drop their membership during 1923. Fortunately, the number dropped is not so great as in the previous year. The Employment Service conducted by the four Founder Societies bears witness to the trend in business. For the young men just out of college, there are plenty of opportunities at small salaries, there are plenty of opportunities for them as laborers; but for the mature members, those of experience, there are few calls. During the last eighteen months, our Employment Service has been able to place only six of our members out of every hundred engineers for whom it has found work. Another loss which this Society has suffered, but which is not felt so keenly by our sister societies, is in its foreign members. The A. I. M. E. has always had a large foreign membership, but of recent years exchange has been so heavily against many European and South American countries that a large number of members residing abroad have been compelled to relinquish their membership. Almost invariably these members express keen regret because of the necessity that confronts them, and almost invariably the writers express hope that present conditions will not last long and that they will soon be able to ask-for reinstatement. Having stated the darkest side of the picture first, it may now be drawn to your attention that in spite of these losses the number of persons applying for membership was decidedly encouraging.

Jan 2, 1924

By Helmer Heldstrom

Gravity surveying with the torsion balance or the pendulum for ore prospecting purposes has generally not been considered practical or even possible. It is the intention of this paper to show that a fast and sensitive gravimeter can be very useful in ore prospecting, as an auxiliary to the electrical and magnetic instruments. A number of gravimeters have been constructed and put in practical use in the last seven or eight years; for instance, by Ising, Lejay-Holweck, Haalck, Hartley, Thyssen, Noergaard, the Humble Oil and Refining Co. and the Gulf Production Co. Their main application, apart from their use for geodetic surveys, has been for structure mapping in oil prospecting. There is no record that any of them have been used for ore prospecting. About the middle of 1934 the Boliden Mining Co., in Sweden, began experiments in constructing a static gravity meter sensitive enough for ore prospecting. Calculations and considerations that will be discussed later in this paper showed that this would necessitate an accuracy in the measurements of 0.1 milligal—roughly, one ten-millionth part of the total force of gravity. The first successful practical field tests of the instrument were made in January 1936. About the middle of 1937 the Boliden gravimeter was perfected. Ore prospecting with this instrument is now regular practice in Sweden, especially for the testing of indications given by geoelectric and magnetic methods. Gravity Anomalies that May Be Expected from Ore Bodies According to Newton's law, a mass M attracts the unit mass in a distance r with the force , GM where G = the gravitational constant = 6.68 . 10-8 c.g.s units. In the c.g.s., or centimeter-gram-second, system the force of attraction is expressed in the unit "dyne," which has the physical dimension c.g.s.-2 and denotes the force needed to accelerate the unit mass in one second to

Jan 1, 1940

By Helmer Heldstrom

Gravity surveying with the torsion balance or the pendulum for ore prospecting purposes has generally not been considered practical or even possible. It is the intention of this paper to show that a fast and sensitive gravimeter can be very useful in ore prospecting, as an auxiliary to the electrical and magnetic instruments. A number of gravimeters have been constructed and put in practical use in the last seven or eight years; for instance, by Ising, Lejay-Holweck, Haalck, Hartley, Thyssen, Noergaard, the Humble Oil and Refining Co. and the Gulf Production Co. Their main application, apart from their use for geodetic surveys, has been for structure mapping in oil prospecting. There is no record that any of them have been used for ore prospecting. About the middle of 1934 the Boliden Mining Co., in Sweden, began experiments in constructing a static gravity meter sensitive enough for ore prospecting. Calculations and considerations that will be discussed later in this paper showed that this would necessitate an accuracy in the measurements of 0.1 milligal—roughly, one ten-millionth part of the total force of gravity. The first successful practical field tests of the instrument were made in January 1936. About the middle of 1937 the Boliden gravimeter was perfected. Ore prospecting with this instrument is now regular practice in Sweden, especially for the testing of indications given by geoelectric and magnetic methods. Gravity Anomalies that May Be Expected from Ore Bodies According to Newton's law, a mass M attracts the unit mass in a distance r with the force , GM where G = the gravitational constant = 6.68 . 10-8 c.g.s units. In the c.g.s., or centimeter-gram-second, system the force of attraction is expressed in the unit "dyne," which has the physical dimension c.g.s.-2 and denotes the force needed to accelerate the unit mass in one second to

Jan 1, 1940

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the length of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel per day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel per day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from the commonly understood barrel per day value, in that the conditions surrounding the sale of one lease or property at a fair market value may

Jan 1, 1922

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By John Fritz

MEMBERS of the American engineering societies who were in London and Paris during the last days of. June and early July were present at many interesting gatherings. The official delegates of the Founder societies were the specially honored guests of the foreign engineering societies, but other American engineers took part in the meetings. The members of the delegation were: Arthur S. Dwight, Charles F. Rand, William Kelly, representing A. I. M. E.; Ambrose Swasey (general chairman of deputation), Ira N. Hollis, Jesse M. Smith, representing A. S. M. E.; F. B. Jewett, A. E. Kennelly, G. O. Squier, representing A. I. E. E.; Charles T. Main, Robert A. Cummings, John R. Freeman, D. C. Henny, representing A. S. C. E.

Jan 1, 1921

By Arnulf Muan

PHASE relations in three isothermal sections (l000°, 1100°, 1200°C) of the system Ag-Fe-Pd have been determined as part of a program to develop improved crucible materials for containing low-melting iron silicates at low oxygen potentials. The following experimental method was used: Two- to 3- g samples of each of forty different alloys within the system Ag-Fe-Pd were made up from metals of 99.9 pct purity. The mixed metal powders were contained in a 1-cc crucible of dense recrystal-lized alumina and heated in a protective atmosphere (90 vol pct A, 10 vol pct H2), first to complete melting for approximately 30 min and subsequently at the desired equilibration temperature (1000°, 1100°, or 1200°C) for approximately 24 hr. The samples were then quenched rapidly to room temperature and examined metallographically as well as by X-ray techniques. Unit cell dimensions were compared with standards obtained by study of one-phase alloys of known compositions. The results are summarized in diagrams (a), (b), and (c) shown in Fig. 1. Heavy solid curves outline areas comprising compositions of mixtures consisting of the phases labeled for each area. Mixtures in which liquid is the only condensed phase present are confined to very narrow areas adjacent to the Ag-Pd join at high silver contents. An enlarged, distorted picture of the phase relations prevailing in these areas is shown in the upper-left circular insert. Particular attention is directed toward the misci-bility gap which occupies major parts of the composi-

Jan 1, 1962

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette' recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.'."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy's law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969

By Jei Y. Choi, P. G. Shewmon

Using a scratch smoothing technique, the magnitude and the ratio of the surface diffusion coefficients (D,) in two orthogonal directions have been measured on copper for over 100 different surface orientations. Anisotropy was found for all surface orientations except those lying near the (100) and (111); however, these anisotropies were rarely greater than 2.0. The direction of maximum D, appears to coincide with the direction of step edges on any given surface, and if no such steps exist, no anisotropy is found. Thus the jump frequency along a step edge is shown to be faster than the frequency of a jump over the step. The values of Ds and AH for the (100) and the (111) orientations agree quite well with those obtained earlier by the grain boundary grooving technique. It is proven that the directions of maximum and minimum D, (the principal axes) for any surface orientation are known if the perfectly ordered plane corresponding to the given surface orientation possesses a plane of mirror symmetry. Thus the principal axes of D, for orientations lying along the sides of the unit stereo-graphic triangle are always known independent of the extent of thermal disorder or impurity adsorption. The merits and shortcomings of King and Mullins' recently published equations relating Ds to the rate of scratch smoothing are discussed. 1N an earlier paper the authors have reported the variation of the surface diffusion coefficient (Ds) with surface orientation on copper.' In that study Ds was determined from the rate of growth of grain boundary grooves on symmetric bicrystals. This gave values of Ds from 850° to 1070°C in a given direction on each of the six surfaces. It was found that the activation energy for surface diffusion was essentially the same for all six surfaces. The theory developed to explain these data assumed that the free energy of any given type of surface site depends only on the number of nearest neighbors the atom has. This same theory predicted that on any given surface Ds should be independent of direction. The primary aim of this study was to check the validity of this prediction for a wide range of surface orientations on copper. The growth of grain boundary grooves is ideal for studying Ds in a given direction on a given surface over a range of temperatures, because the same specimen can be repolished and used again. However, there is considerable work involved in growing a symmetric bicrystal, and for a survey of Ds in two or more directions on many surface orientations, the technique would be arduous. A better technique appeared to be the scratch method used primarily by Mykura. 2 If a scratch is placed in a surface whose surface tension is independent of orientation, the surface will smooth out in time under the influence of surface tension. To determine D, from this flattening, Blakely and Mykura2 used an approximate solution which was assumed to describe the rate of flattening. Recently King and Mullins3 (hereinafter K and M) have given a more exact analysis of the flattening of an isolated scratch. A second aim of this paper was to check the validity of this newer analysis and compare the values of Ds determined thereby with the values obtained from grain boundary grooving techniques. EXPERIMENTAL PROCEDURE In an effort to work with a particular predetermined surface orientation, light orthogonal scratches

Jan 1, 1963

By William Kent

Mr. ASHBURNER's paper on the Classification and Composition of Pennsylvania Anthracites, read at this meeting, well shows the need of new and accurate determinations of the heating value of these coals. A similar need exists for the determination of the value of bituminous coals, since the variation in quality of the latter is greater than the variation in anthracites. The recent extensive use of liquid and gaseous fuels, " patent" fuels, tan-bark, and other refuse fuels, also makes a necessity fix some correct method of determining the relative values of each of these fuels. Mr. Ashburner has recommended that tests of coals should be undertaken by the Second Geological Survey of Pennsylvania, and Professor Dewey, as stated in Mr. Ashbnrner's paper, has suggested a plan for tests of American coals, by the Smithsonian Institution, for which an appropriation by Congress will be asked. It is to be hoped that if any extensive series of tests of coals is carried on under either Government or State auspices, the erroneous methods of test which were followed by Professor Johnson in 1842, and by Quartermaster-General Meigs in 1882, will not be adopted.* The first requisite in determining the heating-power of a fuel is proper apparatus, such as has not been used in any of the tests of American coals yet reported. In the hope that more accurate means may be used in future tests, the writer desires to call attention to an apparatus which he has designed for the purpose. Not having had opportunity for making a trial of it, nor even of having it criticised by others, he does not offer it as the best possible apparatus; but if it contains any points of value, and leads to the design of still more suitable devices by others, the object of the presentation of this paper will be accomplished. The tests by Professor Johnson and General Meigs were made by evaporating water into steam in ordinary steam-boilers. A steamboiler of ordinary construction is not a good apparatus for determining the heating power of a fuel, for the following reasons:

Jan 1, 1886