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By R. S. Olson

An analysis of the wash thickener-two stage filtration circuit was undertaken to quantitatively describe the circuit performance. On the basis of information developed in this study, the factors of major importance in reducing soluble loss are: filter wash, wash zone size, filter capacity, filter feed pulp dilution, blow back, filter cloth, water to repulp, water to primary wash, water to feed pulp and thickener underflow. The wash thickener-two stage filtration circuit has been used in many hydrometallurgical plants to separate solute from leach solids. As many as 20 to 30 plant operating variables determine the performance of the wash circuit and hence the soluble loss. The complex relationships of these variables, with each other and with soluble loss, make the evaluation of their effect on mill performance difficult. An analysis of this type of circuit was undertaken to quantitatively describe the circuit performance. THE CIRCUIT The diagram in Fig. 1 represents the operation of the wash thickener-two stage filter circuit. This circuit provides for counter current, cross current or for a combination of countercurrent-cross current operation. The feed pulp stream, J, is intended to include any solution or water, other than primary and secondary filtrate, which enters the wash thickener. Except for filter washing, the operations in the circuit are simple mixing operations which can be described by material balance. The concentration of solute in the filtrate and cake solution after application of wash liquor cannot be described by simple material balance. The displacement washing equation, derived by Rhodes1 and extended by Choundhury and Dahlstrom,2 appears to best describe this case of miscible displacement in porous media. In a useful form, it is

Jan 1, 1963

By FRABK HERVEY PETTINGELL

THE stock exchange and its functions is about as well understood by the average individual as the fourth dimension. What is a stock exchange? Divested of the rules and regulations by which it is governed, and the facilities it provides for the convenient handling of securities, it would be in its nude state nothing more or less than a meeting place for brokers. The stock exchange in America dates back to 1752, when a group of merchants of New York established a meeting place at the foot of Broad Street for the purpose of dealing in meal and slaves. The first definite orgarization, however, had its beginning in 1792 when 24 New York brokers signed an agreement not to buy or sell public stock for less than one quarter per cent. commission. From this small group has grown by gradual degrees, the greatest organized security market in the world, namely, the New York Stock Exchange. At the present time there are 27 stock exchanges in the United States and 5 in Canada. Based on the volume of business transacted, the Los Angeles Stock Exchange ranks 6th among them. This is attributable to the fact that strictly speaking Los Angeles has never been a stock exchange town, like some other large cities. Take for instance San Francisco, which supported one stock exchange from 1862 to .1882 and has since supported two. No city, by the way, should tolerate two stock exchanges at the same time. It is an economic folly and a senseless duplication that can be compared with rival telephone companies or competing street railway systems, paralleling each other's lines and always leads to trouble and confusion, and sooner or later one or the other falls by the wayside. While Los Angeles has had stock exchanges of one kind or another since 1896, none of them attracted much attention until 1899 when the present exchange was organized and it did not get well under way until along in 1906.

Jan 1, 1925

By H. P. Willard, R. W. Gates

Basic Inc., has been mining magnesite and brucite for 27 years at Gabbs, Nev. This is a medium sized open-pit mine. The magnesite deposits are in north-western Nye County about 30 miles east of Luning, Nev., on the west slope of the Paradise Range, at an elevation between 5000 and 6000 ft. The magnesite and associated brucite is used to make magnesia refractories employed principally in the steel industry and magnesium oxide for various chemical uses.

Jan 10, 1963

By K. E. Gray, M. S. Seth

In Part I of this work,1 equations of elasticity were formulated for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure. Equations of elasticity and the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant rate of pressure or a constant rate of flow is maintained at the wellbore. In this paper, the approach presented earlier is extended to finite reservoirs for the cases of (1) steady-state flow, (2) constant pressures at the well bore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Results of this work show that radial and tangential stress gradients are high near the wellbore but diminish rapidt; away from the well; the vertical stress gradient behaves in the same way but is less severe. Radial stresses are compressive or neutral, whereas tangential and vertical stresses may be tensile, neutral or com-pressive, depending upon the boundary conditions, the physical Properties of the system and the radial distance involved (vertical stresses are always compressive in an unbounded system1. For constant boundary pressures, both radial and tangential stresses increase with time whereas they both decrease for a closed outer boundary and constant pressure at the wellbore. The vertical stress decreases with time for both systems. For steady-state systems, radial displacement may be positive or negative, depending upon the dimensions of the system, the pressure differential and the porosity. Radial displacement may be positive or negative for a closed outer boundary but is positive for constant pressures at both boundaries. INTRODUCTION The importance, utility and complexity of a realistic appraisal of the stress state at and local to a wellbore were indicated in Part I. In this paper the analytical approach presented earlier is extended to finite, cylindrical reservoir geometry for the cases of (1) steady-state flow, (2) constant pressures at wellbore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Other than the outer boundary of the reservoir being finite, the physical system and assumptions pertinent thereto are the same as before. The reader may wish to review the mathematical development through Eq. 49 of Part I before proceeding here. SOLUTION FOR GENERAL BOUNDARY CONDITIONS THERMAL STRESSES AND DISPLACEMENTS Since normal stresses do not exist at the free boundaries of a system subjected to thermal stresses, the boundary conditions are

Jan 1, 1969

By L. E. Fish, G. S. Wyman

CHUQUICAMATA open-pit mine is capable of producing a total of 105,000 tons daily. When the sulphide plant is operating to capacity the distribution of this quantity will be approximately 30,000 tons sulphide ore, 30,000 tons oxide ore and 45,000 tons of waste. At that time the combined capacity of the oxide and sulphide plants will be about 540 million lb of copper per year. Twenty one benches have been opened to date and all are still active except the three top ones at the northeastern limit of the pit. These have been pushed back to final slope line. The pit is 8850 ft long, 3540 ft wide and 980 ft deep. Benches are not all developed to a standard height as the large development shovels used in cutting new benches have been of different size and range. At this time new benches 521 ft high are being developed with an' 11-yd shovel. Ore haulage through the greater part of the pit operation has been on down grades to the crushing plant. With the opening of bench F-4 in April 1944 the first adverse-grade ore haul was encountered. Of the total tonnage now being mined, 35 pct comes from the four benches that are below the level of the crushing plant yard. Waste had been dumped on the same or nearly the same level as the bench from which it was removed up to the opening of bench F-4. Waste from this and lower levels is hauled to the level of the crusher, yard where it must cross the flow of ore traffic to reach the only available dumping space to the east of the mine. The average ore haul is 3.13 miles one way shovel to crusher, and the average waste haul from that portion handled by railroad is 3.32 miles one way from shovel to waste dump. Waste that is being removed by truck haulage from the upper part of the -mine is hauled an average of 1 mile. Ore loaded by trucks is hauled 3/4 mile to a car loading ramp and then by rail to the crushing plant. Drilling and Blasting There are two types of development for blasting being used: One for opening new benches and the other for bank shooting. The former consists of 9a in. diam churn-drill holes drilled 11.8 ft center to center in rows 10.2 ft apart with the holes staggered in the rows thus giving an equilateral-triangle pattern of 11.8 ft on a side. After the first block, 492 ft long by 71.5 ft wide, is shot in the pattern described above, the cut is advanced by smaller shots consisting of four rows of holes spaced 23 ft center to center with the rows 23 ft apart. These shots are fired in conjunction with side shots in which the holes are drilled 33 ft center to center and 29.5 ft back from the toe, thus squaring up the bank for subsequent shooting. An average bank shot consists of about 60 holes drilled in two rows parallel to the face, 30 holes to

Jan 1, 1952

By R. M. Waterstrat

X-ray diffraction and metallographic examination of binary Mn-rich alloys with Ti revealed the presence of intermediate phases in this system. A binary R phase has been identified and also a phase having an a-Mn type structure. The X-ray pattern of the phase TiMn3 is presented and a tentative phase diagram for the Mn-rich portion of this binary system has been constndcted. MANGANESE-rich alloys with titanium have been subjected to thermal analysis at temperatures down to 1100°C by Hellawell and Hume-Rothery.1 Their results indicate the existence of an intermediate phase TiMn3 in this binary system. This phase appears to coexist with the Laves phase TiMn2, and with terminal solid solutions based on the allotropes of manganese, at least down to 1100°C. The above investigators did not attempt to determine the crystal structure of this phase, however. Since, by analogy to the binary systems Mn-V and Mn-Cr3 one might expect to find a phase in this region of the diagram, it seemed desirable to obtain X-ray diffraction patterns of alloys in the concentration range in question, in order to ascertain whether the sigma phase or related structures occur. EXPERIMENTAL PROCEDURES Alloys were prepared by arc-melting electrolytic manganese and iodide titanium in a water-cooled copper crucible under a helium atmosphere. Excess manganese was added to each melt in order to allow for losses incurred during melting. The alloys were then wrapped in molybdenum foil and sealed in evacuated quartz tubes for annealing at various temperatures, as shown in Table I, followed by quenching in cold water. Although the inside of the tubes showed evidence for some loss of manganese from the specimen during annealing, there was no evidence of any reaction between the specimen and either the molybdenum foil or the quartz tube at these temperatures. It was later found that the manganese loss was considerably reduced by annealing these alloys in sealed quartz tubes containing one atmosphere of purified argon. As an added precaution the surface of each specimen was ground off before crushing the alloys to -270 mesh powder, using a hardened steel mortar and pestle. X-ray powder patterns were obtained using either FeKa or CrKa radiation in an asymmetrical focusing camera, which gave excellent dispersion of the closely spaced lines. Pictures were also obtained using a Debye camera of 5-cm radius which provided data in the angular region not covered by the focusing camera. The alloy specimens were polished and examined metallographically, using an etchant consisting of 60 pct glycerine, 20 pct nitric acid, and 20 pct hydrofluoric acid. The 10-g buttons were in each case broken in half and found to be well-melted and free of any gross segregation. One half of certain alloy buttons was submitted to chemical analysis in the "as-cast" condition. No appreciable change in composition seemed to occur during annealing . RESULTS The X-ray pattern of alloy Ti1.17Mn0.83 was found to agree well with that of the ternary R phase which was first found in the Mo-Cr-Co system,' and re-

Jan 1, 1962

Jan 1, 1968

By W. C. Phalen

The production of salt in the United States divides itself at the outset into two distinct classes…

Jan 1, 1915

By H. D. Outmans

A method has been developed for determining the relative water wet-tability (fraction of the surface wet by water) of porous media. This method involves the adsorption of methylene blue dye from an aqueous solution onto the solid surfaces of rock contacted by the injected dye solution. Experiments on Berea snndstone cores have shown that water-wet cores adsorb a large amount of dye from solution. In oil-wet cores, however, the injected aqueous dye solution is prevented from contacting the adsorptive surfuces by a film of oil and virtually no dye is adsorbed. This method was tested by experiments on mixtures of water-wet and oil-wet sand. Using the dye adsorption method, it was possible to determine quantitatively the fraction of water-wet and oil-wet sarzd in such mixtures. The dye adsorption test is readily applied to determinitrg the relative water wettability of fresh oilfield cores. The cores are not extracted before testing. Observed values of the wettability of field cores tested to date have varied from 100 to 6 per cent water wet. INTR OD UCTIO N Recent articles1 ' have emphasized the important role that wettability plays in almost all phases of reservoir rock behavior. It has been shown that wettability has a profound effect on the interstitial water saturation, residual oil saturation, capillary pressure, relative permeability, waterflood behavior, and resistivity index of oilfield cores. A quantitative investiga- tion of the effect of wettability on these core properties is severely handicapped by the lack of a simple technique for measuring the wettability of a porous medium. If such a technique were available, it would provide investigators with a means of gaining insight into the distribution of phases within a core. A number of qualitative methods of estimating wettability are known. These include contact angle measurements, flotation tests and studies of displacement pressure: imbibition7 and relative permeability data.' Using these tests, it is usually possible to classify a core as water-wet, oil-wet, or some intermediate degree of wettability. One recently proposed method involving measurement of nuclear magnetic relaxatione offers promise of determining quantitatively the fractional wettability of cores. The equipment is rather elaborate and necessary treatment of the cores before testing probably alters the natural wettability. This latter point also applies to most of the cited qualitative methods. This paper presents a new technique for determining water wettability of cores; it is based on measurements of the dye adsorption capacity of the core. This method has the advantage of requiring relatively simple equipment and involves minimum handling of the core before testing. It is important to distinguish between the various concepts of wettability referred to in the literature. The term "wetting" is defined by Bartell as that phenomenon which occurs when a solid and liquid phase come in contact in any manner so as to form a solid-liquid interface. A preferentially water-wet solid is defined by Jennings in terms of the advancing contact angle in the solid water-oil systems. Brown and Fatt regard fractional wettability as the fraction of the total surface area that is preferentially oil-wet or water-wet. However, none of these definitions adequately describes the type wettability measured by the dye test. This calls for the introduction of a new term, "relative water wettability", which we define as the fraction of the total surface area of a core contacted by injected water. DESCRIPTION OF METHOD The ability of a porous medium (especially the clays) to adsorb large quantities of surfactants, dyes, etc., is well known. It is reasonable to assume that a substance can be adsorbed from solution onto a solid surface only if the solution contacts the surface. In this connection Shapiro" has shown by experiments on silica gel that completely dry gel will adsorb methyl red dye from a benzene solution. On the other hand, if a film of water more than several molecules thick is present on the silica gel, the adsorption capacity of the gel for the dye is drastically reduced. Thus, a study of the dye adsorption capacity of cores should give some clue as to the fluid distribution on the surface of the core. TEST OF METHOD As a qualitative check on this theory, dye adsorption tests were run on similar Berea sandstone cores (Table 1, Cores 1-5). Cores saturated initially with water and flooded with 0.01 per cent aqueous methylene blue adsorbed 0.58 mg dye/gm of core. Similar cores saturated initially with water, driven to irreducible water with oil, and then flooded with the same dye solution also adsorbed 0.58 mg dye/gm of core. Another core, treated with a 5 per cent Dri-Film solution, dried and saturated with oil (Soltrol) adsorbed no dye when the dye solution was injected. These tests confirm

By J. Douglas, W. T. Ford, G. E. Henderson, I. F. Roebuck

An implicit numerical method is presented for simulating the differential and algebraic relations governing one-dimensional three-phase flow in porous media. The method is based upon compositional representation of the hydrocarbon system. Variable physical properties and water-oil capillary forces are included in the formulation; however, the effect of gravity is ignored. The effects of changing composition and mass transfer are considered through the use of known phase behavior concepts and correlations. The differential and algebraic equations and the numeric approximations to these equations are presented, and the computing algorithm is discussed in detail. This method is used to simulate a single-phase, two hydrocarbon-component gas displacement laboratory experiment. The method is also applied in simulating a solution gas drive and a gas injection problem using a reservoir oil represented as a nine-component mixture. For comparative purposes, the latter two problems also are examined with a one-dimensional volumetric model. The results of the simulation of the laboratory experiment demonstrate the relevance of this method to problems wherein the effects of mass transfer significantly enter the displacement process. The comparison of the results of the volumetric and compositional methods applied to a reservoir system illustrates not only the advantages and benefits derived from examining the hydrocarbon system composition, but also the necessity of this approach in application to a general reservoir problem. INTRODUCTION The advent of large memory, high-speed digital computers enabled reservoir engineers and mathematicians to pool their knowledge in the development of sophisticated techniques for the prediction of oil and gas reservoir performance. These techniques have progressed from volumetric and trend analysis calculations to the development of "mathematical models", or reservoir simulators. These latter models, in general, utilize finite difference approximations to the rather complex partial differential equations that mathematically describe the physics and thermodynamics of fluid flow in porous media. Many forms of this "model" type are available today, and much of the recent literature has been devoted to either improving known methods or developing new techniques for use in these prediction methods. The more advanced techniques in use at this time consist of the solution of differential and algebraic relations that describe a reservoir geometry in one, two or three dimensions and that incorporate reservoir hydrocarbon and water fluid systems that obey specified physical laws, having properties that might easily be measured in the laboratory. This type of model utilizes formation volume factors and other volumetric data, expressed directly as functions of pressure, to represent the reservoir fluid system. Experience gained with this type of simulator, commonly known as a "beta-factor model", has indicated that the approach has many outstanding defects, most of them due to the assumption that those properties measured in the laboratory completely describe the behavior of the fluid system throughout the life of the project under study. The effects of varying hydrocarbon composition and mass transfer between the phases of this hydrocarbon system must, by definition, be ignored. These defects, which may often be ignored in

Jan 1, 1970

By B. H. Caudle, L. G. Loncarie

Pilot flooding is one method of evaluating a proposed secondary recovery project. However, the amount and rate of oil recovery from an unconfined pilot area is not usually the same as from an equal area in a large-scale flood. This is true because fluids are free to move across the boundary of a pilot area. The result is that some of the oil produced in a pilot flood may come from outside the designated area and some of the displaced oil may leave the pilot area completely. This paper presents the results of fluid-flow model studies on a five-spot pilot flood. Mobility ratios between 0.1 and to have been studied. The effects of changing the ratio of injection to withdrawal rates are shown. INTRODUCTION A small-scale field test, or pilot flood, is an accepted method for evaluating the applicability of a secondary recovery operation and the economic potential of that operation for a reservoir. The pilot flood is carried on in the same manner, with the same injected materials and at the same pressures as would be used were the secondary recovery program to be expanded to a larger area of the field or to the entire field. If the reservoir fluid and reservoir rock properties are the same in the pilot area as in the rest of the reservoir, the production, injection and other pertinent data associated with the pilot test will represent and measure what should be expected from a full-scale development of this secondary recovery program. There is one major exception which, unfortunately, has been overlooked by many and which has been awaiting quantitative definition. This is the sweep-out pattern the reservoir engineer must use in interpreting the pilot flood and in extrapolating it to the full-scale development. The sweep-out area in a pilot flood is not contained within the five-spot pattern. Further, there is oil flow into and/or out of the five-spot during a pilot test. Thus, production data from pilots must be interpreted with this different flow system and sweep pattern in mind. We have studied the sweep-out pattern that will exist for some conditions of operation of pilot flooding a single five-spot (four injection wells and one producer). In our study, reported here, we have assumed that the reservoir is relatively homogeneous and of uniform thickness in the pilot area. The results of this study en-able the engineer to predict the recovery, injection requirements and project life for a full-scale operation from the pilot flooding data. The effects of various injection to withdrawal-rate ratios and mobility ratios in a relatively gas-free (10 per cent pore volume or less) system are shown. Experimental Method The technique used in this study was the same as that for the X-ray shadowgraph studies of sweep-out pattern efficiencies.' The model of the pilot and surrounding area was made from a uniform packing of round-grain sand consolidated with an epoxy resin. Fig. 1 shows the relation between the model and the pilot area. Only one-eighth of the pilot area had to be represented in the model because we assumed equal injec-

By Charles De Witt

The ore treated at the reduction plant (called Yangdei) of the Chiksan -Mining Co., Korea, is brought from four of the company mines, and from the small tribute mines. The largest shipments conic from Sajunkohl mule, situated about a mile and a half from the mill (Fig. 1). The ore is quartz of medium hardness. The overage assay value in gold is $6.95 per ton. At the mine the ore is put into bin,, and is Mien trammed over an 8 per cent. grade to the tipple bins above the mill, where the ore is drawn through the hull holes as desired. The capacity of the tipple bins is about 3,500 tons. On, from Moonsukohl, Chung Tarrie, Yang Chun, and the tribute mines is brought in by bulls and bull wagons. The bulls carry from 350 to 800 lb.; the average wagon load is about 1,200 lb. (Fig. 2). One shovelful of ore out of every ten is taken as a sample. Considerable ore

Jan 5, 1915

By John T. Norton

N order to attempt to arrive at a better under-Jl standing of the whole basic problem of sintering, these remarks will serve as an introduction for discussion that is included and will, perhaps, help to isolate specific questions which need to be answered or to suggest some definite avenues of investigation which should be followed. To bring some sort of logical order into the presentation, I will consider the various types of interaction between the metal to be sintered and the atmosphere which surrounds it, depending upon whether the phenomena are essentially chemical or physical in nature. For example, when the only necessary criterion for the satisfactory sintering of a certain powder is the removal of an oxide skin, then the problem of choosing a suitable atmosphere is primarily chemical; however, if a special surface condition as a consequence of the oxide skin removal is necessary for particularly effective sintering, then the problem becomes a physical one. Of course, the two aspects overlap considerably, but it may be possible to make a distinction in principle if not in practice. The chemical characteristics of the phenomena will be emphasized, since these are the better known. Metal-gas reactions involved in sintering are controlled primarily by the thermodynamics of the processes involved. In which direction will a reaction go and how far before it stops? The answer is to be found in the magnitude of the free energy change associated with the reaction. If a constituent is to be removed from the specimen as completely as possible or if a constituent is to be formed in the specimen as completely as possible, then one chooses conditions which are far from equilibrium so that the reaction is driven toward completion. On the other hand, if the composition is to be maintained at a desired value, then conditions are adjusted as closely as possible to the equilibrium point. This aspect of the problem is susceptible to quite precise analysis, provided, of course, that the significant reactions can be recognized and the required thermodynamic data are available. Conversely, if one asks how fast the reaction goes or how far it proceeds in a given time, the answer is frequently much more difficult to answer in quantitative terms. Yet the rate-con trolling factors of the reactions may be of primary importance in the success of a particular operation, especially where competing processes are at work. Both equilibrium and rate factors must be understood if a clear picture is to be obtained. For instance, in a process for carburizing titanium dioxide, is the difficulty of obtaining a stoichiometric Tic due to a true limitation of the equilibrium or simply to a very slow rate of reaction? An example of this appears in the work of Kalish and Mazza.' They showed that the oxygen content of sintered iron compacts was lower when sintered in pure hydrogen than in the case where the hydrogen was diluted with either argon or nitrogen. The equilibrium oxygen content of the iron would be the same in the two cases, since it is determined by the ratio of the partial pressures of water vapor and hydrogen and this pressure ratio is unchanged by dilution. The rate of oxygen removal, however, under the conditions of a constantly replaced furnace atmosphere, depends upon diffusion and thus upon the concentration of hydrogen in the furnace atmosphere. Possibly the clearest way to illustrate the interplay of these two factors is to consider in more detail some of the typical metal-gas reactions. Adsorbed Gases It is common experience that fine metal powders with their very large surface areas often contain large quantities of gas. This gas, which results from exposure to air or perhaps from some step in the

Jan 1, 1957

By L. W. Pommier, F. B. Brien, A. K. Bhasin

In the field of mineral processing, although many operations are applied to suspensions of ore particles in fluids, there is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. Previously proposed equations, based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids, are exam ined in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. As more knowledge is acquired in regard to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow predictions of conditions to achieve optimum results for engineering purposes. In the field of minerals processing, many operations are applied to suspensions of ore particles in fluids. The differential movement of solids of various sizes and densities in suspensions is of utmost importance to gravity concentration, wet classification, flotation, hydrometallurgy, and pipeline transport of solids. The subject is also of importance to other branches of engineering; for example, those involved with soil mechanics, ceramic slips, and oil-well drilling fluids. There is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The problems encountered in the direct application of the well-known Stokes and Newton's Laws to non-Newtonian systems have been examined in a previous paper.' Equations were proposed based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids. This present paper examines these equations in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. It is thought that, as more knowledge is acquired as to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow prediction of conditions to achieve optimum results for engineering purposes. The purpose of this paper is to make an initial assessment of the nature and magnitude of pertinent suspension variables. In order to avoid too voluminous a document, the examination of kinetics and mechanisms will be omitted at this time. THEORY A Newtonian fluid is defined as a fluid in which the stress is proportional to the rate of strain, 2 i.e.: H = viscosity; see Table I. for list of symbols The following equations are conventionally used to assess the motion of spherical particles moving under laminar and turbulent flow conditions through Newtonian fluids: When these relationships are applied in practice to suspensions, the liquid density is substituted by a composite suspension density, and viscosity is usually taken as that of the suspending liquid or an approximated "apparent viscosity." However, suspensions are non-Newtonian in character3 and thus, more than one viscosity parameter is required to describe their behavior. A number of models have been proposed for non-Newtonian fluids;2,4 among these the simplest is the Ostwaldde Waele or power-law model for incompressible fluids which for one dimensional flow may be reduced to:

Jan 1, 1970

By J. C. Martin

Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators in which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the aduantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. INTRODUCTION In recent years, computers have been used to calculate the performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The situation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; and, for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow re1ations.l-3 In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation.l.2. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir's thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoir. This requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats' et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats' assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. DISCUSSION SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate: (1) that the fluids along any line perpendicular to such a reservoir's upper surface are in static capillary equilibrium (vertical equilibrium); (2) that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; and (3) that hydrostatic pressure gradients exist along any line perpendicular to the reservoir's upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together.

Jan 1, 1969

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers' knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By H. J. Gerritsen

From presently available components a portable, rugged, reliable apparatus can be built which will be able to detect methane concentrations of 0.1% and lower in air. Sensitivity and design considerations of the apparatus are given. Ways to build even simpler and cheaper apparatus in the future are indicated. Traditionally the problem of detecting and monitoring the presence of dangerous gases present in small concentrations in air has been a difficult one. Whether canaries,' or sophisticated chemical or thermal conductivity methods are used, they seem to be either slow, cumbersome, or otherwise not completely satis factory. A seemingly natural way of gas detection is to measure the strength of absorption undergone by light of a wavelength that the gas to be detected absorbs. This method has been difficult to apply in view of the low power output over a narrow wavelength range in the infrared from traditional glow bar light sources. Besides, the apparatus to select such a narrow band of wavelengths is quite costly and complex. The use of a laser solves these problems simultaneously. Although a variety of lasers are available to detect a variety of gases (such as carbon monoxide or methane) whose early detection would be desirable, this paper deals exclusively with the use of lasers for methane detection. ABSORPTION SPECTRUM OF METHANE IN AIR The absorption spectrum of pure methane is very well known.2-4 There are four fundamental vibrations, all occurring in the infrared of which only two absorb strongly. They occur at 3.3 µ and 7.7 µ. The absorption spectrum is quite complicated due to the fact that the methane molecule can rotate in a variety of rotational quantum states. These rotational states are furthermore split by anharmonic forces such as the Coriolis force.4 When methane is present in air at atmospheric pressure, much of the very fine structure due to the anharmonic force is washed out since the pressure broadening is of the same magnitude as the splitting due to anharmonicity. For most of the spectrum at 3.3 µ, the rotational lines are typically separated by 0.01µ while the individual linewidth is 0.0001 µ. It is thus very important that the laser emit at a wavelength that coincides with one of these rotational lines. Before elaborating on the point that such a laser exists and how it performs, it is necessary for later discussion to point out that in the

Jan 1, 1967

By L. F. Elkins

In 1946 Littlefield, Gray and Godbold published a thorough geologic description of the West Edmond Hunton Lime reservoir, located in Central Oklahoma, and discussion of its early performance.l They stressed implications of the nature of the reservoir rock on performance to be expected with production both by natural means and by pressure maintenance with gas injection. The essence of their analysis was that presence of an extensive interconnected system of fractures and solution channels constituting about 10 percent of the total reservoir void space in otherwise very low permeability reservoir rock would result in severe channeling of naturally encroaching water or injected gas through the fractures with little or no benefit to ultimate recovery of oil. Considerations were in progress to unitize the reservoir for pressure maintenance by gas injection. Some other engineers involved in the project had considerably different opinions at the time regarding continuity of fractures and regarding effects of such fractures on performance. The field was unitized Oct. 1, 1947. Subsequently, pilot gas injection tests were conducted in four areas of the field; large scale waterflooding was conducted in two parts of the field in the Bois d'Arc or Upper Hunton; and pilot waterflooding was conducted in the Chimney Hill or Lower Hunton. Full scale water-flooding is now in progress in the Chimney Hill section where it is oil productive. The primary purpose of this paper is to divine some of the secrets of this reservoir through analysis of all aspects of its performance, with the hope that it will be of help to engineers and operators in developing and operating other low permeability fractured reservoirs. In part, this considers variance of actual performance from some widely used conventional reservoir engineering assumptions. For brevity, other aspects of unit operation and its benefits to the owners are not discussed. Oil and Gas in Place For unit participation, net pay in the Bois #Arc defined by the gross SP anomaly on electric logs totalled 2,100,000 acre-ft in the 30,000-acre reservoir. Development of West Edmond predated modem logging techniques that now would be used to determine "net" or "productive" pay. In Fig. 1 this log pick is compared with detailed core analysis and core descripfion by Littlefield et a1.l for one well identified as A on the index map in Fig. 2. Not all of the gross Bois #Arc section had oil staining, but all cores with measureable intergranular permeability were stained. (The committee selection of the Bois d'Arc SP interval also includes the Frisco section as identified from cores by Littlefield.) The Bois d'Arc is oil productive throughout the entire 600-ft monoclinal accumulation from the eastern upstructure erosional pinchout to the west-side oil-water contact. (See Littlefield et al.l and McGee and Jenkins for geologic detail.)

Jan 1, 1970

By W. A. Burns

Vertical flow is an important mechanism in many petroleum reservoirs. Yet no adequate method has heretofore been proposed for determining the in-situ vertical permeability in a reasonable length of time. Core measurements of vertical permeability do not necessarily represent effective in-situ values. Cores may be representative of only localized pockets of high or low permeability, and total reliance on cores might cause one to overlook the presence of vertical fractures altogether. Conventional single-well tests, interference tests, and pulse tests commonly are used to determine horizontal transmissibility, khh/u, but generally are not designed to measure vertical trans-missibility or other groups containing vertical permeability, ku. A new well test described here provides a measure of in-situ vertical permeability as well as the previously measurable horizontal permeability. This "vertical test" determines the vertical diffusivity, kv/gcu, and horizontal transmissibility, khd1/u (where dl is the length of injection or production perforations). The test is basically a short-term interference or pulse test normally lasting less than a day. Conventional down-hole equipment is used between two isolated sets of perforations in the same well, as shown in Fig. 1. A "layer-cake" description of a reservoir can be obtained by running two or more vertical tests in the same well, each over different vertical intervals. Each test can be analyzed for the effective vertical and horizontal properties of the interval tested. In addition, a vertical well test can determine the effective- ness of a shale barrier or tight zone by testing across it. Field use to date of vertical testing has confirmed its utility in reservoir description. Mathematical Basis Interpretation of vertical tests for ku and kh is based on comparison of measured pressure response with computer-generated response. Pressure behavior during a vertical test in a homogeneous, anisotropic, infinite-acting reservoir (infinite in radial extent and bounded in both directions vertically) is given by the diffusion equation for slightly compressible fluids with negligible gravity effects.l A schematic diagram of the problem is presented in Fig. 2, and an analytic solution, based on the image

Jan 1, 1970

Who's Who in Mineral Engineering - The 1978 Membership Directory of the Society of Mining Engineers of AIME

Jan 7, 1978