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By Rodney L. Stone, David S. Cahn

As part of an over-all laboratory and plant test program to determine mixing ad other techniques for a more economic use of bentonite as an iron ore pellet binder, a settling test for measuring the bentonite content within a pellet or a batch of pellets has been developed. Through this test, it has been shown that dry fracture load is directly proportional to bentonite content in batches of pellets, but inversely propor tional to bentonite content in individual pellets of the same batch. This apparent paradox is explained by a negative correlation between a pellet's size and its bentonite content and the fact that large pellets can withstand a higher fracture load than small pellets. In past attempts to characterize green and dry iron ore pellets, the authors found large variations in the results of strength tests on closely sized pellets from the same batch.' Reasons advanced for such variations in the quality of pellets in which the binder is bentonite were the presence of internal flaws and the nonuniform distribution of the binder. Even when resulting pellet strength is good, there is still the question of whether the same strength could have been attained through a more effective use of a smaller amount of bentonite. The authors' own and other studies 2-3 have pointed out the strong dependence of pellet strength on the degree of "mixedness" of the iron ore concentrate and the bentonite binder. However, before such a relationship could serve as a guide for the development of better mixing techniques and the associated economy of

Jan 1, 1969

By Maxwell Gensamer

Jan 1, 1960

By E. H. Herron, J. H. Perry

Mathematical simulation of reservoir behavior may be used to help understand reservoir processes and to predict reservoir behavior, thereby leading to the most economically desirable form of exploitation. In addition, simulation can be used as a tool for reservoir description to learn more about the physical nature of the reservoir and the mode of primary recovery. This use is essential in most reservoir studies and represents one of the more significant applications of simulation. Prediction of reservoir behavior provides information concerning displacement efficiency, optimum well locations, and the comparison of alternative producing processes. Since oil, water and gas all commonly occur in many reservoirs, a simulation that takes into account the simultaneous flow of three immiscible phases is a prerequisite for obtaining such information. Furthermore, a simulation that describes this flow in two dimensions provides the capability of evaluating combination gas- and water-drive reservoirs with either an areal or a cross-sectional description. Many reservoir problems require such a simulation. The objective of the research described here was to develop a mathematical model and associated computer program for accurate, efficient, and economical prediction of the reservoir flow of three phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases.l-3 Gottfried et al.' presented an analy- sis of three-phase simulation in one dimension. Fagin and Stewart" and Garrett6 have discussed the simulation of three-phase flow in two dimensions, but their solution techniques were different from the method discussed in this paper. In particular, previous models and computer programs have usually involved either fewer capabilities or inefficient and less rigorous descriptions resulting in limited applicability. In the following sections, we present a description of the model, an evaluation of the method, and the application to reservoir problems. Additional and supporting material is presented in the Appendix. The Three-Phase Model General Description The three-phase model consists of the mathematical description of the flow of oil, water and gas in a reservoir. Conceptually this description considers flow in all three space dimensions, but in the subject simulator it is assumed that no flow occurs in the third dimension. The model includes the effects on reservoir behavior of fluid and rock compressibility, viscosity, gravity, capillary pressure, relative permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. The differential equations governing multiphase, multidimensional flow in a reservoir are too complex to be solved analytically, so they are approximated by a system of finite difference equations and solved

Jan 1, 1970

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969

By R. W. Raymond

On the Manchuria. SOMEWHAT fatigued with excess of enjoyment and strenuous continuity of movement on the trip to and through California, the members and guests of the Institute party embarked Tuesday, Oct. 17, on the Pacific Mail S. S. Manchuria for a further journey to and through Japan. The good ship displayed the flag of the Institute (blue cross-hammers on a white ground), together with the Stars and Stripes and the ensign of the company. Uninterrupted fair weather and smooth water attended the passage to Honolulu. The Manchuria proved herself most commodious, comfortable and clean ("A sweeter steamship never sailed," quoth President Hunt) ; Captain Dixon and his officers were most agreeable, as well as most efficient; the passenger list comprised many congenial people besides ourselves-among them a score of missionary folk, and also Mr. M. H. de Young, Vice-President of the Panama

Jan 1, 1912

By L. Adler

Two basic cases involved in the design of an opening in bedded rock are: 1) where the beds deflect from each other so as to be separated; and 2) where the beds deflect onto their lower neighbor, loading the latter while reducing their own load. Analysis of case 1 is relatively simple, while the interference of the original deflection curves in case 2 complicates analysis of the latter. Figures and formulae are presented for determination of interference loading in this situation. The design of an opening in bedded rock involves two basic alternatives.1'2 In one case the beds deflect away from each other, so as to be separated from their neighbors; in the other case the beds deflect onto their lower neighbor, loading it, while reducing their own load. This is shown in Fig. 1. The first case lends itself to a simple analysis, since the upper and lower boundaries of each beam remain a free surface. In the latter case, however, due to the interference of original deflection curves, the analysis is more complex. Earlier investigators of this interference problem solved it by making the tacit assumption that this type of loading was uniformly distributed along the beam's length. While there is no intuitive justification for this assumption, its use does lead to an approximate solution. Still, a more exact solution does not require this apparently unrealistic restriction. To achieve initial simplicity, the analysis will at first be limited to a two-bedded sequence, as in Fig. 2. Since both beams have identical end conditions and spans, the original deflections of their center lines are members of the same family of curves, as shown in Fig. 3. Therefore, if interference occurs at one point along their center lines, it will occur at every point. For convenience, the midspan point is that usually examined. Deflection at midspan for a uniformly loaded beam regardless of end conditions is: where c is a constant depending on end conditions; w is the body load and equals yh, lb per ft; y is the specific weight of rock, lb per ft'; L is the span, ft; E is Young's Modulus, lb per ft2; I is moment of inertia (for a rectangular section), I = bh3/12 = h3/12, (ft4); b is the width of beam and equals one; and h is the thickness of beam, ft; or 3U > yB an Substituting the appropriate values into Eq. lb, interference between the two beds can be predicted. Should it occur, the additional loads along the lower boundary of the upper bed and the upper boundary of the lower bed must be determined. From the principle of action and reaction, these added loads are known to be equal and opposite, as indicated in Fig. 4. Since the final deflection curves for both beds are identical (Fig. 3), their successive derivatives of y with respect tox must also be identical. That is:

Jan 1, 1961

By Edward J. Felten

THE oxidation resistance of chromium and Fe-Cr alloys is increased by small additions of yttrium or other rare earth metals.1,2 In addition, the presence of the additives increases the resistance of these alloys to spalling of the external oxide above 1000°C. This ability to prevent spalling appears to be related to the formation of an internal oxide in alloys containing yttrium or the other rare earth metals. The internal oxide is found in the form of a filamentary growth concentrated in the grain boundaries of the unoxidized metal. In alloys containing yttrium this internal oxide was found to be either Y2O3 Or YCrO3.' In an earlier report,' the growth of the external oxide was found to be controlled by diffusion through the oxide layer. Thermal balance studies were used to establish the kinetics of external oxide formation. In this related study the rate of growth of the internal filamentary oxide has also been studied. The results obtained indicate that the growth of the internal oxide is also diffusion controlled. Internal oxidation appears to occur in at least two ways. Using copper alloys containing small amounts of silicon, Rhines 3 found that between 600" and 1000oC a subscale was formed which consisted of particles of silica dispersed in the metallic matrix. The conditions requisite to internal oxidation as suggested by Rhines are: 1) a solubility of oxygen in the alloy, 2) the ability of oxygen to diffuse at an appreciable rate into the alloy, 3) the possibility of the formation by the alloying element of an oxide more stable than the oxide of the host metal, and 4) a relatively low solubility of this oxide in the metal. These conditions are fulfilled for a number of other copper alloys.3-5 Furthermore, the relationship between the depth to which the internal oxide is formed and the oxidation time follows the simple parabolic law.6 The activation energy for copper containing small amounts of silicon, germanium, iron, or manganese as calculated from Rhines data6 is about 48 kcal per mole. In some cases the internal oxide is found segregated at the grain boundaries, especially near the the surface. Observations of this type of oxide formation have been reported by stead,7 Rhines,* and Lustman. Evans" cites these cases as examples of the simultaneous movement of anions and cations during oxidation. Furthermore, Evans states that the presence of a minor constituent with a high

Jan 1, 1962

By L. Adler

Longwall caving, one of the most economical and attractive mining methods, is yet one of the most difficult and hazardous.1 This dualism is inherent in a method which manipulates the mine supports themselves to aid in excavation. The difficulty is further compounded by the lack of an analytical method to predict and control results. This paper is intended to meet this need by providing a first approximation to the mechanics involved. The analysis will be limited to materials which are linear-elastic, homogeneous and isotropic. The rock structure is assumed to consist of beds of uniform thickness with no interbed bonding.2 Consequently, the mine roof can be likened to a beam, in which the action characteristic of longwall caving is the controlled deflection of the barrier supports. This deflection causes load to be intentionally transferred from these barrier props to the working face.3 Two of the requirements of this method, shared in common with other mining methods, are the provision of (1) adequate and (2) safe working space. The third requirement is the one characteristic of longwall caving and is somewhat in conflict with the second; (3) the development of near-failure static loads at the face. Requirement (1) is handled by spacing the barrier props sufficiently far from the working face for efficient operation. Requirement (2) limits the static stresses in the structure to predetermined allowable values. This means that it is not desirable to induce a maximum load on the working face as requirement (3) may imply. Such a condition could produce collapse in the whole structure. It is the purpose of the undercut to limit the depth, and thereby control the failure of the face. Therefore, requirement (3) really means the development of an optimum, not maximum, load which, in conjunction with undercutting, produces failure at the working face, with minimum powder consumption. Stress analysis requires an exact delineation of the structure and loads. The structure will be defined as the immediate roof and its supports. Since the roof is severed at the caving line, the supports reduce to the barrier props and the working face, as shown in Fig. 1. The mechanics of failure within the working face itself are complex and beyond the scope of this study, since the face represents a typical mine invert structure.4 However, this lack can be made good by the judicious collection of field data. The primary load on the structure is its own weight or body load which can be considered uniformly distributed over its upper surface. Additional loading occurs due to interference of overbeds with the structure. Wherever this occurs, the effect can be approximated by a load uniformly distributed on the upper surface of the structure.5 When this interference is intermittent, as with a much thicker overbed, the elastic curve for the overbed is superimposed on that for the structure and the extent of interference noted, as Fig. 2 shows. However, for simplicity, this study will ignore such intermittent loads without impairing the generality of approach. Consequently, the free-body diagram is that of a uniformly loaded cantilever beam with an inter-mediate support, as shown in Fig. 3. For convenience of analysis, the diagram will be divided just to the

Jan 1, 1961

By Norman F. Schulz

The technical excellence of separation achieved in a mineral concentration process, or any other process where two constituents of any kind are physically separated from each other, is expressed uniquely and quantitatively by the separation efficiency (E,): E. = (R - R,), where R is the percentage of the valuable constituent and R, the percentage of the waste appearing in the concentrate. The separation efficiency meets all the usual requirements of a true efficiency and is independent of the nature of the process used. It can be visualized as the percentage of the feed material that, in effect, actually undergoes complete separation while the rest of the feed is distributed randomly and unchanged into the two separation products. The problem of quantitatively assessing the results of a mineral concentration process recurs whenever one tries to decide which of two similar test results is more desirable. Although economic factors may greatly influence the eventual choice of process, they usually have very little to do with the technical excellence of a separation and are, therefore, not a consideration at this point. Concentrate grade and recovery, used simultaneously are the most widely accepted measures of performance, and if both the grade and the recovery are greater for one case than for another, the choice is simple. However, when the results of closely competitive operations are compared, it often occurs that one set of test results shows a higher grade and a lower recovery than another and the choice is no longer obvious. Laboratory investigations of a mineral concentration process applied to a given feed material can often be designed to yield successive paired values of concentrate grade and recovery over the practical range of the course of a separation process.' These results may be plotted as some combination of the cumulative values of grade, weight recovery, or unit recovery in the concentrate. The resulting correlations for two slightly different sets of conditions can then be compared qualitatively, or even quantitatively in particular cases.2 Such comparisons are not applicable, however, to individual concentration test results. The reduction of a separation test result to a single efficiency figure, preferably as a percentage of ideality, would afford the simplest and most precise means for comparing the results of competitive tests. The effective proportion of feed material that undergoes complete separation in any real concentration process, hereafter referred to as "separation efficiency," is such a figure. It is essily calculated from the usual feed and product data and can even be evaluated, in many cases, from data in publications describing various concentration processes. Mineral Concentration Processes and Their Evaluation Mineral Concentration Processes: The overall concentration process may be subdivided into a liberation process which severs the bonds between unlike mineral species, and a separation process, which sorts the resulting liberated particles into two products—a concentrate rich in mineral A and a tailing lean in mineral A. A perfect mineral concentration process is represented by the idealized scheme shown in Fig. 1 in which liberation and separation are not differentiated. The feed mixture consists of two mineral types which are completely liberated early in the process and then sorted by type. All the mineral particles of type A which respond uniquely to the selection forces acting in the ideal separator, report to the concentrate, while all the mineral particles of type non-A report to the tail-

Jan 1, 1971

By H. J. Modi, D. W. Fuerstenau

pH effectively regulates the flotation of corundum through its control of the surface charge. Since collector ions function as counter ions in the double layer, the collector must be anionic when corundum is positively charged and cationic when it is negatively charged. Even a long-chained xanthate will float positively charged corundum. Association of the hydrocarbon chains of the adsorbed collector ions gives rise to increased adsorption and increased rate of flotation. Because of this phenomenon, neutral organic molecules aid flotation although the unionized collector cannot promote flotation independently. Na2SO4 was found to depress the flotation of corundum with animic collectors through ionic competition whereas the same salt activates corundum for flotation with cationic collectors. A close connection between ion association, electrokinetic behavior, and floatability is suggested. As part of the increasing interest in the physical chemistry of flotation, strong experimental evidence has been obtained which indicates that organic ions are adsorbed as counter ions by non-metallic oxide minerals mainly because of the electrical forces which exist at interfaces(1-3). Thus flotation of such minerals without activation should then be appreciable only when the mineral and the collector are oppositely charged. Since only limited work has been reported on the effect of surface charge upon flotation behavior(3) this general hypothesis on the flotation of insoluble oxide minerals has not been tested thoroughly. Investigating the flotation of a mineral for which extensive electrokinetic data exist yields a way to test this hypothesis more extensively. The electrokinetic behavior of corundum in solutions containing both organic and inorganic electrolytes has been studied quite thoroughly' Electro-kinetic measurements have shown that in the case of corundum, simply by controlling pH the solid surface can be charged either positively or negatively. For this reason corundum was chosen for study. The object of this paper is to present a study of the flotation of corundum and to explain the results in the light of our knowledge of adsorption mechanisms gained from streaming potential investigations. This paper is concerned mainly with the effect of surface charge on flotation with anionic and cationic collectors, but in addition such flotation phenomena as collector hydrolysis, Van der Waals attraction between hydrocarbon chains, ionic competition, and activation are discussed. While the present paper is confined to a reporting of the data obtained and some of the more immediate conclusions, it will be seen that the results, in combination with those on other systems, do promise a

Jan 1, 1961

By M. R. J. Wyllie, Michael A. Torcaso

With the continued deep drilling of today, increasing numbers of high pressure and high temperature gas-condensate reservoirs are being discovered. Correspondingly, the ranges of properties of gas-condensate reservoir fluids are also being increased. The literature1*'." contains several excellent reviews of the property ranges in presently known condensate reservoirs. When one examines these property ranges, it becomes apparent that the need for reliable data is great if the engineer is to evaluate properly or appraise a gas-condensate reservoir. It is the purpose of this paper to present phase-behavior data that will point out some of the important variables that influence recovery from gas-condensate reservoirs produced by pressure depletion. All these variables may be resolved into two major categories: the hydroc:arbon composition of the reservoir fluid and the physical properties of the reservoir. But the variables which we will consider are those which are usually determined from well tests shortly after discovery and are, consequently, readily available to the engineer. They are as follows: (1) the producing separator gas-stock-tank liquid ratio, (2) stock-tank liquid gravity, and (3) reservoir temperature. Laboratory depletion studies have been performed on several reservoir fluids to illustrate the effect of changes in the cronsidered variables upon ultimate recoveries. The deviation factors, Z, of a series of reservoir fluids were determined experimentally to illustrate their order of magnitude and their effect upon the calculation of in-place reserves existing at high pressurcs and temperatures. The procedures followed in conjunction with the performance of these studies and their associated calculations are illustrated in Fig. 1. For the purpose of this paper, the depletion recoveries are expressed only in terms of pcr cent of initial stock-tank liquid, with the abandonment pressure assumed to be 500 psig. VARIATION OF RECOVERY WITH INITIAL PRODUCING SEPARATOR GAS-STOCK-TANK LIQUID RATIO The producing separator gas-stock-tank liquid ratio has long been one of the principal criteria in assumptions and generalized correlations' used for the estimation of ultimate recovery from gas-condensate reservoirs. Fig. 2 presents a plot of the cumulative recovery of stock-tank liquid at abandonment as a function of the initial producing separator gas-stock-tank liquid ratio. The graphical illustration represents the results of 44 laboratory depletion studies performed on actual gas-condensate fluids. These data are presented not only to illustrate the general trend of ultimate recovery increase with initial producing ratio increase but to emphasize the considerable variation in possible recovery at any given producing ratio. Table 1 presents the properties of two actual reservoir fluids chosen to illustrate the approximate extremities of producing ratios for gas-condensate systems. The fluids designated as A and B exhibited initial producing ratios of 3,400 and 114,000 scf/bbl, respectively. Fig. 3 presents a graphical comparison of the cumulative stock-tank liquid recoveries, calculated from the well-stream compositions and produced volumes for each fluid during depletion. It is to be noted that Fluid A exhibited a recovery of only 16.5 per cent when produced to an assumed abandonment pressure of 500 psig while the corresponding recovery for Fluid B was calculated to be 62.2 per cent. This difference in recovery, which exemplifies the general trend of recovery increase with initial producing ratio increase, is readily explained by consid-

By D. N. Dietz

Jan 1, 1969

By M. E. Wadsworth, T. D. Chatwin

The kinetics of sulfidization of hematite (Fe203) by H2S gas at various partial pressures have been determined over the temperature range of 170° to 500°C. The process was controlled by thin films of pyrite (FeS2) and troilite (FeS) which were protective and formed diffusional layers. At higher temperatures the thermodynamic drive to form FeS2 decreased, and consequently the rate of formation of FeS, decreased. Conditions for the development of thin layers of FeSz consisting of 10 to 100 atomic diameters are presented. Laboratory flotation results on synethetic ores indicate floatability identical to that of pyrite of normal xanthate flotation. The prospect of high-temperature sulfidization of metal oxides using H2S, S, or other sulfur bearing compounds is intriguing as a potential activation process for flotation since the thermodynamics are very favorable for a large number of systems. If the kinetic parameters are sufficiently well understood it may be possible to provide surface sulfide layers a few angstroms thick, thus imparting normal sulfide floatability characteristics to the oxide. For thin layers the total sulfur pick-up would be small except for very high surface area materials but in most cases this sulfur could be readily removed by roasting if necessary. The general reactions for the sul-fidization of metal oxide MxO, to a metal sulfide MpSq using H2S may be written for the three conditions py > xq; py < xq; and py = xq: A large thermodynamic advantage is obtained in many systems because of the relatively large negative free energy of formation of H,O compared to H,S. For the temperature range 2S° to 1500°C &apos; where AFOis the standard free energy and T is absolute temperature. As is evident from Eqs. 4 and 5, the free energy of formation of H ,0 is approximately 35 to 37 kilocalories per mole greater than that for H,S over broad variations of temperature. For oxide-sulfide systems as outlined above, sulfidization may be expected to occur for the conditions: Groups I and 111: that is, if the terms on the right are more negative than those on the left the reaction is expected to occur thermodynamically. The value hFg,(,) is included in Eq. 6 since hFLzs is based upon gaseous S2 rather than the normal reference state, orthorhombic sulfur. The

Jan 1, 1969

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.&apos; 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 R. W. Parsons

The over-all apparent single-phase permeability of fracture-rock systems was studied using two different two-dimensional models. In a strict sense the results are applicable only to these models, yet may give some insight into real reseruoir behavior. The regular fracture-matrix model can have any number of regular fracture sets. All fractures within each set have the same orientation, width and spacing. The gross behavior is amlytically equivalent to that of an anisotropic permeable medium. In the heterogeneous fracture systems, individual fracture conductivities vary within a two-dinensioml network pattern. A computer program calculates the overall permeability after the conductivities are randomly placed in the network. The calculated permeability depends upon the distribution of these conductivities and the particular fracture pattern into which they are placed. Although detailed information on actual reseruoir fracture systems is not available, this study shows how some of the possible variables may affect obserued gross reservoir characteristics. INTRODUCTION Characteristics of reservoir rocks are determined by direct (core analysis) or indirect (logging and production tests) examination. Both methods, singly and together, are widely used in reservoir evaluations. For fractured reservoirs a problem exists in relating characteristics of cores to the in situ reservoir properties. Knowing fracture characteristics can be of value in determining production mechanisms. Because of the limitations of observation, the intimate details of a fractured rock system will never be known. One approach in analyzing fractures is to study the behavior of some conceptually simple models. The two models analyzed contain features which may be realistic, yet are mathematically tractable. Flow is considered in two dimensions only, with the plane of interest at right angles with the fractures. This concept represents the horizontal flow in a reservoir system with the fractures oriented vertically. Only single-phase, laminar flow is considered. The regular fracture-rock system permeability is calculable from a simple analytical expression. The heterogeneous system requires a computer program for calculating overall permeability.

Jan 1, 1967

By John Chipman, Wayne L. Worrell

Using recent thermodynamic data for the carbides and oxides of tantalum, columbium, and vanadium, the stable solid phases aboue 1300°K and at 1 atm CO(g) pressure in each M-C-O system have been determined. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures necessary to obtain these metals by carbothermic reduction under reduced pressures. TANTALUM, columbium, and vanadium react with carbon to form the M,C and MC carbide phases. The M,C carbides have narrow homogeneity ranges, but the MC phases possess considerable ranges of homogeneity.&apos; The free energies of formation of the MC carbides were recently measured, and those of MC and M2Ccarbides have been estimated., (The notations MC and MC denote, respectively, the carbide compositions at the carbon-rich and at the metal-rich boundaries of the homogeneous MC phase.) In this paper, these carbide data are combined with thermodynamic data for the oxides to predict the stable phases in the Ta-C-O, Cb-C-O, and V-C-O systems at specified temperatures and oxygen pressures. M-C-O PHASE DIAGRAMS The solid phases in equilibrium above 1300°K for each M-C-0 system are shown in Figs. 1, 2, and 3. Above 1300°K, the vapor would consist entirely of carbon monoxide; and these phase diagrams were obtained by specifying the vapor pressure of CO(g) to be 1 atm. The temperature at which any two solid phases become unstable is specified along the two-phase equilibrium lines in each diagram. To simplify the diagrams, all solid phases in the Ta-C-O and Cb-C-O systems are represented as stoichiometric compounds. However, the homogeneity ranges of VO and VC are indicated, because they form a complete series of solid solutions.3 It also should be noted that the homogeneity range of

Jan 1, 1964

By W. J. Kroll

Jan 1, 1960

By R. L. Whiting, H. J. Ramey

The basic study from which this paper was prepared was started as the result of the growing need throughout the world for increasing quantities of energy in all forms. Quite obviously, natural forms of energy that are readily available at low development cost are those in greatest demand. The underdeveloped countries — and particularly those having little or no petroleum resources — are the countries in which the most interest is being shown in the newer energy sources. One of the least expensive energy sources is natural geothermal steam.&apos;-* Although this form of energy has been recognized for centuries, it has been only during the past 20 years that serious efforts have been made to harness it. Natural geothermal steam energy in Italy, New Zealand, Mexico, Japan, and California is now being produced through wells to drive turbines and generate electricity. Further, active exploration for natural geothermal steam is being conducted in Hawaii, Fiji, Taiwan, Chile, Russia, Greece, and Katanga. It is surprising to find that most geothermal steam exploration is in the "steam seep" stage. That is, surface studies are made and exploratory wells are drilled in the general area of steam seeps. However, in the larger geothermal steam areas, there have been efforts to apply the most modern geological and reservoir engineering principles in order to define the reservoir parameters, particularly those relating to estimates of reserves and future productivity. This paper is concerned with the development of appropriate equations and techniques to facilitate these estimates. Production of natural steam or hot water presents problems different from those experienced in the production of oil and gas. For example, steam or hot water systems may be essentially single-component systems, while hydrocarbon systems are most frequently multicomponent fluid systems. Heat effects are much larger for water than for hydrocarbon systems; and the natural steam production may or may not be isothermal, while production of petroleum reservoirs is considered normally to be isothermal. Petroleum reservoir engineering principles may be applied to natural steam or hot water reservoirs if the inherent differences in the systems are considered. The basic considerations involved in geothermal steam reservoir engineering are: thermodynamics, physical and thermal properties of water, materials and energy balances, fluid influx, and performance matching and predicting. Thermodynamics Fig. 1 is a pressure-temperature diagram for the liquid-vapor region for pure water, showing the critical point and five other points representing possible initial conditions for a geothermal steam reservoir. To generate a physical appreciation for the mechanics of natural steam production, it is helpful to consider

Jan 1, 1970

Jan 1, 1967

By A. Timur

Fluid flow properties of porous media have long been of interest in such varied disciplines as geology, geophysics, soil mechanics, and chemical, civil, and mechanical engineering. This interest has resulted in numerous models of porous media that have been proposed, tested, and found to be useful under, at best, only special circumstances. A critical review of most of these models is given by Scheidegger. 1 The application of each new tool to the study of porous media has helped to test some of the existing theories and to form new ideas based on the new parameters being measured. In the application of nuclear magnetic resonance (NMR) techniques to the study of the properties of fluids in porous media, the theoretical studies of Korringa et al.2 resulted in a model for the relaxation of spin polarization of protons in a hydrogenous fluid in a pore of a solid. Seevers3,4 verified this model, established a method for measuring the surface-to-volume-ratio distribution in a porous medium, and proposed a technique for determining specific permeability in sandstones. In the present investigation, the uses of NMR methods are extended and a simple model of porous media is developed from an analysis of pulsed NMR measurements. In this model, the pore spaces of a porous medium are divided into three groups on the basis of their surface-to-volume ratios. To evaluate predictions of the NMR model, laboratory measurements of spin-lattice relaxation time, porosity, permeability, and residual (irreducible) water saturation were conducted on more than 150 sandstone samples obtained from four oil fields in North America. Applications are discussed for estimating the volume of movable fluid, ?p, and the specific permeability, k, of sandstone samples. The former parameter, which can be considered as producible porosity, is expressed by ?p = [1 -- (Swr/100)]? , .... (1) where + is porosity in percent of bulk volume and Swr is the residual (irreducible) water saturation in percent of pore volume at a capillary pressure of 50 Psi. Fast, nondestructive laboratory methods are described for determining porosity, movable fluid, and permeability of sandstone samples from measurements with a pulsed NMR (spin-echo) apparatus. Procedures are given for adapting these methods to samples of irregular shape and small size. Theory General In the Korringa, Seevers, and Torrey2 (KST) model the observed decrease in the spin-lattice relaxation time, T1, of protons of a hydrogenous liquid contained in the pore spaces of a porous solid is attributed to an increase in the correlation time for the random motion of the water molecules and to the presence of paramagnetic centers at the liquid-solid interface. This KST model predicts the observed relaxation time of a hydrogenous liquid in a pore of a solid through

Jan 1, 1970