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By Ted C. Briggs

Twenty-two compressibility runs were made with helium over the temperature range -5° to 80° C and at pressures to 800 atmospheres. A Burnett apparatus was used. Data from the runs were fitted to a fourth degree polynomial equation of state in the pressure and a weighting factor of Pr-3/4 was used. All data for a particular isotherm were treated simultaneously. A temperature function was found to represent the parameters B and C. Compressibility factors determined by this investigation are believed to be accurate to better than 0.05 percent.

Jan 1, 1970

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970

By N. N. Moebs

The Bureau of Mines air-sealed a 77-acre) above-drainage coal mine to evaluate sealing as a means of reducing the acid and metallic salt contents in drainage from abandoned mines. An approximate reduction in acidity of 150 ppm (equivalent to 193 pounds per day) and in iron of 98 ppm were directly attributed to sealing. The topographical, hydrological, and other factors involved in air-sealing are discussed, and the construction used to seal the mine is described.

Jan 1, 1970

By Karl A. Bauer, Cornelis Bezemer

The deposition of calcium carbonate scale on surface and subsurface production equipment creates an operation problem in many oil fields. The formation water in which the carbonate-scale-forming components are initially dissolved becomes supersaturated with calcium carbonate as a result of the drop in pressure during production. The continuous flow of a supersaturated solution through the production equipment results in the growth of a dense layer of calcium-carbonate crystals. For a scale layer to be built up, the supersaturated formation water should contact the walls of the production equipment. The tendency for scale to be deposited, therefore, will be low, if the crude has a low water cut and if the water is finely dispersed in the oil. A scale problem will occur, if at a high water cut part of the water is present as free water. The rate of scale deposition will then be approximately proportional to the rate of free water production. Depending upon where the formation water becomes supersaturated, scale may be deposited in the flow line only, in both flow line and tubing, and in some cases even in the perforations and in the formation near the wellbore. In the South Sumatran fields (Indonesia) the main difficulties encountered due to the deposition of calcium-carbonate scale have been restriction of flow through tubings and flow lines, wear and abrasion of plungers and liners, and stuck plungers or wellhead valves. So far, the only methods of combating the *Presently associated with Brunei Shell Petroleum Co., Ltd.. Seria. scale problem have been routine acidizing and additional well pulling. As for the pumping wells, it was estimated that some 50 percent of the total well-pulling effort was directly attributable to scale deposition. The most promising alternative was to prevent the deposition of calcium carbonate scale by means of chemicals. Inorganic polyphosphates such as sodium hexametaphosphate and trisodium polyphosphate are known to retard the formation of scale by the "threshold action". They are adsorbed on specific faces of the crystal nuclei and thus prevent crystal growth, thereby stabilizing supersaturation. Polyphosphates are effective at very low concentrations ( a few ppm), and far less than stoichiometric quantities are required to keep the scaling ions in solution. Recent investigations on barium sulfate scale1 have confirmed this mechanism. The types of polyphosphate mentioned can be applied as concentrated aqueous solutions either squeezed into the formation, lubricated down the annulus or injected via macaroni string. Several squeeze jobs with polyphosphate solutions have been carried out in the South Sumatran fields, however, with disappointing results. Lubrication down the annulus and injection through a macaroni string were not considered attractive in this area because of the kind of equipment and the degree of supervision these techniques require. Polyphosphates are also available in a granular, glassy form, which, in contrast with the readily soluble types already mentioned, show an extremely low

Jan 1, 1970

By P. E. Baker

An experimental study of heat flow in steam flooding was carried out with steam displacing water in a plane-radial fluid-flow model. Temperature distributions in the model reservoir, overburden, and substratum were measured at frequent intervals during flooding by means of a fixed array of thermocouples. Heat losses to overburden and substratum and the division of heat between the steam and hot-water zones in the reservoir were calculated from the temperature data by performing numerical integrations over the appropriate volumes. Temperature profiles and heat distribution results are presented. Some results were (1) the fraction of injected heat that is lost to overburden and substratum, when expressed as a function of time, did not depend on injection rate; (2) a significant portion of the injected heat was contained in the hot-water zone ahead of and underlying the steam front in the reservoir. The division of heat between the steam and hot-water zones did depend on injection rate; and (3) considerable gravity override was observed. The experimental results are compared with those of several published theoretical studies of heat transfer in hot-fluid injection; approximate agreement on heat losses is found with some of the most idealized theories. A valid comparison cannot be made in regard to steam us hot-water zone; basic interpretation of the hot-water zone, in terms of a vertical steam front, is clouded by gravity override in the experiments. INTRODUCTION The experimental study reported here primarily concerns two problems of heat transfer in steam flooding that have economic and engineering importance. These are (1) the fraction of injected heat lost to the overburden and substratum, and (2) the division of the remaining heat between a zone containing steam and a zone of hot water at lower-than-boiling temperature. The volume of the steamed region, which has a direct effect on oil recovery, can be calculated readily from these results. Several valuable theoretical studies have been published on this problem, but no experimental tests of the theories have previously appeared. Tests were needed because the effects of the necessary simplifications in the theories could not be determined otherwise. The basic, untested theoretical problem is the effect of "decoupling" heat and mass transfer, and the resulting inability to include the effects of heat transfer and condensation on fluid flow. The theoretical problem solved so far has been a heat transfer problem in which fluid is present as a heat carrier and flows in a stipulated manner, either linear or plane-radial. The simplifications that have sometimes been made in regard to thermal conductivity by, for example, Marx and Langenheim,l Lauwerier2 and Thomas3 apparently do not have an important effect on heat loss calculations, although the results of the different methods disagree to a certain extent, as shown by Spillette4 and by Ramey.5 A recent paper by the author6 compared the results of experiments in hot-water flooding with several theoretical results and showed a rather poor agreement. It will be seen that the experimental heat loss results for steam flooding, however, show acceptable agreement. These comparisons are discussed in a later section. EXPERIMENTAL APPARATUS AND PROCEDURE The system studied was one in which a sand pack, initially water saturated and at a uniform temperature, was flooded with steam at a constant rate and temperature. The temperature distribution in the "reservoir" and adjacent "strata" was measured with an array of thermocouples, and heat losses were determined from these measurements. The sand pack contained no oil because the only concern of the experiments was heat flow, and it was important to have the flow pattern as simple

Jan 1, 1970

By Donald E. Ralston

The Huntsville study area in northeastern Alabama consists of Jackson, Limestone, Madison, and Marshall Counties. Major emphasis was placed on the Huntsville urban area in Madison County to analyze the relationship of urban growth and the minerals industry. Huntsville was delineated into its component urban, suburban, and rural parts for 1964, and the primary area of growth was predicted for 1990. Population estimates were made for the four-county area as a unit and Madison County separately, and projected to 1990. Demand estimates for crushed stone and sand and gravel were made for the same area units and projected to 1990. Analysis of quarry sites in the Huntsville area was made for the present and for the future. The mineral operations of the study area are all located in rural areas; in the case of Huntsville, the mineral sites are located in areas defined as "rural" in the component urban-suburban-rural system. The operations outside Madison County can expect to have minor problems with urban encroachment, while those operations in Madison County can expect major problems associated with urban growth and development. Some of the problems associated with limes tone production can be reduced if producers invest in capital equipment that will reduce the nuisances inherent in this activity. Although urban expansion endangers some quarry operations in Huntsville, topographic and political restrictions which prevent urban expansion can effectively shield quarry operations for some time.

Jan 1, 1970

By Larman J. Heath

Wellbore enlargement was tested using hydrazine hydrate in a gas-storage well in Ohio to increase the well productivity. The wellbore was to be enlarged by chemical disaggregation of the sandstone adjacent to the wellbore. Productivity immediately declined 49.1 percent and gradually declined to zero in 7 months. A down-hole camera survey showed a white-to-gray precipitate covering the entire wellbore surface. The precipitate was chemically analyzed and identified as mostly carbazic acid, a hydrazine derivative of carbonic acid. Formation of this precipitate was not anticipated; this viscous sub-stance caused the gradual loss in productivity of the well. The wellbore was not enlarged. Laboratory tests were run to determine what clay stabilization measures could be taken in sandstone cores to prevent clay swelling and particle migration caused by hydrazine hydrate. Normal clay stabilization methods did not prevent the virtually complete loss in permeability to hydrazine hydrate. Other laboratory tests using natural gas diluted with small amounts of carbon dioxide confirmed the ease with which carbazic acid could be formed in a hydrazine hydrate-saturated environment within and adjacent to the wellbore.

Jan 1, 1970

By Lawson F

A rotating disc geometry has been used to provide a uniformly accessible surface for a kinetic study of the cementation of the metals cadmium, lead and silver from dilute aqueous solutions. This work is an extension of studies carried out on the Cu/Zn and Cu/Fe systems for which the rection rate was found to be completely solution-phase mass-transfer controlled. When the amount of material deposited was greater than 0.2 to 0.4 mg/cm2 there was an apparent enhancement in e which is attributed to the formation of a roughened deposit. This same phenomeon was obseived in the Cu/Zn Cu/Fe systems. Again, the rate of reaction of each system investigated was found to be solution-phase mass ,..~sfer controlled.

Jan 1, 1970

By J. B. Wagner, p. Hembree

The iron tracer diffusion coefficient of umstite has been measured at 110(fC across the phase field and at a single composition at 800°C. Assuming a simple cation vacancy model the tracer diffusion coefficient was found to be a linear function of the cation vacancy concentration at 1100°C. The equation is D = 3 x 20 29 where denotes the concentration of vacancies in numbers per cc. The tracer work at 800°C was carried out to investigate the reported "pinning" of tracer to the wustite surface at low temperatures. No evidence for the "pinning" of the tracer was found at 800°C in COz-CO gas mixtures. HIMMEL, Mehl, and Birchenall,&apos; Carter and Richardson,2 and Desmarescaux and La combe3 have measured the diffusion of iron tracer in wustite at several temperatures and compositions. The present work was undertaken to extend the measurements over a large composition range at 1100°C and to resolve certain apparent discrepancies in the data, expecially at lower temperatures. EXPERIMENTAL Wustite was prepared by oxidizing rectangular iron plates* in C02-CO mixtures. The samples were •The iron was supplied by the Battelle Memorial Institute courtesy of the American Iron and Steel Institute. The analysis is presented in Table I. quenched. Due to the inward flow of cation vacancies during oxidation, the center of the sample contained a thin void. The edges of the wustite slab were sanded until the sample could be split into two parts. Each part was then sanded on the front and back flat area until a smooth surface was obtained. The specimens were then replaced in the furnace and equilibrated at llOO°C in a predetermined COa-CO mixture by methods described elsewhere.4"6 The specimens were again quenched and the surfaces were lightly sanded to remove any roughness following the first equilibration. The specimens were then reequi lib rated in the same C02-CO mixture for thirty minutes in order to relieve any mechanical damage on the surface due to the polishing. The specimens were then quenched and the tracer was applied by an electroplating technique. The work of Carter and ~ichardson&apos; demonstrated that there was no systematic difference in the iron tracer diffusion coefficient in wustite if the tracer was plated, dried, or evaporated on the specimen. In the present study a piece of filter paper was saturated with an iron chloride solution of pH <* 3 that contained the tracer FeS5. The wustite was placed on the filter paper and made the cathode. A current density of 0.4 to 0.6 ma per sq cm was passed for about five to ten minutes. The thickness of the tracer layer was estimated to be about 7 x lom6 cm. This estimate was made by considering the area plated, the current flow, and time for plating and the activity of the iron in the plating solution. Different areas of the specimen were counted using a collimator to determine the uniformity of the tracer. Any specimen which exhibited a variation from the initial count rate (about 1500 cpm) by more than 15 pct was rejected. An estimate of the time necessary to convert the thin layer of iron tracer to wustite was made using the data of Pettit and wagner." he estimated time was 1 sec at 1100°C assuming linear oxidation kinetics. The shortest diffusion anneals were 1800 sec. The samples were suspended in the hot zone of a furnace by two platinum wires. Two separate specimens were run at the same time. Only the edges of each sample were in contact with the wires. The C02-CO gas of the same composition as that used in the pre-diffusion anneals flowed freely around the samples at a linear velocity of 0.9 cm per sec. To initiate a run, the specimens were lowered from the cold zone of a furnace to the hot zone by a magnetic lowering device." bout 60 sec were required for lowering. To terminate a run, the sample was withdrawn from the hot zone to the cold zone. Time zero for the beginning of the experiment was taken when the sample blended into the red glow of the furnace and conversely for the end of the experiment. The surface decrease method of measuring the tracer diffusion coefficient was used to collect the data. This method requires that counting geometry be reproducible because the specimen is counted before the diffusion anneal and after the anneal. A special jig was constructed for each specimen so the specimen could be removed from the jig and returned to the jig such that the well geometry was reproducible.

Jan 1, 1970

By Don K. Smith

The Reclamation Program for the Northern Zone of the Indus Plains in West Pakistan involves the construction of 30,000 irrigation wells to serve 20 million acres with an annual pumpage of nearly 40 million acre-ft. Detailed hydrologic studies indicated that mild steel would be satisfactory for casing; however, within two years after construction, about 10% of the wells began to fail due to encrustation and corrosion of the casing. A search to find a noncor-rosive substitute for the steel casing disclosed that only fiberglass-reinforced plastic pipe satisfied all requirements. The results of initial use of fiberglass have been highly satisfactory and have resulted in a lower over-all well cost. Advances in technology pomise further reduction in prices and improvement in performance. The northern zone of the Indus Basin comprises a vast area of essentially level land in West Pakistan which is irrigated by means of a complex system of canals that distribute more water to more land than any other irrigation system in the world. In spite of the development of this extensive irrigation system, production of food and fiber has not met the requirements of the country. The major reasons that crop production has not reached anticipated levels are the lack of adequate irrigation supplies and effective subsurface drainage. As a result, yields per acre are among the lowest in the world for areas where irrigation is practiced, and many thousands of acres of valuable crop land have been removed from production or seriously affected by salinity and waterlogging. To rectify the problems of irrigation supply and drainage the Government of Pakistan has undertaken a program of Salinity Control and Reclamation which is being administered by the Water and Power Development Authority. The Authority retained Tipton and Kalmbach, Inc., of Denver, Colo., as engineers for the program in the northern zone of the Indus Basin. This program consists of the construction of about 30,000 irrigation wells to provide drainage for waterlogged lands and full irrigation supplies, including leaching requirements, for all cultivated lands. The program will ultimately ensure the productivity of 20 million acres and involve an annual pumpage from groundwater storage of nearly 40 million acre-ft of

Jan 1, 1970

By R. H. Adams, A. M. Khan

The Huntington Beach oil field is on the Pacific Coast, southeast of the City of Los Angeles (Fig. 1). It lies both onshore and offshore. Most of the onshore section is operated by Standard Oil Co. of California, WOI. The Tar reservoir is of upper Pliocene age, about 200 ft thick, and consists principally of fine-grained, unconsolidated, somewhat shaly sand, with thin inter-bedded shale stringers throughout (Fig. 2). The reservoir is a broad, highly faulted, elongated anticline, with an areal extent of about 370 acres. Most of the faults bisecting the structure are normal, trend north-south, and are the main cause of reservoir discontinuity (Figs. 3 and 4). From 1964 to Dec., 1967, 259 steam stimulations were performed on a total of 125 Tar sand wells. Eighty-six new wells were drilled and steam stimulated. Of the total, 96 have been stimulated twice, 34 three times and 3 four times. During this same period, a two-injector steam drive pilot has been in progress. The response obtained from this project has been compared with the response to cyclic stimulation. This paper presents an analysis of the field observations for the two methods of thermal recovery. History of Development Drilling to the Tar pool commenced in 1924 with an initial well production of 40 to 50 B/D of 12o API gravity oil. Complete primary development of the pool has been spread over several years. Approxi- mately 40 wells were drilled during the first phase of development, which was completed in 1945. The subsequent primary development started in 1960 with initial well productions of 30 to 40 B/D oil. Thirty-seven wells were completed in the Tar pool during this phase. For the most part, slotted, gravel flow packed liners have been used in the wells in this pool. A cyclic steam stimulation pilot was initiated in March, 1964. Based on the very successful stimulation in the pilot area, the cyclic stimulation project was expanded to include all of the Tar pool wells producing at the end of 1965 (Fig. 5). Also, a development drilling program was begun at this time. To date, 86 new wells have been drilled under this program. The number of wells drilled each year in this secondary phase of development is also shown in Fig. 5. New Well Completion Practices Most of the new wells have been completed to produce from both the Upper and Lower Tar zones. Generally, a casing stub is cemented from the top of Lower Tar to the base of clean Upper Tar sands to exclude intermediate water-bearing sands. The water string is then cemented from the top of Upper Tar to about 1,500 ft with neat cement and 30 percent silica flour. The annulus from 1,500 ft to surface is then filled with a petroleum-based gel through a high-temperature port collar. Once again, a history of sand-free production dictated the use of 60-mesh gravel flow packed liners. The Upper and Lower Tar

Jan 1, 1970

By J. Vance Batty

The Permian Red Bed copper deposits of the South Central States are a potentially important resource. Only the higher grade, near-surface ores are now exploited because conventional froth flotation does not recover oxidized copper minerals which comprise 10 to 15 percent or more of the copper content of typical ore. Laboratory-scale beneficiation studies were initiated to devise a method capable of recovering both sulfide and oxidized copper mineral. Testing established that the high clay and gypsum content of typical ore prevented effective flotation of the oxide mineral using sulfidizing, fatty-acid, or oil emulsion techniques. A modified leach-precipitation-flotation (L-P-F) procedure recovered over 90 percent of the copper, compared to a recovery of 77 percent obtained by conventional sulfide flotation. The higher costs of the L-P-F method would reduce the increased revenue from higher copper recovery. An increase in copper price and/or an increase in oxide copper content of the ore would make the L-P-F process comparatively more attractive.

Jan 1, 1970

Samples weighing O&#183; 2 g are digested with 2 ml of 72 per cent perchloric acid for 2 hr at 180&#176;C, and then diluted to 10 ml. with water. After settling, an aliquot of clear solution is reduced with ascorbic-citric acid, and then a zinc dithiol solution is added to form a coloured molybdenum complex which is extracted with petroleum spirit for comparison with standards.Concentrations down to 2 p.p.m. may be analysed at rates up to 150 determinations per day.

Jan 1, 1970

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

By Laurance L. Oden

The Bureau of Mines is developing melting data for binary combinations of the alkaline earth fluorides and yttria to facilitate the formulation of slag composition. Liquidus and solidus temperatures and solid solubilities were determined for the BaF2-Y203 system, and the information is presented as the phase diagram. The phase diagram was constructed from data obtained by ceramography, X-ray diffraction, and thermal analysis of specimens encapsulated in small molybdenum ampoules. The data indicate a simple eutectic system with maximum terminal solid solubilities of less than 1 mole pct. The eutectic temperature is 1,343° C, and the composition of the eutectic is less than 1 mole pct Y203.

Jan 1, 1970

By R. F. Lynch, J. D. Wood

The Al-1.0 pct Mg alloy 565 7 was studied using optical microscopy and electron microprobe X-ray analysis. Constituent particles were found to exist inter-dendritically in the as-cast material in a region of precipitate free a -aluminum. Five phases besides a fine precipitate and a-Al were identified in the cast structure: Fel3, Fe2Al7, Mg2Al3, CUMgAl2, and Cu2FeAl7. Thermal treatments conducted for 100 hr at 1180°, 1130°, 1080°, 1030°, 980°, and 880° F revealed a general dissolution and spheroidization of the in-terdendritic constituent network observed in the cast structure. The principal constituents present in the thermally treated structures were FeAl3 and Fe2Al7 with the relative amount of Fe2A17 to FeAl3 increasing with a decrease in the treatment temperature. The phases Present in the wrought structure were identical to those observed after the thermal treatments, with the constituent particles strung out in the direction of rolling. ALLOY 5657 is a nonheat-treatable commercial purity Al-1.0 pct Mg alloy utilized extensively because of its bright finishing characteristics. This investigation was conducted to determine the constituents present in 5657 alloy, and to study the effect of extended thermal treatments on morphology. Numerous studies have been carried out to establish the equilibrium diagrams for various aluminum systems,1-3 with phase identification based on X-ray analysis, morphology, and the etching response of relatively large particles. Phragmen4 conducted a study of the phases in aluminum eutectic systems and compiled a "corrected" table of etching responses, drawing on his work plus that of Schrader,5 Keller and Wilcox,6 and Mondolfo.7 A review of the original work of Keller and Wilcox, and Mondolfo, which was concerned with the constituents found in commercial alloys, reveals that in numerous cases their etching responses differ from those reported by Phragmen and from each other. These inconsistencies may occur because a specific constituent will react to a given etch in a varying manner depending upon its size, the elements dissolved in the phase, the other constituents surrounding a phase, and the solute content of the matrix. Work with a commercial orientation was conducted on alloys 2024 and 3003 by Sperry8,9 and on alloy 3003 by Barker,10 where the relationship between the phase diagram and the nonequilibrium structure of an alloy was examined. Backerud11 investigated the A1-Fe binary system and found that at high cooling rates the equilibrium eutectic reaction forming a-A1 and FeA13 is replaced by another lower temperature eutectic reaction forming a-A1 and metastable FeAl6, a constituent first identified by Hollingsworth et al.12 Most of the above mentioned studies were conducted on materials having a significantly greater alloy content than 5657 alloy, where the relatively small size and sparse distribution of second phase particles hinders the process of identifying constituents. EXPERIMENTAL PROCEDURE Material with a composition as given in Table I was examined in the as-direct chill cast, hot rolled and cold rolled conditions, and after thermal treatment of the cast structure. Thermal treatments were terminated by a water quench. Microscopic examination was conducted under various lighting conditions following the application of standard etchants as specified in Table 11. A semi-quantitative electron microprobe X-ray analysis was conducted for Al, Mg, Fe, Cu, Si, Zn, and Ti. RESULTS AND DISCUSSION Microstructure of the As-Cast Material. Particles of second phase material were found to exist inter-dendritically, principally in regions of precipitate free a-Al, as illustrated in Fig. 1. Adjacent to the ingot edge was a region of inverse segregation, resulting in an increased amount of second phase material containing large sized particles which aided in phase identification. Phase Identification. Cast Structure. Five phases besides a-Al and a fine precipitate were identified using optical microscopy and electron microprobe X-ray analysis, as presented in Tables II and III, respectively. FeA13 and Fe2A17 are often found with Fe2A17 forming a sheath around the core of FeAl3, resulting from an incomplete peritectoid reaction. These phases have a nearly identical appearance under white light, although they are easily differentiated under crossed polarizers, as characteristically illustrated in Figs. 2(a) and 2(b), respectively. Microprobe analysis con-

Jan 1, 1970

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6&apos; dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

By J. D. Hunt, R. J. McDonald

It is proposed that extensive fluid motion occurs between the dendrites of a Partially solid casting and it is suggested the A segregates in steel castings are a direct result of this motion. The fluid flow arises because of density differences between liquid ahead of the dendrites and the interdendritic liquid. Experiments are described on a model system investigating this fluid motion. The importance of interdendritic fluid flow is discussed with reference to longitudinal segregation. SERIOUS macro segregation is often found in large killed steel ingots. Among the most common segregates are those known as A and V, Fig. 1. The A segregates are arranged over the surface of cones, the wide parts being at the base of the ingot. The A segregates are pencil like in shape and extend from the columnar into the equiaxed region. The V segregates are distributed over inverted cones but have a less well defined shape. They occur at the center of the ingot. Because of the commercial importance of macro inhomogenities these segregates have attracted wide-scale attention. The segregates contain alloying elements and impurities which depress the freezing temperature and are thus the last liquid to freeze. A number of explanations have been proposed to explain their presence. It has been suggested1&apos;&apos; that the segregates are the result of the equiaxed zone growing towards the columnar region together with the interaction of convection within the bulk liquid. It has also been proposed that the segregates are the result of nucleation and rapid growth ahead of the dendritic front.3 Neither of these explanations is completely satisfactory because A segregates are pencil shaped and are not found as continuous cones. In this paper an alternative mechanism is proposed, and experiments are described on a model system to determine whether the mechanism occurs in practice. It is thought that A and V segregates are not peculiar to steels but should occur in many other large castings. Fluid motion within the bulk liquid region of a casting has been extensively discussed. Little attention has been paid to fluid motion within the partially solid regions. The work415 that has been done has been mainly concerned with the fluid motion which results from the volume contraction on freezing. The volume contraction is used to explain various types of macro segregation. The present authors suggest that in many cases the fluid flow resulting from volume contraction will be small compared with that due to other causes. When the columnar region is growing, the liquid still remaining between the dendrites has a much lower temperature near the ingot walls than at the dendrite tips. The composition of the liquid in contact with solid will vary with temperature. The density of the liquid will thus vary both because of changes in temperature and composition. The layers of different density liquid will give rise to a slow but steady liquid flow through the interdendritic regions. If there is no density change with composition, the temperature gradient within the dendritic region should give rise to a downward flow between the dendrites, shown schematically in Fig. 2. When the liquid density changes appreciably with alloy concentration this motion could either be en-

Jan 1, 1970

By K. Thirumalai

This study forms a part of Bureau of Mines continuing research on thermal fragmentation of rocks. The potential of internal heating techniques for rock fragmentation is discussed. A concept of rock fragmentation with rapid inter¬nal heating of a localized inner volume of rock is advanced The energy required for rock fragmentation is made available by creating a required vol¬ume of localized heating. The fragmentation of rock using the proposed method is analyzed and qualitatively compared with the results of experiments with Charcoal granite, Dresser basalt, and Sioux Quartzite. High frequency dielec¬tric heating below 100 MHz is used in the study as an example to examine the working of the concept. The selection of operating conditions for the experi¬mental heating is explained. Fragmentation of Charcoal granite and Dresser basalt test rock blocks is achieved for localized heating below 550° C. The heated volume required for fragmentation is observed to be less than 2 percent of the test block volume and the electrical energy consumption is in the order of 3.5 to 6 5 kwhr/m3 The method offers a possibility for in situ fragmenta¬tion of rocks, favorable for internal heating. The method is highly dependent on rock properties governing internal heat generation The efficiency of dielectric heating in the experimental study is observed to increase with increasing dielectric loss of the rock material, ranging from about 10 percent in Sioux. Quartzite to about 50 percent in Dresses basalt

Jan 1, 1970

By J. B. Cheatham, M. D. Biggs

This paper presents a systematic method for determining the forces on a simplified roller bit. The kinematics of an actual roller bit drilling in rock is complex; nevertheless, it is desirable to obtain an accurate analytical model.. As a preliminary study, the roller bit is represented here by a simple two-dimensional bit and the rock by a Coulomb plastic material. Results from previous work, plus additional assumptions, are incorporated into a computer program to determine the forces required to move the bit in a specified manner. Example problems are worked by use of this program. By studying similar drilling problems and by supporting laboratory work, one could eventually obtain an accurate analytical model for drilling by an actual roller bit. This could lead to the compilation of a catalog of results that, in turn, would allow selection of the optimum drill bit for any given situation. INTRODUCTION

Jan 1, 1970