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By L. M. Kaas

Production planning techniques, particularly a production scheduling model are proposed for use in taconite mining in Minnesota. Applications of the scheduling model, on a two-year mine plan, which evaluates the equipment involved, are detailed. Data and tables are included. INTRODUCTION Fifty years ago Walter Swart, a mining engineer investigating the Minnesota taconites for the Jackling interests, made this report: "There is no doubt in my mind that this taconite mining is a game worth playing and that it can be played to a successful finish. It seems now only a question of men, money, methods and details."' The prosperous industry envisioned by Swart and other taconite pioneers is today a reality. Its growth has been spurred by technological advances in mining and beneficiation, depletion of natural ore reserves, and improvement of the economic climate. However, the massive problems that were solved to make this development possible are only a foreshadowing of the questions of "men, money, methods and details" that will be encountered in the future. The increasing demands for higher quality taconite pellets have already forced producers to examine better methods of quality control for their operations. THE NEED FOR PRODUCTION SCHEDULING The maintenance of fairly constant crude ore characteristics is of major importance to mill quality control. Through careful mixing of ore from storage bins, the concentrator staff can partially reduce the deviations of the feed analysis from the analysis desired. However, the limited effectiveness of bin mixing systems has caused some mining companies to utilize large capacity blending piles to reduce grade variations. Although the analysis of material being reclaimed from such a pile is relatively uniform, raw materials still must be scheduled from the mine into the pile in such a manner that the average analysis of all material is close to the feed analysis prescribed by the mill. PRODUCTION SCHEDULING MODEL Minnesota taconite mining companies have used three analyses to estimate how a certain ore will react to concentration. These factors are the crude magnetic iron content of the ore, the iron content of the plant concentrate produced from the ore at a standard grind, and the grindability index of the ore. The actual laboratory tests used to determine these factors have been described by Apuli.2 These data are obtained from analysis of diamond drill cores, and are the established criteria used by mine planning engineers to formulate taconite production schedules. Variations in the grade of mine output should be controlled by any production scheduling system. However, to be truly practical, production scheduling methods must also consider many of the less tangible variables that affect mine operation. These include pit layout, available equipment, and ownership of ore leases. The number and scope of the variables inherent in this type of mine planning suggested that a computer simulation could be used to solve the problem. The preparation of information for use with a computer simulation program was the initial phase of this project. Meaningful data was developed from logs of diamond drill cores. Analyses were related to their respective areas of influence by means of mine maps, Fig. 1. The three assay variables and tonnages for each area were punched on cards. In addition to these values, a location code number was punched in the first eight columns of the cards. This code is explained as follows: Column 1 Bench number Column 2 Quadrant location as determined by mine reference lines Columns 3-5 East-west coordinate Columns 6-8 North-south coordinate The heart of any simulation techniques is a well engineered mathematical model. To develop a model for taconite production scheduling, the relationship between the three assay variables had to be established. Because changes in each analysis factor affect the mill circuits in different manners, a weighting system was used to determine the relative im-

Jan 1, 1967

By George L. Gates

The Bureau of Mines studied pressure-buildup data from a number of California gas wells to determine if the reservoir properties calculated from these data correlated with field-observed reservoir properties. Pressure-buildup curves from 24 wells showed distinct changes in slope, indicating changes in permeability of the reservoir rock. Calculated distances from the wells to indicated permeability changes were in fair agreement with distances deter-mined in the field. Pressure-buildup curves from three wells had more than one distinct change in slope, indicating multiple permeability changes. Thus field data supported the theoretical relations used to calculate reservoir properties from pressure-time relations measured in gas wells.

Jan 1, 1967

By G. W. Thomas

Jan 1, 1967

By J. T. McCartney

OPTICAL PROPERTIES of U.S. coals of differing rank have been investigated by the Bureau of Mines, for about 20 years. These investigations have been remade to further the development of an objective basis for petrographic analysis of coal and to add to knowledge of the structure and composition of coal and coal components by determining their optical constants in various regions of the electromagnetic spectrum. Various experimental techniques have been used in these studies, including determination of reflectance from bulk specimens and transmittance of thin and ultrathin sections, interferometry, electron microscopy, and election diffraction. Similar studies leave also been made of graphite, the end product of coal metamorphism. The bureau of Mines conducted the first U.S. investigation of reflectance properties of coal components, laying the foundation for petrographic analysis based on arbitrary reflectance classes and for automated reflectance analysis of coals. Optical constants of coals of differing rank and of graphite have been determined in the ultraviolet-visible-near infrared spectrum. Maxima in the optical constants of graphite were observed in the ultraviolet region and were interpreted to be related to transitions of electrons between the valence and conduction bands. Similar maxima for coals, especially high-rank coals, appeared to be characteristic of the presence of graphitelike layers. A special application of optical theory to absorbing, anisotropic materials like graphite and high-rank coals has been developed. Electron microscopic and electron diffraction studies of coals have revealed various ultrafine structures in coal components and have shown the evolution of an oriented, crystalline graphite structure in high-rank coals.

Jan 1, 1967

Jan 1, 1967

By D. R. E. Whitmore, J. M. Harrison

There are five logical stages in the search for orebodies in virgin territory, namely: (1) reconnaissance inventory of geology, and related investigations; (2) development of broad concepts as a basis for selecting regions of potential mineral deposits; (3) assessment of criteria leading to specific localities within these regions; (4) geo-physical and geochemical studies that will delineate small anomalous areas; and (5) stripping, drilling or other means of locating ore. In addition, the development of new means of extracting mineral resources and the finding of new uses play a vital role in our mineral industry. The continued growth of this industry will be largely governed by our ability to develop or to adapt new concepts and techniques, and to produce a greater number of scientists and engineers. It should always be remembered that more than one-third of Canada's exports are dependent upon our ability to find, develop and economic-ally exploit new orebodies.

Jan 1, 1967

By H. O. McLeod, J. M. Campbell

Data analysis of pentane and hexane adsorption from natural gas in a fixed bed of silica gel shows that constant length mass transfer zones form, the curvature of the adsorption isotherm controls the growth of the mass transfer zone and surface diffusion of molecules inside the silica gel particle controls the mass transfer rate. Curvature of the hexane isothem is more than the curvature of the pentane isotherm. Because of this curvature the hexane adsorption zones reached a constant length. In contrast, the pentane adsorption zones were always increasing in length during each run. A procedure was developed to obtain correct mass transfer coefficients using effluent curve slopes. These transfer roefficients increase with the amount of hydrocarbon adsorbed on the silica gel particle. The characteristic shape of the hexane effluent curves also show that molecular diffusion inside the silica gel particle controls the adsorption rate of pentane and hexane. INTRODUCTION The purpose of this study was to determine the mechanisms that control the dynamic adsorption of hydrocarbons from a natural gas onto silica gel. Before one can deal effectively with multicomponent adsorption, the transfer mechanisms by which a single hydrocarbon component is adsorbed from the gas stream must be defined. Two principal investigations of this system have been published ' and indicate that diffusion through the gas around the particle controls the adsorption rate. Some of the experimental observations in each study either do not support this transfer mechanism or are inconsistent with the mathematical model used in analysis. In this study surface diffusion of molecules inside the particle controls the mass transfer rate of pentane and hexane. This mechanism is indicated by the effluent curve shape for a constant length transfer zone and by the variation of the mass transfer coefficient with concentration of the adsorbed hydrocarbon. THEORY AND DEFINITIONS — MATHEMATICAL MODELS Mathematical solutions for the isothermal adsorption of a trace component from a carrier gas are derived from three relationships: the mass balance or continuity equation, the equilibrium relationship between the gas and solid phases, and a mass transfer rate equation. The transfer rate is proportional to the adsorbate concentration gradient within either the gas or solid phase. Mathematical solutions of these equations usually give the adsorbate concentration as a function of time and distance from the bed inlet. That part of the bed in which the adsorbate concentration changes from a maximum to a minimum value is called the transfer zone. This transfer zone is directly related to a plot of the effluent concentration vs time which has a characteristic S-shape. This general shape is determined by the continuity equation and occurs in many processes of diffusional transfer.

Jan 1, 1967

By S. G. Gibbs, A. B. Neely

Jan 1, 1967

Over half of the molten aluminium produced at the 52,000 tons/ year eapacity plant operated by Comalco Aluminium (Bell Bay) Limited in Tasmania is cast into saleable produets by the direct chill process. Considering the importance of direct chill casting to the aluminium industry it is surprising that so little published literature on the subject is available, although Easton (1947), Smart (1954), and Uppert (1940, 1944, 1945) have contributed much toward lifting the veil of secrecy surrounding the process.The direct chill, or D.C. process as it is commonly called when related to aluminium, consists basically of feeding molten aluminium or its alloys into; water-cooled mould from the bottom of which solid aluminium is continuously extracted. Although the casting procedure is continuous in principle, the equipment is normally operated in an intermittent manner. Castings up to 20 ft long are formed during a cycle. At the end of the cycle casting is stopped and the pit into which thc castings are dropped is cleared before a new cycle commences. Depending on the size of the casting in relation to the cross sectional area of the pit and the support mechanism (commonly a hydraulic ram), 'drops' of up to 15 tons are not uncommon. This method of D.C. casting IS termed vertical D.C. casting and is the one most commonly employed in the aluminium industry.Horizontal casting has come more to the fore in recent years with the casting being extracted from the mould in the horizontal plane and is a truly continuous casting method since flying saws can be simply used to cut the continuously cast shape into required lengths as it emerges from the mould...

Jan 1, 1967

By W. Gordon Muir

This paper deals with the exploration, development and current operations of the salt mine at Goderich, Ontario operated by the Sifto Salt Division of Domtar Chemical Limited. The rock salt is obtained from a bed 1,760 feet below the surface, 75 feet thick, extending under Lake Huron. Annual production is in excess of one million tons. Large mobile equipment is used. Details of this equipment, as well as the shaft layout, which permits the equipment to be lowered underground with a minimum of trouble are outlined. Mining, crushing and screening procedures' are rev1ewed. Reference is also made to productivity salt distribution and uses.

Jan 1, 1967

By John Sasadi

The mining industry depends upon inexpensive water transportation. Today, large quantities of mined products are transported by ships over oceans, from continents to continents, over lakes and waterways to the ultimate users. Sometimes, the routes these Bulk Carriers travel cover only a few hundred miles, sometimes thousands of miles halfway around the world. Most of the products of the mining industries are relatively inexpensive. A significant portion of their cost to the ultimate users are in the cost of transportation and not in loading and unloading these commodities at the ports of origination or destination. So far, the industry has produced very efficient loading and un- loading installations, but has very little influence over marine transportation or the design of the vessels themselves. Very little was ever published dealing with integrated transportation systems properly correlating all phases of the operation; namely, loading, marine transportation and unloading bulk materials.

Jan 1, 1967

By Thornton L. Neathery

Geologic investigation of a mineralized zone in eastern Alabama indicates that large quantities of talc and soapstone are scattered over a wide area close to the surface. Laboratory experiments show that this material may be upgraded to a high-quality talc. A market survey indicates that the talc deposits may be of current and long-range interest. The anthophyllite asbestos which is associated with the talc does not appear to occur in sufficient quantities to be considered as a primary commercial source.

Jan 1, 1967

By P. T. Allsman

INTRODUCTION The honor of being the recipient of the Mining Society's Daniel C. Jackling Award for 1966 imposes on me the responsibility to search for the subject that I would be best qualified to discuss. It seems that my experience in the mineral industry — nearly 15 years in private and 30 years in public employment — should uniquely qualify me to comment upon the relationships between the mining industry, mineral engineering as a profession, and government, and the changing economic, technologic, political and social changes that dictate their relationships. Such conditions, the increasing knowledge of the world mineral resource base, the greater demands of an expanding population with a rising standard of living, shall be evaluated with respect to our profession — mineral engineering. In all of these forty or so years, I have been in close touch with many phases of the mineral and energy resource industries, especially those of the United States. Particularly during the past 10 years, I have had a ringside seat at the "goings on" in Washington. During all of this period I have observed and analyzed many of the problems of the industry and its relations with the government. During the past few years, I have had increased opportunity for doing research and have found a need to learn something about the mathematical techniques that are undergoing such a revival since electronic computers were developed. One of these techniques is multivariate analysis, which is a system for correlating a large number of complex variables. By applying this technique to the seemingly chaotic present-day situation, there emerges a course of steady improvement in the minerals resource industries that wars, depressions, and political strife have failed to obstruct for long. In short, I advocate a need for new concepts in mineral engineering to cope with the changes, pos- sibly adding many more specialized areas on one end of the spectrum, and broad engineer-generalist approaches at the other. The meeting place shall be where the intricate mineral resource problems at the frontier of knowledge merge into the socio-techno-logical problems of the world. HISTORICAL INVOLVEMENT OF GOVERNMENT IN MINERAL RESOURCE PROBLEMS Involvement of government in mineral resource problems undoubtedly is as old as government itself. But passage of the Mining Act of 1866, superseded by the Act of 1872, was the first major entry of our Federal Government into the problems of mining. Passage of the law was necessary to resolve many conflicting claims and disputes in mining. The General Mining Law of 1872 and the Mineral Leasing Laws of 1920 apply to millions of acres of public lands and to certain privately owned land on which the mineral rights have been reserved to the Federal Government. The extensive involvement of government in the mineral industry business today often comes as a shock to the mineral engineer who has begun to climb the ladder to the top in his company. He is often poorly prepared to cope with the situation and becomes frustrated and even hostile. Better knowledge of the role of government perhaps would ease his situation. In our political system, private industry is responsible for producing minerals. To make certain that the production is adequate for a peace-time economy, and to guarantee the Nation's security in an emergency, the Federal Government finds it expedient to develop policy and engage in regulatory, educational, and research activities. A few examples will illustrate the varied role of government in relation to mineral problems. In varying degrees many agencies of the Executive Branch of Government have responsibilities that influence the functioning of the mineral and energy industries. In addition, of course, Congress, the Judiciary, and State and local governments exercise great influence. The Department of the Interior is primarily responsible for activities to promote the development and conservation of mineral and fuel resources, and the

Jan 1, 1967

By Robert C. Bates

Variations in water percolation rates through saturated cohesionless hydraulic backfill (mill tailings) have been studied in relation to the many physical aspects of the system to determine the most important factors in causing these variations. A multivariable least-squares regression analysis of 135 separate tests shows that a reliable estimate of the water percolation rate through typical hydraulic backfill can be made if the bulk density (unit weight), specific gravity, and grain-size distribution are known or can be estimated. Equations for predicting percolation rate, coefficient of permeability, and seepage velocity are developed both for the range of data analyzed and for extrapolation. The prediction equations for use within the range of data studied are quite accurate, while the ones developed for extrapolation are less accurate but still give reasonable approximations of flow rates. The equations given are valid for cohesionless materials that are free of clays and micas, exemplified by classified mill tailings. The equation developed for predicting percolation rates is as follows: 1nP20 = 11.39147 + 2.853422 1n(VR X D10) + 0.1747436 VR X Cu -178.8039 D10 X D50 + 311.7034 (DSO )3, (1) where P20 = percolation rate, inches per hour at 20° C; correction factors for other temperatures are given in the text, VR = void ratio, dimensionless, D10 = effective size (diameter in millimeters of the 10-percent-finer grain size), Cu = coefficient of uniformity (ratio of the diameter of the 60-percent-finer grain size over D10), D50 = average size (diameter in millimeters of the 50-percent-finer grain size), and In = natural logarithm (log to the base e). The prediction equation for percolation rate is rather complicated, so for practical use a nomograph that simplifies the solution of the prediction equation was developed.

Jan 1, 1967

By K. Leutwyler

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

Jan 1, 1967

By C. N. J. Wagner, E. N. Aqua

The bee alloys of the terminal solid solution of rhenium in niobium were investigated by X-ray diffraclion methods. The analysis of the broadening of the powder pattern peaks from the niobium-rich alloys, cold-worked by filing, showed evidence for faulting on (211) planes. The alloys with larger rhenium concentrations were brittle, and fractured when filed. The analysis of the shapes of the diffraction profiles from powders produced by hammering with steel plates) of these brittle alloys indicated that the broadening was due predominantly to platelets bounded by clibe planes. This result was consistent with the Laue patterns from single-cleazlage facets which showed evidence for clearage fracture on {100} planes. The influence of faulting on the mechanical properties of face-centered cubic (fcc) metals and alloys, i.e., how faulting affects the various dislocation configurations in fcc metals, is well-known.' The important question is whether or not faulting occurs in body-centered cubic (bcc) metals and alloys, and, furthermore, if faulting does occur, to what extent it affects the mechanical properties. Theoretical calculations indicate that the stacking-fault energy is rather high in most bcc metals.2 The results of sev-eral studies using transmission electron microscopy have indicated that faults are present in well-annealed and lightly deformed bcc metals and alloys, such as tungsten,3 vanadium,4 and Mo-Re alloys.5,6 These faults, as have been observed, may be stabilized by the presence of interstitial (C,N,O) atom segregation to the extended dislocations. In addition, there is considerable X-ray diffraction evidence for faulting in bee metals,7-8 using the same techniques that were successful for the study of faulting in fee metals and alloys.7 This X-ray diffraction method is currently the only technique applicable for the investigation of faulting in metals with high stacking fault energies, i.e., when severe amounts of deformation are required to produce sufficient amounts of faulting to be detectable by X-rays. The thinned films of heavily deformed metals will become opaque in the electron microscope due to the high dislocation densities present. In a previous investigation of faulting8 in bee metals of group Vb and VIb, the authors observed that niobium was ductile when filed at room temperature, and showed the highest density of faults on the (112) family of planes. A niobium-base alloy system was therefore chosen to study the effect of alloying on the occurrence of faults in a bcc alloy. There is a large range of terminal solid solubility of rhenium in the alloys of the bee refractory metals. All of the Group VIb-rhenium alloys, i.e., Cr-Re, Mo-Re, and W-Re, exhibit solid solution hardening without loss of ductility.9 In fact, the ductility reaches a maximum for alloys with compositions near to the limits of solubility. This enhanced ductility has been attributed to the lowering of the stacking-fault energy in the alloy; i.e., the increased amounts of twinning provide an additional mode of deformation, resulting in the observed high ductility.' Because of this demonstrated effect of rhenium in bee alloys, it was decided to study a series of alloys of Nb-Re. Using the same X-ray diffraction methods as described in the previous investigation,' one is able to identify the possible causes of broadening of the powder pattern peaks, e.q., particle size, microstrains, stacking faults, and/or twin faults. The separation of these various contributions to the measured peak shape is accomplished by the Warren-Averbach analysis.7 I) EXPERIMENTAL PROCEDURE A series of seven bee solid solution alloys containing from 2.5 to 21.5 at. pct Re (remainder niobium) were prepared at the General Electric Research Laboratory. Buttons, weighing 25 g, were alloyed from electron-beam-melted niobium chips and random rhenium sheet by arc melting in a water-cooled copper crucible, under an argon atmosphere. The buttons were inverted and completely remelted to promote homogenization. The nominal alloy compositions are listed in Table I. Samples of the cold-worked alloys were obtained by filing to produce a powder for the X-ray study. Alloys too brittle to be filed were hammered with steel plates. The resultant filings or brittle impactings were screened through 150-mesh classifiers and compacted to the required shape for the diffractometer holder. The X-ray diffraction peaks were automatically recorded by fixed time counting at uniform 28 intervals, or by continuous registration with a ratemeter. In all cases, the (110)-(220) and (200)-(400) pairs of peaks and the (211), (310), (222), and (321) reflections were measured on a GE-XRD5 diffractometer using CuKa radiation with nickel filter or MoKct radiation and a LiF monochromator in the diffracted beam. The first part of the data reduction, completed with the aid of a series of programmed computations,10 was the analytical resolution of the Kol component of the diffraction profile. Subsequent computations were then made with reference only to the resolved Kol peak shape. These included the measurement of the

Jan 1, 1967

By Robert G. Pinkerton

Boyles Bros. Drilling Co. and Gibbons and Reed Company, both of Salt Lake City, Utah, have successfully combined into two joint ventures on the San Juan-Chama project of the U. S. Bureau of Reclamation. The Azotea Tunnel is 12.7 miles in length; the inlet portal is on the Navajo River in Archileta County, Colorado, and the outlet portal is in New Mexico, about 10 miles south of the state border. The Oso Tunnel lies immediately to the north of the Azotea Tunnel and discharges water directly into it. We are presently driving both tunnels with mechanical boring machines from their portals at the Navajo River. Both tunnels are circular, fully concrete lined. The Azotea Tunnel has a finished diameter of 10 ft. 11 inches while the Oso Tunnel is 8 ft 7 inches in diameter. Both tunnels are supported with circular, structural steel rings as required by ground conditions. In good ground rock bolts and steel roof plates are used.

Jan 1, 1967

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 K. H. Coats, M. H. Terhune

Analysis and example applications have been performed to compare the accuracy and computing speed of alternating-direction explicit and implicit procedures (ADEP and ADIP) in numerical solution of reservoir fluid flow problems. ADIP yields significantly greater accuracy and requires about 60 per cent more computing time than ADEP, not 300 or 500 per cent more as reported elsewhere. l,2 INTRODUCTION Several recent papers 1-3 discuss an alternating-direction explicit difference approximation (ADEP) to the diffusion equation. Example applications of ADEP and ADIP4 were reported to support conclusions that ADEP is comparable in accuracy to ADIP and requires one-fifth to one-third the computing time of ADIP. Applications of ADEP in calculation of two-phase flow in reservoirs was also proposed. 3 This study was performed to compare further the relative merits of ADEP and ADIP in simulation of two-dimensional flow of one and two fluid phases in reservoirs. Since two-phase flow equations are often essentially elliptic rather than parabolic, the efficiency of ADEP in solving the elliptic equation was also examined.

Jan 1, 1967

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

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

Jan 1, 1967