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By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By Persifor Frazer

There is always a difficulty in assigning limits to the scope of a science or art, and among the dificulties of that kind besetting practical or stratigraphical geology is that of determining what kinds of natural objects shall be considered as the goals of its search. The term mineral, in its broader sense, includes every solid, liquid, or

By C. H. Mathewson

MICROSCOPIC rnetallography has been exploited quite well enough to bring about a very general understanding that the typical metal or alloy is composed of minute crystalline particles blended into a coherent microstructural mosaic. One does not have to be a specialist in metallography to realize that the properties of such an aggregate are essentially a summation in appropriate form of individual effects derived from the shape, size, placement or orientation and cohesive characteristics of the component particles. It is clearly of great importance to consider the various forms of discontinuity which may occur at the boundaries between these crystalline particles. When a number of particles each possessing the same orderly arrangement of atoms are brought together into a close-fitting system of purely haphazard contacts, not unlike a handful of snowflakes compacted into a snowball, the particles are said to possess random orientation. There are no generally accepted views concerning the arrangement of the atomis or the constitutional reaction between atoms where one crystal meets another, but these contact regions are characterized by strength rather than weakness and it is customary to require the presence of many rather than few boundaries in preparing metal for useful service. Under certain circumstances all of the particles in a metal may be nearly alike in orientation. Other general tendencies of orientation may be associated with particular forms of mechanical and thermal treatment. In contrast with these cases of fortuitous or statistical diversity of orientation, we often find adjacent particles united along a plane which possesses a grouping of atoms belonging equally well to both structures. This, of course, determines a fixed relationship between the two orientations and it is always possible to derive one from the other by some form of rotation or reflection prescribed by the symmetry of the crystal structure under consideration. Particles united in this manner are known as twin crystals although the term refers to the form of association rather than the number of individuals concerned.

By R. W. Snyder, H. J. Ramey

This paper presents the results of applying the Buckley-Leverett' displacement theory to petroleum reservoirs consisting of a finite number of layers. The layers are assumed to communicate only in the wellbores, and the reservoir may be represented as a linear system. Most previous investigations of this nature were limited by assumptions and by inconsistent calculation techniques. This study improves on previous work by applying the Buckley-Lev-erett displacement theory to a noncommunicating layered system where permeability, porosity, initial saturation, residual saturation and relative permeability vary from layer to layer in a logical and consistent manner. Gravity and capillary-pressure effects are neglected. A modification of the Higgins-Leighton calculation method was used in this study. Waterflood predictions were made with all properties varying, and then with only permeability varying using several inability ratios. These results were compared with the Stiles and Dykstra-Parsons predictions. It is shown that the latter methods generally give poor values for the breakthrough recovery and pessimistic predictions for the performance after breakthrough. Similar results were obtained for a gas-displacement case. lNTRODUCTION Field experience with immiscible displacement usually shows constant producing conditions until breakthrough of the displacing fluid. Then oil production continues at increasing displacing-to-displaced fluid ratios until the economic limit is reached. Three different ideal mechanisms are known that will produce this behavior: (1) relative permeability effects as described by Buckley-Leverett frontal advance theory,' (2) vertical stratification as considered by Stiles,2 Dykstra and Parsons5 and others and (3) different path lengths involved in areal (two-dimensional) flow between wells as described by Dyes et al.4 Without question, a combination of these factors modified by formation heterogeneity and other known and unknown factors actually does control the behavior of real systems. This paper presents results of an investigation of certain factors that should affect performance but which have received little attention to date. In 1944, Law5 demonstrated that porosity and perme- ability are often found to have normal and logarithmic-normal distributions, respectively. throughout cored intervals in natural formations. This led to the concept of the noncommunicating, multilayered reservoir model for immiscible displacement. This model assumes that the reservoir is composed of a number of layers that communicate only at the wellbores. Each layer is individually homogeneous, but may be different from every other layer. Stiles' presented one of the earliest applications of this model to waterflood performance. In addition, Stiles assumed that the initial saturations and relative permeabilities were the same for each layer, porosity was the same. displacement was piston-like, fluids were incompressible and injection into each layer was proportional to that layer's permeability capacity (permeability-thickness product). The last assumption would be true if the mobility ratio for the displacement were unity.21 Dykstra and Parsons" used the same model as Stiles, but rigorously included mobility ratios other than unity for piston-like displacement. Dykstra and Parsons used their general result to produce charts for log-normal permeability distributions between layers. Similarly, Muskat6 Pub1ished analytical solutions for linear and exponential permeability distributions. In 1959, Roberts' described a scheme for calculating water-drive performance for the noncommunicating, layered reservoir model which considered two-phase flow in the displaced region. Roberts used the same model and assumed that the injection rate into a layer was proportional to that layer's permeability capacity, but that flood front locations could be evaluated from the Dykstra-Parsons results. These assumptions are inconsistent, and a material balance cannot be maintained except for a mobility ratio of unity. At the same time, Kufus and Lynch8 coupled Buckley-Leverett displacement theory with the layered model to provide an improvement of the Dykstra-Parsons method that was consistent. In 1960, Higgins and Leighton9 resented a numerical method for calculating waterflood performance also considering two-phase flow in the displaced region. The result was used to investigate variation in absolute permeability and oil viscosity. An excellent, detailed history of using the noncomrnunicating, layered reservoir model was presented by Nielsen.'" The preceding techniques (and many related ones) were similar in that differences in initial saturations, residual saturations and relative permeabilities from layer to layer were neglected. It is well known that the irreducible water saturation is an important function of absolute permeability. Calhoun11 showed that the irreducible water saturation

By A. M. Skov, L. F. Elkins

Inclusion of anisotropic permeability in mathematical analysis of pressure transients observed during development of the huge Spraberry field indicates a major fracture trend which is in good agreement with that observed by fluid-injection tests spread over a 12- by 17-mile area. Delineation of this trend is important in selecting a pattern of injection for the pending large-scale water flooding in this field. Determination of reservoir parameters yielding best agreement between calculated pressures and observed reservoir pressures in newly completed wells was made using an IBM 650 computer. INTRODUCTION The Spraberry field covering 400,000 acres is a tight sand of less than 1-md permeability cut by an extensive system of vertical fractures. Primary recovery dominated by capillary retention of oil in the fractured sand matrix blocks is less than 10 per cent of oil in place. Strong forces of capillary imbibition of water into the sand, coupled with water flow under dynamic pressure gradient, indicate considerable increase in oil recovery can be achieved through water flooding. Best results will occur if the pattern of water injection is selected to force the water flow across the grain of the major fracture system. Existence of an oriented vertical fracture system in the Spraberry, observed first in cores, was highlighted more recently by the 144-fold contrast in permeability along and at right angles to the major fracture trend required to match relative water breakthrough times in Humble Oil & Refining Co.'s waterflood test there. Spraberry operators since have conducted two gas-injection tracer tests for further areal confirmation of the fracture trend. Re-analysis of early reservoir pressure transients for evidence of anisotropic permeability has permitted many more local determinations of major fracture trend without resort to further field tests. This paper is limited to updating analysis of reservoir pressure transients to include anisotropic permeability as a test for orientation of the major fracture trend in the Spraberry. The reader is referred to Refs. 1 and 2 for information about general Spraberry reservoir performance and to Refs. 3 and 4 for information about significance of fracture orientation in selection of the injection-well pattern for water flooding the Spraberry. RESERVOIR PRESSURE DATA—DRIVER AREA During early development of the Spraberry Driver area, Sohio Petroleum Co. made the extra effort to measure the initial pressure in each of the 71 wells in a 5-mile-long area immediately after completion. Progressively greater reductions in pressure ranging up to 400 psi were observed throughout the six-month development period. Detailed data are presented in Ref. 1. Since the reservoir oil was undersaturated some 300 psi initially, early reservoir performance involving 55 new well pressures is subject to analysis as flow of a single compressible fluid in a porous media. Assumption of uniform permeability in all directions yielded good agreement between calculated pressures and observed pressures of these wells in the earlier study,' but subsequent, additional, mathematical development to include anisotropic permeability in the transient pressure considerations and present availability of electronic computers to perform the much more extensive arithmetical calculations now yield even better agreement. The previous analysis, assuming uniform permeability, consisted essentially of calculating pressure reduction expanding circularly around each producing well and summing these effects at the time and location of each newly completed well for comparison with the measured pressure reduction. Permeability, effective fluid and rock compressibility, and permeability X thickness were varied until the best match with measured pressures was obtained. The present analysis, assuming anisotropic

A Colloquium and General Meeting were held on 17th March 1971, the theme being 'Future trends in steel production'. Mr V. C. Robinson (President) was in the Chair. The Colloquium was attended by 121 delegates and was opened by the President at 10 a.m. OBITUARIES THE PRESIDENT: 'It is my sad duty to announce the death of the following: F. O. Read, Fellow, who joined the Institute in 1957 and passed away on 13th January, 1971. P. G. M. May, Member, who joined the Institute in 1969 and passed away on 10th August, 1970. R. J. J. Rademeyer, Life Fellow, who joined the Institute in 1942 and passed away on 23rd September, 1970. As a mark of respect to the memory of the deceased and in sympathy with the bereaved I would ask you all to rise and observe a few moments silence. CONFIRMATION OF MINUTES THE PRESIDENT: 'May we confirm the minutes of the monthly general meeting held on 21st October and 18th November, 1970, as published in the Journal'. Agreed. MEMBERSHIP THE PRESIDENT: 'I have much pleasure in announcing that the names of the undermentioned candidates, having been published in accordance with ByLaw 5.2.2, Council has elected them to membership of the Institute in the following grades: FELLOWS: Romain August Lathioor, Paolo Piga, Renato Ribacchi, Willem Frederick Jacobus Smith, Matthew Churchill, Thomas Anthony James Braithwaite, Hugh Patrick Hart, Eleanor Innocentius Muller, David Alton Smith. MEMBERS: Douglas Adendorff, Petrus Jacob du Plooy, James Valentine Grant Middleton, Karl Anders Ullerstam, Josephus Theodorus Johannes van Wyk, Frank Douglas Abbott. GRADUATES: David Mervyn Gilbart-Smith, John Philip Wilcocks Bennie, Hendrik Theunis Burger, Johann Wilhelm Coetzee, Johannes Stephanus StOols, Leon van Tonder, Brian George Harvey, John Kennedy McLean. ASSOCIATES Richard Cyril Lee Stoyell, Terrence Brian Gouws, Alister Rodney Frederick MacDonald. STUDENTS: Andries Groenewald, Christiaan Johannes Hattingh, William Hendrik Hofmeyr, Stanley Thomas Vincent. I welcome the new members to the Institute and congratulate them on their election. COLLOQUIUM The President welcomed everyone present and mentioned that this was the first of the Colloquia which are to replace the Institute's monthly meetings. He stressed that discussion at Colloquia would be completely informal and would not be recorded unless the contributor requested publication. In conclusion, he thanked the organising committee, the authors and the contributors, and introduced the author of the first paper. The following papers were presented:- 'The future development of the Iron and Steel Industry' by J. P. Coetzee (Published in the Journal March 1971). Among those who contributed to the paper were Dr Bleloch, Dr K. Gebhard, Dr Way and Professor Müller. The main point made by Dr Bleloch related to the reserves of coking coal and of coal for power generation this in country and he deduced that in South Africa we are critically short of coking coal. On the basis that 4 million tons per year of coking coal are consumed for our present steel production, over 16 million tons would be required to meet the anticipated expansion in steel output by A.D. 2000. This must be set against the grim forecast made by the Coal Advisory Board in 1967 that our national reserves of coking coal will be exhausted before A.D. 2000. This gives tremendous significance to the development work presently being carried out by Iscor on alternative methods for coke production. On the other hand the blast furnace may have to be replaced by an alternative process for the reduction of iron ores, e.g., the use of rotary kilns followed by electric arc smelting. Dr Bleloch also expressed grave forebodings about the reserves of bituminous coal, pointing out that with present methods of mining the recoverable coal in any given reserve is in general only 50 per cent of that reserve. He stated that in the past seventy years great quantities of coal have been forever placed beyond the reach of mining by being undermined by extraction of lower seams or lost by being burned. A final point made by Dr Bleloch was the fast rise in the capital investment in a fully integrated steel plant, the figure having risen in the past decade from just over R200 to R350 per ton of finished steel per annum. Dr Gebhard spoke of the direct reduction processes for iron making pointing out the difficulties of securing a high percentage of reduction and the relatively high cost of smelting in electric arc furnaces. As an alternative he suggested briquetting the high carbon sponge iron

By J. P. Proulx, Richard O’Meara, Ruilin Yang

A blast optimization project was carried out at an Open Pit Metal Mine using the Multiple Blasthole Fragmentation (MBF) Model and the Multiple Seed Waveform (MSW) blast vibration model. The aim of the project was to optimize rock fragmentation of the ore blasts to significantly increase metal recoveries while keeping the blast vibration levels at the highwall under control. The project also examined the blasts in the waste rock using the Fragmentation model to expand the blast pattern and select economical explosives for drill and blast cost savings while minimizing any adverse effect on the dig rates. Two sets of near field signature blasthole tests were conducted in both hard ore and relatively soft waste rock. The information from the near-field signature blasthole vibration was used as input to both the MBF and MSW models, as site specific geological information interacting with blasting. The implementation of the full blast design is also input to the MBF and MSW models. A production blast for each rock type was monitored for blast vibration and rock fragmentation. The full blast information and the blast results are used to calibrate and validate the models. The Fragmentation and Vibration model were established for the two rock types at the mine. At each site the Fragmentation modeling was conducted in parallel to the Vibration modeling to ensure blast vibrations were under control while the rock fragmentation was improved. The Fragmentation MBF and MSW are each an integral part of the blast optimization tool. Various scenarios using different explosives, hole delays and blast patterns were modeled for rock fragmentation and blast vibration. The recommendations from the modeling project were to be field trialed at the mine. The implementation of the recommendations was expected to help the mine significantly in terms of the mining economics, and high wall stability and safety.

By W. S. Ayres

The boiler from which these stay-bolts have just been obtained was that of the locomotive Catasauqtia, Lehigh Valley Railroad, built at the company's shops, South Easton, Pa., in 1864. The iron is Lowmoor, and has been in use nearly ten years. The stay-bolts have become highly crystallized from some cause, and are very brittle, only requiring three blows of an ordinary machinist's hammer to break them. On the other hand, when annealed they are remarkably tough, as shown by the doubled sample. The majority of the broken bolts were found to be along the curve of the shell from a to c, Fig. 6. All of them were broken just inside the shell, and in no case next the fire-box. The fractures seem to have been of slow procedure, beginning at the top of the bolt, gradually working deeper and deeper until the pressure of steam overcame the tenacity of the remaining parts. Unequal contraction and expansion of the parts of the boiler seems in this case to be the only existing cause for a fracture. We cannot, from the data obtained, prove to an absolute certainty the manner in which the combined forces generated by the unequal contraction and expansion of the parts have arrived at their resultant work ; but we can, from these data and from existing circumstances, arrive at what seems to be a fair supposition, and thus at least anticipate the truth. The contraction and expansion in locomotive boilers has a large range between its extremes, and is very variable, both with reference to time and to their component parts. The shell and fire-box do not, perhaps, at any time, contract and expand at the same rate, nor proportionally; but, on the contrary, owing to the great changes in temperature that take place both in the atmosphere around the shell, and in the fire in the fire-box, their condition is often changed suddenly, and widely from that which they just previously had. This racking tendency produces strains in the different parts, and it is fair to suppose that the continual motion of the two

Today’s world relies upon advanced green technologies that are made of critical elements with unique properties. Examples include rare earth elements (REEs) that are critical in the manufacturing of wind turbines and electric/hybrid vehicle batteries, key components of a greener future that face supply uncertainty and near zero recycling. To tackle their supply challenges, activities have begun for urban mining from waste electrical and electronic equipment (WEEE) that contain considerable amount of REEs, but their current level of recycling is less than 1%. Current recycling practices use either pyrometallurgy, which is energy intensive, or hydrometallurgy that utilizes large volumes of acids and solvents and generates large volumes of hazardous waste. In this study, we developed a novel and sustainable process to recycle REEs from WEEE, NiMH batteries in particular. The developed process relies on supercritical fluid extraction (SCFE) utilizing CO2 as the solvent, which is abundant, safe, cost effective, and inert. The effect of seven operating parameters, namely temperature, pressure, residence time, sample to chelating agent ratio, agitation rate, complex formulation, and methanol addition on REE extraction efficiency was investigated, and optimum operating conditions were determined. This work is the first to utilize a very efficient and safe process that runs at low temperature to extract metals from postconsumer products with minimum hazardous waste generation, while offering about 90% leaching efficiency for REEs. We expect our process to find widespread applicability in urban mining of REEs using green chemistry.

By Thomas H. Dubaniewicz, Gerald R. Cucci, Gregory M. Green, Kenneth L. Cashdollar

New types of industrial instruments use fiber-coupled law energy to power remote serum. Fiber-optic based instruments are useful in classified (hazardous) locations found in many industrial plants because the fiber provides a natural barrier against accidental electrical discharge into potentially explosive atmospheres. However, current safety standards do not cover the use of laser-powered fiber-optic instruments in potentially explosive environments such as found in coal mines. The U. S. Bureau of Mines began an investigation of laser-powered fiber-optic instruments in explosive atmospheres in support of the standards-making process. A commercial fiber-optic interface system, modified to sin relate several worst-case operating conditions, ignited explosive hydrogen-air mixtures. Worst-am simulations consisted of disabling a safety shutoff feature, operating the laser at significantly higher powers than intended for normal operations, and cleaving fiber-optic connections to direct laser energy onto selected absorptive materials. At the highest power level available, the fiber-optic interface system did not ignite selected methane-air mixtures. The obtained data should prove useful in establishing appropriate safety standards.

By J. A. Drummond

The duties and efficiencies of a number of main and auxiliary fans were determined by standard and thermal methods. Some observations on the effect of water and dirt accumulation on fan performance were made.

By J. B. Cheatham

Applications of the mathematical theory of plasticity promises to lead to the solution of many drilling and rock mechanics problems. ,Because of mathematical considerations, the inelastic behavior of rock has frequently been represented by a perfectly plastic model in conjunction with a yield criteria of the Coulomb or Mohr type. The totality of all stress states for which a solid ceases to behave elastically can be represented as a limit surface in stress space. ,Probing of such limit surfaces indicates details of strain hardening which are not provided by the standard triaxial testing procedure. Probing tests of the limit surfaces have been performed on Cardova Cream limestone to provide data for extending plasticity theory to cover situations in which consolidation and strain hardening are present. Test results indicate that this highly porous limestone undergoes a permanent volume decrease when it is subjected to hydrostatic pressures in excess of 3,500 psi. A virgin sample tested under a confining pressure of 1,500 psi has a yield strength of 1,700 psi; however, if the sample is subjected to a consolidation pressure of 5,000 psi, before testing at 1,500 psi, the yield strength is raised to 2,300 psi. Thus, both consolidation and strain hardening are important considerations in describing the mechanical behavior of this limestone. Tests conducted with the axis of the core having different orientations indicate that this rock is also anisotropic. Portions of the initial and subsequent limit surfaces are determined for samples loaded either perpendicular or parallel to the bedding planes. INTRODUCTION Previous experimental work in rock mechanics indicates that no mathematically tractable constitutive theory is inclusive enough to describe the mechanical behavior exhibited by all types of rocks under all conditions of stress and temperature. Indeed, the type of deformation encountered in a single type of rock is known to depend upon the stress and temperature conditions in the rock during deformation.l-5 Certain rocks and minerals, notably those minerals composed of ionic salts, have been shown to exhibit plastic deformation when tested under conditions of high confining pressure.2 Since the mathematical theory of plasticity provides simplifications over the theory of elasticity in certain types of problems, such as those in which limit analysis can be applied, it is of interest to know under what conditions plasticity theory may be applied to rock mechanics problems. The following factors determine the nature of the deformation a particular specimen will undergo: (1) the microscopic structure of the rock, i.e., the structure visible under an optical microscope, including number of phases, porosity, distribution of phases, (2) the mineralogical structure of the solid phases, (3) the conditions of stress and the rate of change of stress and (4) the temperature. Extensive experiments on Yule marble, Carthage marble, Solenhofen limestone and other calcerous rocks indicate that these relatively nonporous rocks deform plastically under certain conditions of loading, and creep under other conditions of loading.l-3 This study is concerned with the behavior of Cordova Cream limestone (Austin chalk) which is also composed almost entirely of calcite and thus has the same mineralogical composition but, because of a rather large porosity, it possesses a different microscopic structure. This investigation was undertaken to learn if Cordova Cream limestone deforms plastically despite the embrittling effect of the pore spaces, and to provide data which can be used to determine whether the mathematical theory of plasticity can describe the mechanical behavior of Cordova Cream limestone. A brief discussion is given of some of the underlying principles of plasticity theory concerning stress space and limit surfaces. Strain hardening is defined and a discussion is given of how the mechanical behavior of a material can depend on the previous history of the loading. This is followed by a description of the experimental procedures

By K. H. Ribe

Water often enters an oil reservoir during completion or workover operations on a well and forms a partial "water block" to oil production. A mathematical study of radial two-phase flow, neglecting capillary effects, has been employed to study the formation of such a water block and subsequent re-moval by production from the well. The effects of reduced oil permeability about the well on the well productivity were studied. The fluid saturation distributions about the well during formation and removal of the water block have also been computed. Several relative permeability relations and viscosity ratios were employed. If water has invaded the formation, its influence through relative permeability effects alone can cause the following. 1. Oil productivity will be depressed for extended periods after production is resumed and will build up only gradually as the water is removed. 2. Oil injected for treatment of water blocking will delay rather than promote restoration of full well productivity by enlarging the region invaded by water. Thus, unless the specific action of chemicals contained in the oil is needed, oil injection appears undesirable. INTRODUCTION During oilwell workover operations, water may enter the oil-bearing formation from the wellbore. When production is resumed, oil must flow through the region invaded by this water. The presence of this region can cause both well productivity and oil production rate to be low and oil to be produced with high water-oil ratio for some time after production is initiated. This situation is sometimes described as a water block. The introduction of water into the formation may result in other actions which also lead to reduction in well productivity and which are also usually included in the connotation of the broad term, water block. Often considered, for example, are the possibilities of clay swelling by contact with fresh water and the formation of emulsions with the formation oil. If it is suspected that such specific actions have taken place, remedial treatments are undertaken which usually involve the injection of chemicals in oil. Since the introduction of water, even in the absence of specific interactions with the formation or oil, will cause a temporary water block (which might be misinterpreted as evidence of a more severe situation), it is of importance to evaluate the magnitude and duration of this blocking which results purely from the reduction in relative permeability to oil in the vicinity of the wellbore. It is also of interest to evaluate the effect of oil injection on the productivity of a well blocked by water in this manner. Inasmuch as this unfavorable condition may persist for some time, it may lead to premature condemnation of a workover or premature abandonment of a potentially productive pay zone. A quantitative evaluation of the influence of water entry on the oil productivity through changes in relative permeability was made by solving a radial form of the Buckley-Leverett equation. The distribution of water saturation around the wellbore during the entry of water was calculated and was followed by a similar calculation of the saturation distribution during the period of resuming production. At any stage in the removal of the invading water, knowledge of the distribution of its saturation permitted calculating the attendant loss in oil productivity. The influence of the shape of the relative permeability relationships was also evaluated by carrying out the calculations for two hypothetical cases. Further, the effect of the oil-water viscosity ratio was examined by repeating the calculations, for several ratios of unity and greater, with the same relative permeabilities. Fi-nally, results are presented to show how the length of time a well must be swabbed to resume production depends on the length of time it has been subjected to invasion by water. STATEMENT OF THEORY Differential Equations Water is assumed to enter a producing formation which is initially at the connate-water saturation and contains no gas. The water and oil are treated as in-

By Dr. Calvin J. Konya, Anthony Konya

Beginning on the Niagara Power Project, presplitting became a widely used blasting technique to obtain smooth walls in mining and construction projects reducing scaling, creating more stable pits, allowing the application of slope steepening to reduce waste removal and increase mining depths, and increasing the safety of mine and construction workers. This technique has been minimally studied in comparison to production blasting and currently two separate theories are present on the mechanics behind the presplit. The first is that shockwave collisions between boreholes cause a tension zone to develop causing the split formation. The second is that gas pressures build in the boreholes causing hoop stresses between holes leading to a presplit formation. Practical blasting methods in presplitting such as propellant presplitting and precision presplitting would not be applicable based on the shockwave theory yet are widely used and documented in the industry. Along with this, modern research using a borehole simulation device and advanced pressure gauges have allowed the authors to obtain true borehole pressures in decoupled blastholes. This paper will present this research which correlates the borehole pressure to variables such as the Young's Modulus and Tensile Strength of various rock types giving blast designers the ability to design a presplit to function in many rock conditions, including weak rocks such as siltstones and mudstones.

By W. P. Diamond, F. Garcia, J. K. Marshall

Many longwall mines rely on methane drainage to supplement traditional fan-based ventilation systems. However, the surface production facilities for methane drainage systems, including gob gas ventholes, are commonly located in remote locations, sometimes without convenient access to electrical power, and they may be monitored infrequently. The first evidence that a methane drainage system may not be operating efficiently, or not operating at all, can be an increase in methane concentrations at a return air shaft or underground where the workforce is exposed to the risk of a methane explosion. A solar powered, remote gob gas venthole monitoring and cellular telephone-based real-time data transmission system has been developed and successfully field tested by the National Institute for Occupational Safety and Health (NIOSH) to address this problem. With this system, individual methane drainage boreholes can be monitored from the mine office to determine current operational performance parameters, as well as review past data to anticipate maintenance needs and troubleshoot operational problems.

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By Grant A. Brackebusch

Paste tailings disposal was successfully implemented at the New Jersey mill in Kellogg, ID with two different types of ore feed, a gold ore and a silver ore. The purpose of this paper is to describe the production of paste tailings, including operational problems during commissioning, and also highlight the environmental and economic benefits that were realized versus conventional tailings disposal such as the recycling of process water, increased shear strength and reduced permeability of the tailings mass, and reduced environmental permitting.

By Andrew B. Cecala, Robert J. Timko, Alexander D. Prokop

Bag loading and stacking processes are the highest dust-exposure job categories in the metal/nonmetal mining industry.1 To cost-effectively decrease respirable dust levels, the Pittsburgh Research Center of the National Institute of Occupational Safety and Health (NIOSH), formerly of the U. S. Bureau of Mines, designed and tested a system called the Bag and Belt Cleaner Device (B&BCD). [ ]

By J. P. Heller

The purpose of this discussion is to comment briefly on one of the points raised in the paper. The topic is that referred to in the Conclusion 2, in which the authors note a "disproportionate increase in mixing rate" as they proceed from a displacement performed at viscosity ratio 0.998 to one at 1.002. The recovery curve of this displacement, Fig.2A, shows a quite noticeable difference between the two runs in which displaced and displacing liquids were interchanged. This difference is ascribed by the authors to the change in viscosity ratio between the two experiments. This interpretation of the experimental results must certainly be based on rather precise measurements of the fluid viscosities or, at least, of the ratio of their viscosities. The ordinary Ostwald viscometer, employed in the usual way, is only just able to distinguish between liquids whose viscosities differ by two or three parts per thousand. The experimental refinements which then must have been necessary to measure with any precision a viscosity ratio of 1.002 would be worthy of mention. Indeed, one would have expected the authors to devote at least a paragraph to the display of this technique. For the same reason - to emphasize that the details of such unusually critical experimental work should be reported and discussed in the literature — I would have liked to see some comment by the authors on the requirements for temperature control during both the viscosity measurements and the displacement experiments. The temperature coefficient of viscosity of Soltrol C at room temperature has been measured in this laboratory at about - 1.9%/1°C. How much did the coefficients for the fluid mixtures used in the experiment differ from this and from each other Even if the two fluids were identical in this respect, it would appear that a temperature difference of .l°C between them in the flow system would produce a viscosity con- trast equal to that imposed by their composition. Reference to the experimental solutions of these problems would render Conclusion 2 more credible. Published theoretical work on the stability problem contains no indication of such extreme sensitivity to the viscosity ratio in the immediate neighborhood of unity. On the contrary, perturbation calculations such as those made by Chuoke1 and Perrine2 lead to initial finger growth rates proportional to the first power of the viscosity difference. The later instability growth calculated by Scheidegger,3 using the assumption of zero pressure gradient perpendicular to the average flow, is also simply proportional to the viscosity difference. The conflict regarding the sensitivity of the dependence of instability growth or mixing rate on the viscosity contrast needs explicit recognition in the literature. In particular, it would seem that the experimental work reported here should be supported by a more detailed description of the viscosity controls. Further discussion of possible alternative interpretations of the data would also be in order. For instance, is it possible that the unconsolidstted bead pack used changed its characteristics between the runs (due, perhaps, to the handling and inverting involved in the injection of the front) Or, are the data points of Fig. 2A averages from several runs performed in a series in which the two liquids alternated as displaced and displacing fluids? To summarize, it seems to me that the relationship asserted by Conclusion 2 in the paper needs the support of more detailed experimental evidence. REFERENCES 1. Chouke, R. L., van Mews, P. and van der Poel, C.: "The Instability of Slow Immiscible Viscous Liquid-Liquid Displacements in Porous Media", Trans., AIME (1959) Vol. 216, 188.

By R. W. Raymond

THE question, what is the best proportion among weight, fall, and speed of stamps, is one which has not yet received thorough and systematic examination. In considering the economical application of stamping machinery, we meet, at the beginning, with serious difficulties in obtaining accurate data for comparison. The weight and fall of stamps vary as the shoes and dies wear out; and this may lead to a change of speed also. Moreover, defects in engines, boilers, or machinery for the transmission of power, may occasion serious losses, which cannot fairly be charged to the arrangements of the stamps proper. Again, the capacity of stamp-mills is directly dependent, in some degree, upon the nature and extent of discharge, fineness of screens, and other peculiarities of the battery. Finally, the hardness and tenacity of the rock crushed varies so much that comparisons between different localities cannot be implicitly trusted. The safest experiments are those made in the same mill, by changing first one and then another condition of working; but this is seldom possible for such conditions as weight and lift of stamps, and only within narrow limits for their speed. We may eliminate of friction, transmission, and generation of power, in the case of stamps, by measuring the power actually developed by their fall. Thus, the weight, multiplied into the fall in feet, and the number of drops per minute, gives us exactly the number of foot-pounds exerted by each stamp. Dividing by 33,000, the number of foot-pounds per minute in one-horse power, we have the horse-power per stamp, from which the effective power of the whole mill may be obtained. Dividing the amount of rock crushed daily by the effective horse-power, gives us the daily amount per horse-power ; and this is the best measure that can be obtained for the effectiveness of the stamps. A complete discussion of the subject would require us to determine the exact influence of the discharge, etc., and the exact resistance offered by different classes of rocks, for both of which points the data are wanting. Professor J. D. Hague, in the third volume of the United States Geological Exploration of the Fortieth Parallel, gives a valuable