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By A. A. Mathews

During the past year (1967-68), there have been many instances of either partial or complete failure of a tunnel-support system. It looks like the art is in a pretty sad state, but as long as we permit the field of tunnel design to remain basically an art, that's about what we can expect. The application of scientific principles to tunnel design involves much more than assigning values to a series of factors in an equation. I am reminded of the case where the engineer calculated that steel ribs with struts were required to support a horseshoe-shaped tunnel in firm ground. The contractor had driven several hundred feet without installing the struts when the engineer visited the job. When he was informed that the struts had been left out, he fled the tunnel in alarm. As one authority has so aptly put it, "There is far too much calculating and too little observing." Initially, one might think of a tunnel support as a structural member, such as a strut or arch which is installed in order to support some definite load. Similarly, a tunnel lining might be considered as a treatment of the interior surface of the tunnel in order to produce desired aesthetic, hydraulic, or architectural results, or to serve a protective function. Actually, many linings, such as a concrete lining, serve a dual purpose and support a load as well as satisfy other requirements. Not too many years ago a tunnel, during the driving or excavating stage, was considered to be either supported or unsupported. In recent years, however, several techniques have been developed, which by helping the tunnel to support itself, permit the elimination of separate structural support. Since these techniques in many cases actually become a substitute for the conventional types of supports and linings, a state-of-the-art review would hardly be complete without including them for consideration. Thus, for the purpose of this discussion, we shall define tunnel supports as any system or technique which effectively maintains the integrity of the tunnel opening. In their chapters, both Jacobs (No. 6) and Lippold (No. 7) pointed out how support systems have advanced from timber supports to steel supports

Jan 1, 1970

By W. D. Bachman

A study has been made of wet, autogenous grinding of disseminated copper ores, including testing of a large number of samples from Kennecott Copper Corporation's Chino mine. The efficiency with which the various samples could be ground was found to vary over an extremely wide range, even among samples taken from different locations within the same ore body. These variations in grindability can be qualitatively correlated with the composition of the rock and the fracturing and alteration that had occurred. Because of the large-scale non-homogeneity of disseminated copper ore bodies, extensive and careful testing of autogenous grinding is needed. An accurate correlation of the grinding data from various samples with the geology of the ore body and with mining plans will indicate if variations in grinding mill throughput can be avoided in practice by mixing or blending of mill feed and if, therefore, autogenous grinding can be applied successfully.

Jan 1, 1970

Builders have been very familiar with iron since ancient times, but because of its weathering characteristics it was relegated to use as a fastening material in unexposed places and bronze became the popular metal for exposed applications. It is of interest that iron nails buried deeply about A.D. 87 at a Roman fortress and carefully covered with clean beaten earth under conditions practically excluding oxygen were found to be almost unrusted 1870 years later. (1) Today, weathering steels, which contain less than 2% of alloying additions, can be used in exposed situations without protection and without experiencing continuous wastage. As we all know the steady access of atmospheric oxygen to the surface of plain steel causes continuous corrosion. Weathering steels, on the other hand, due to their alloying additions develop their own impervious surface layer which limits the access of atmospheric oxygen and effectively limits corrosion. Table 1 shows the chemical composition of a plain carbon steel and a typical weathering steel. Fig. 1 shows what we refer to as direct corrosion - time curves in which corrosion loss is plotted against time of exposure in an strial environment. The weathering steel has a high rate initially which then decreases steadily for about three years, as the stable rust film builds up. This is followed by a practically linear relation where the very low corrosion rate, according to one school (2), is due to a blocking of the rust pores by insoluble complex salts formed from interaction of the oxidation products of the separate alloying elements. The start of the linear region represents a total corrosion loss of only about 2 thousandths of an inch.

Jan 1, 1970

By S. P. Ray, B. D. Sharma

THE activation energy values for self-diffusion in pure metals have been correlated with a number of physical properties such as melting points,1 valences,' Debye temperatures,3 and cohesive energy densities.4 Extending the melting point correlation, the self-diffusion activation energy values for the alloys can be similarly correlated with the solidus temperatures. For metals and alloys which exhibit phase transformations, such a correlation is not feasible because of the uncertainty of various physical properties of the corresponding phases. Using thermodynamical approach, Ardell5 calculated the hypothetical melting points of the low melting phases of the polymorphic metals. However, these calculated melting points do not show reasonable correspondence with the activation energy of self-diffusion. Recently, a new approach treating metals and alloys as electron concentration phases has been developed by Engel6 and Brewer.7 These workers have attempted to correlate the crystal structures with the electron configurations of the atoms existing either in ground state or in an excited state of low promotion energy. The basic postulate of this theory is that whereas the contribution to the bonding of the metal comes from the interaction of both d and (s-p) electrons existing either independently or in hybridized states, the existing crystal structure is controlled by the (s-p) electrons alone. Specifically, a metal is supposed to crystallize in bcc, hcp, or fcc phase provided the metal has one, two, or three valence electrons per atom in the (s-p) configurations. The diamond, or ZnO and ZnS structures, occur with four (s-p) electrons per atom. Secondly, the contribution of d electrons to bonding is supposed to increase with atomic number

Jan 1, 1970

By John T. Awald

The Bradshaw Mountains of west-central Arizona cover an area of 1600 square miles and contain numerous old mines and prospects. The area has been geochemically sampled on a reconnaissance basis to relate mineralized areas to regional structure and rock types. Copper analyses of stream sediments have been classified and contoured to show the distribution of low background, high background, and low, intermediate and highly anomalous areas. Contoured results are compared to geology and known mines. Several prospecting areas are indicated.

Jan 1, 1970

By L. W. Sink, B. H. Kear, S. M. Copley, M. F. Hornbecker

IT is well known that under appropriate conditions of chill casting, many metals and alloys develop a columnar grain structure having a high degree of preferred orientation.' In cubic materials, this principle has been employed to produce shaped castings with a unidirectional cube oriented columnar grain structure as well as shaped single crystals with a cube axis parallel to the growth ais.' "he purpose of this note is to describe how this same principle can be enlployed to produce wires, rods, or more complex crystal Shapes with a variety of conlpositions in cube or random orientations by a single casting operation. The procedure for directional solidification of in Fig. 2. Examination under crossed polarizers indicated that the striations were a second phase (presumably the B19 phase) which frequently forms initially at primary grain boundaries and then grows toward the interior as thin ribbons. X-ray studies on filings of this alloy reannealed at 1300°C for 15 min indicated a strong pattern of the fcc phase together with a substantial pattern of the B19 phase. The un-annealed filings, however, showed only the pattern of a cold-worked, fcc structure. In these two-phase alloys it appears, therefore, that the B19 phase is transformed into a disordered fcc structure by cold-working. The mechanical properties of these alloys would be of some interest since a fcc structure might be expected to possess greater ductility than the or-thorhombic B19 structure from which it forms. The author wishes to thank Mr. Harvey Yakowitz and Mr. Richard Manuszewski for obtaining the photomicrograph in Fig. 2. This research was partially supported by Research Grant DE-02455 from the National Institute of Dental Research. columnar grained ingots involves pouring a melt into a preheated mold having a water-cooled copper chill at its base? and controlling the temperature gradient in the mold so as to maintain columnar grain growth from end to end of the ingot.4 This is illustrated schematically in Fig. l(a). It should be noted that the longitudinal temperature gradient promoting unidirectional columnar grain growth is maintained by heat loss primarily through the solidifying ingot to the chill, so that both the temperature gradient and the growth rate diminish with increasing distance from the chill. As the distance from the chill increases? the columnar structure coarsens, and the perfection in preferred orientation tends to increase progressively. Using this same procedure of gradient solidification, Fig. l(b) shows a simple scheme for producing a batch of crystals having the same cube orientation rather than an assemblage of columnar grains. Wires and rods are produced by cementing ceramic tubes to the wall of the mold. The steep temperature gradient produced in the central chamber is controlled by the mold heater to produce favorable conditions for crystal growth. Clearly the success of the operation lies in the selection of individual growing columnar grains by some kind of orifice at the base of each channel in the mold. Using simple constrictions, experience with nickel-base alloys has shown that 4 -in.-diam holes at a distance of -1 in. from the chill yield crystals within 7 deg of (100); closer control of orientation is possible by placing the crystal selector farther away from the chill.

Jan 1, 1970

By Horst Huettenhain

The Rowland Coal Preparation Plant is located on Workman's Creek in Raleigh County, West Virginia, approximately 20 miles Northwest of Beckley and 10 miles Southeast of Ameagle. It is owned and operated by the Rowland Division of Consolidation Coal Company. This paper describes the plant flowsheet, process considerations that were evaluated in its development, and observations made during and since the plant was constructed. The final flowsheet was developed specifically to wash the coal from the Rowland Mine and contains several equipment combinations and applications heretofore never placed in a single, commercial operation. The major process equipment is presented in a functional description of the flowsheet. The coal reserves are leased from the Rowland Land Company and consist primarily of #2 Gas and Middle Eagle coals and various major splits of the Middle Eagle seam. The Rowland Coal Preparation Plant was designed to process 560 TPH of raw coal consisting of 50 percent #2 Gas coal intimately mixed with 50 percent Middle Eagle coal and containing lumps no larger than a 12-inch cube.

Jan 1, 1970

A mechanised sub-level overhead benching method is used at Cleveland, to produce 22,000 tons per month of ore assaying 0.92% Sn and 0.40% Cu. The ore occurs in a series of vertical lenses which can be mined by open stoping. Levels are developed at 60ft., vertical intervals by jumbos. The ore is silled out and the stope block formed between levels drilled out by long hole drilling. Each row of holes is fired and broken ore within safe reach from the stope brow is mucked out by Wagner ST-5A Scoop Trams. The remaining broken ore is recovered on extraction of the next lower level. Ore is hauled by road to the crusher station from the mine. As mining proceeds below the lowest surface portal a spiral decline will be used for ore haulage and mine servicing.

Jan 1, 1970

By G. H. K. Schenck

Weather changes of a daily, weekly, or seasonal period affect mineral production and cause significant losses that are considered unavoidable. Private weather forecasting services are available on a contract basis that can significantly reduce the uncertainty associated with weather-induced changes in the production of and demand for minerals. This paper provides examples of current practice and reviews the opportunities that await those producers who incorporate weather services as an integral part of their operating, scheduling, and planning procedures. Private weather forecasts can be highly accurate because atmospheric trends such as conditions and movement tend to persist and are related to previous meteorological events. Commercial meteorological services are prepared to deal specifically with a mineral producer's special problems (Table 1). Tactical use of private forecasts is a major advance over the severely restricted value of public forecasts which, of necessity, are general in nature and cover a dispersed geographic territory. Private weather services provided on a consulting fee basis offer the mineral producer the opportunity for tactical and strategic response to weather conditions at an acceptable cost. This contrasts with the too-frequent current tendency to view weather as a random variable the costs of which are unknown and about which nothing can be done.

Jan 1, 1970

By William G. Gates

INTRODUCTION The Heath Steele mine is located in the Bathurst-Newcastle area of northern New Brunswick. It is jointly owned by American Metal Climax, Inc. and the International Nickel Company of Canada who hold a 75% and 25% interest, respectively. The ore deposits of lead, zinc and copper sulphide occur in very fine grained pyrite and/or pyrrhotite masses. A consistent spatial relationship with a quartz feldspar porphyry is characteristic of these deposits and the many other similar sulphide deposits in the district. The two principal mineral assemblages of pyrite-sphalerite-galena, and pyrrhotite-chalcopyrite-pyrite, occupy characteristic positions relative to the enclosing rocks. This feature and the nature of the sulphide mineralization are described and the variations in metal content are noted .with special emphasis on the lead-zinc ore zones. The mine product ion rate is 3,000 tons per day of a mixed lead- zinc and copper ore which is extracted from the B-1 zone. The complex nature of the ores presents many metallurgical problems. Optimum metal recoveries are achieved when milll feed grades are relatively consistent and proportions of the contained metals are with in acceptable limits. Ore outlines and stoping blocks are delimited by close spaced diamond drilling. From this information it is possible to forecast the grade of any portion of a stoping block. Production from the various stopes may then be scheduled so as to achieve an acceptable mill feed grade.

Jan 1, 1970

By Martin E. Chenevert

The early work of Terzaghi1 showed that the true stress state of a rock can be expressed by the principle of effective stress. This principle states that effective stress is equal to total applied stress minus the pore pressure. Since the introduction of this principle, a great effort has been made to measure the pore pressure of rocks so that the true stress state can be determined. For clean, permeable sandstones, it is usually found that the effective stress principle can easily be applied. Direct measurement of the pore pressure is achieved with a hydraulic pressure device and the effective stress state thereby computed. However, for fine-grained rocks which contain large amounts of clay (referred to herein as shales), pore pressure measurements are usually quite difficult because of the adsorptive forces of the clay platelets, which produce negative internal pressures. No suitable device is known for measuring internal pressures of dry shales; the effective stress approach is therefore not feasible and data are usually presented in another form. As an example, data from compressive strength tests are presented as a function of rock wetness, rather than effective confining stress. The work of Belopoloskii2 and Colback and Wiid3 are examples of such data. It was pointed out by Lambe and Whitman4 that a better way must be found to express the effective stress of argillaceous rocks. The information presented herein is an attempt to fill that need. Various authors have been able to measure moderate negative pore pressures (0-240 psi) within rather wet, argillaceous rocks by means of various pore pressure devices. In 1961 Lambe5 resented information which shows that pore pressures in argillaceous rocks are indeed negative ; he presented values of suction pressure as low as - 14 psi. Likewise,

Jan 1, 1970

By Edward J. Felten

Binary Cr-A1 alloys containing from 2.5 to 30 wt pct Al and 0.7 wt pct Y were heated in oxygen, air, and nitrogen between 1000" and 1200°C. The reacLivity of the alloys was found to be dependent both on the alloy composition nnd the nature of t he atmosphere. In oxygen, nllojs containing up to 15 to 20 wt pct A1 reacted to produce an external scale of Crz03 and a subscale consisting Predominently of Al203. Alloys contazning 20 to 30 wt pct A1 react in oxygen to produce an A1203 external scale and little m no subscale. The latter alloys were markedly more oxidation resistant than those of low alurninum content. In air, the alloys on which an external Crz03 scale was formed were found to be permeable to nitrogen ns evidenced by the copious amomts of chromium and aluminum nilrides observed ns part of the subscale. The reactizities in nir (or nitrogen) of these alloys increase <m their aluminurn contents increase. However, alloys on which Al,O, us an external scale is formed were nol culnerable to nccelerated attack in air, and no eltldence of nitvide subscnles were observed. For all alloys, yttrium serwed pYimarily to improve oxide adhrence. THE role of chromium in the oxidation resistance of Fe-Cr alloys &apos;-&apos; and that of aluminum in Fe-Cr-A1 al10s&apos; has received considerable attention in recent years. This is understandable since many of these alloys have excellent oxidation resistance due to the formation of either a Cr203 or a-Ala03 film between the metal and the oxidizing atmosphere. Small additions of yttrium or other rare earth metals are effective in preventing spalling of the protective oxide from the metal substrate."" In contrast, little is known regarding the oxidation resistance of Cr-A1 alloys, although some work has been done by Tumarov et a1.&apos; The poor niechanical properties exhibited by Cr-A1 alloys make them undesirable for use as structural components, but their use as coatings cannot be disregarded. The use of chromium-rich aluminide coatings for refractory metal alloys is an example of the potential use of this type of sytem. The purpose of this work is to examine the oxidation behavior of Cr-A1 alloys containing 2.5 to 30 wt pct A1 and 0.7 wt pct Y. The effects of temperature, atmosphere, and thermal cycling have been determined. EXPERIMENTAL PROCEDURE The alloys used in this investigation can be divided into two groups. Those containing 2.5, 5, 7.5, and 10 wt pct A1 and 0.7 wt pct Y were extensively evaluated in the temperature range from 1000" to 1200°C. Alloys containing 15, 20, 25, and 30 wt pct A1 and 0.7 wt pct Y were tested only at 1200°C. All of the alloys were prepared by standard arc-melting techniques in the form of cylinders approximately 4 in. long and 19 in. in diam. Wafers were cut from the cylinders and subsequently subdivided into rectangular coupons. The alloys were brittle and therefore some cracks were found in almost all specimens. The coupons were prepared for oxidation by mechanically polishing through 600 grit Sic paper, and were thoroughly degreased just prior to testing. Two types of oxidation experiments were conducted, namely; cyclic tests in which the specimens were examined and weighed after each 2 hr exposure, and continuous thermal balance tests run in a controlled atmosphere (oxygen, air, or nitrogen) for 20 hr. In the former test the spalled oxide was not included when the specimens were weighed. The physical condition of a specimen was noted visually after each cycle and testing was continued either to failure or until the performance of the specimen was well characterized. Both Micro and Semi-Micro Thermal Balances (Ains-worth) were used in the continuous tests. The oxidized specimens were sectioned and prepared for metal log raphic examination. The specimens were polished through 600 grit Sic paper. After polishing through 6 and l p diamond, a final mechanical polish with Linde B-Alz03 was used. Specimens containing 2.5 pct A1 were etched electrolytically using a 10 pct oxalic acid solution at 4 v for about 2 sec. Selected specimens were examined in the electron microprobe analyzer. Oxide specimens were examined by standard X-ray diffraction techniques. EXPERIMENTAL RESULTS For convenience, the test results have been broken down according to the exposure temperature, and further subdivided according to the type of test and atmosphere employed. Because of the poor quality of the specimens a larger than normal amount of scatter was observed in the measured rate constants. Also, the evaluation of the weight gain data was done on a somewhat arbitrary basis and may not be truly representative. However, the results obtained do show a significant trend in behavior regarding both alloy composition and the nature of the oxidizing atmosphere. I) Oxidation Behavior at 1000°C. A) Continuous Oxidation estsin Oxygen. This series of experiments was run in the Ainsworth Micro-Thermal Balance using pure oxygen at a pressure of 76 mm Hg. Under these conditions all specimens oxidized in accordance with the parabolic rate law over a major portion of the exposure time; the rate constants appear in Table I. The oxide formed externally on all specimens was predominantly Cr,O,, which was generally adherent. In some cases a slight amount of spalling in the form of a fine powder was noted. a-A1203 was observed as a subscale, along with Yz03 in all alloys. Alloys containing up to 7.5 wt pct A1 oxidize more rapidly than the Cr-0.7Y alloy.

Jan 1, 1970

By R. T. Erskine

"IntroductionIn this paper it will not be possible to cover all details of the reagent systems at Brunswick Mining and Smelting but it is hoped that a description of the evolution of these systems will be of some benefit. The concentrator of Brunswick Mining and Smelting located near Bathurst, New Brunswick was originally designed as a 3,000 ton per day operation but before construction commenced was uprated, with 4,500 tons per day being treated by the summer of 1964. Development of the open pit at another ore body five miles away was initiated in 1965 and additional concentrator and crusher facilities went into operation in September, 1966. Present total daily throughput is over 8,000 tons per day. The ore at Brunswick is very high grade but mineralization is very fine grained and requires grinds generally over 75% minus 400 mesh for liberation. The amount of surface exposed using grinds of this order understandably requires great quantities of reagents, Reagent mixing systems for the original concentrator allowed only for batch mixing and were very expensive in labour cost especially.During the first three years of operation total number of men employed in reagent handling reached a peak of four men per shift and six men on dayshift unloading cars for a total of 22 men. At present only one man is employed on shift, and four men on dayshift take care of unloading and mixing reagents, a total of 8 men. The man on shift is almost entirely occupied with checking feeder operation, flow rates, and head tank levels. Most commonly used reagents are tabulated in Fig. 1 showing average monthly and daily requirements in the Brunswick operation as well as pounds per ton of mill feed as found in 1969. It is very obvious that with over seventeen tons each of lime and soda ash and six tons of copper sulphate used each day, opening of bags and mixing batches of solution is an inefficient undertaking."

Jan 1, 1970

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.&apos; and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By E. J. Harvey

The Ozarks has been called "a diamond in the rough". In this region streams have steep gradients, sparkling clear flows of cold water fed by many springs, and a wildness that is almost unique in the central part of the United States today. The Current River and its tributary, Jacks Fork, have been set aside for preservation by the National Park Service as a "Wild River" in the first park of its kind in the country. It is called the Ozark National Scenic Riverway. Similarly, responsibility for the preservation of the Eleven Point River has been assigned to the U. S. Forest Service. Protection of other streams in the Ozarks has been considered by State agencies. The hydrologic system of the Ozarks is a complex network of gaining and losing streams, caves, conduits, and large springs. Increased sewage loads derived from the growing towns and expanding tourist trade are a potential hazard; effluents may flow underground for long distances, polluting springs and wells. To add another dimension to the hydrologic picture a new lead industry is also flourishing in the Ozarks. Although the history of lead mining in the area goes back to 1701 (U. S. G. S., p. 43), the area has not seen a revitalization like the one that has been developing in the last 10 years; and the economic growth promises to continue indefinitely. Although this brings capital expenditures and wages into the area, it also brings potential hydrologic problems. Chemicals, wastes and other substances either stored on the surface or transported across it are subject to accidental spillage. In an area where these substances remain on the surface their effects are subject to surveillance. In the Ozarks, however, this may not be possible.

Jan 1, 1970

By A. Timur

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

Jan 1, 1970

By D. S. Pye, J. P. Gallus

Successful hydraulic pressure treatment of oil and gas wells that have long producing intervals, multiple pay zones, fluid thief zones, or natural or induced fractures has long been a serious problem plaguing the petroleum industry. High fluid-injection rates, straddle packers, ball sealers, and either liquid or solid additives to the treating fluids are being used to cope with this difficult and costly problem.l-6 The use of ball sealers and straddle packers is limited, in practice, to wells that have been completed with perforated cemented casings or liners. Well stimulation with ball sealers and straddle packers is usually successful as long as the cement remains competent. The other techniques of diverting are used with all types of completions. However, there are two significant disadvantages of the high rate method: excessive horsepower requirements, and the need of large treating-fluid volume. Consequently, most well stimulation techniques that involve diverting depend upon ball sealers or granular materials. Liquid diverting agents, and some of the solid ones in use today, frequently will cause formation damage. On the other hand, the most popular particulate diverting agents often are so soluble in the treating fluid that they become largely ineffective; their particle size is severely reduced as they dissolve while being transported through thousands of feet of pipe to the formation face down hole. In our attempts to deal with the shortcomings of these diverting agents, we experimented with a large variety of potentially suitable deformable materials the solubility of which could be controlled. Following are the criteria for the diverting agent sought: 1. The material must be effective in reducing fluid loss to thief zones, including existing fractures and very high permeability layers in the formation to be pressure treated. 2. The material must have enough strength to bridge under the treating pressure. 3. The material must be insoluble or slowly soluble in the treating fluids so that the particles retain sufficient size to be effective after they reach the formation face. 4. The material must be completely soluble in the produced oil or condensate liquid so that it can be removed readily; it must not cause formation damage. A number of products consisting of various polymers blended with waxes and other solid hydrocarbons were examined. All these materials satisfied the criteria for a diverting agent and also exhibited some degree of plastic deformability. On the basis of initial tests of strength and hardness, several blends of wax and polymer were selected for extensive testing in the laboratory and the field. These compounds have congealing temperatures ranging from 140 to 190F; they are insoluble in water and soluble in oil. They conformed, therefore, to the criteria specified for a theoretically superior diverting agent. Laboratory and field tests were conducted using these wax-polymer materials to demonstrate that the use of a deformable diverting agent can significantly improve fluid diverting performance. Data in this

Jan 1, 1970

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By Jacques B. Wertz

Recurring movements remotely connected with the Murray fracture zone and the San Andreas fault complex, together with the slow northwestward drift affecting the Baja California peninsula, could progressively have accentuated the tensional situation already connected with the anticlinorium in southern Arizona. From the fragmentary data gathered on the Texas lineament, it appears that a very mild curvature, concave to the northeast, may be present along this belt throughout Arizona. Those localities where the successive changes in direc¬tion of the strands of the lineament belt seem to occur do generally coincide with intersections of both north-northwestern and northeastern breaks. It is along the outward, southern fringe of the belt (at such structural centers like Bisbee, Baboquivari, Ajo) that the greatest impact of regional movements could be expected to have occurred through tangential-torsional stresses. Although it si accepted that the north-northwestern and more particu¬larly the northeastern fractures in Southeast Arizona are propitious to or partially responsible for mineralization, it seems undeniable that the Texas lineament belt must have greatly increased the potentialities for ore throughout the Arizona copper province. While intrusive bodies occur near major intersections, with the Texas lineament belt as a common denominator, it seems, the ore deposits are to be found close to one of the intrusive stocks, varying in distance from contiguity (Bisbee) to one or two miles away (Silver Bell orebodies).

Jan 1, 1970

By L. B. Davidson

The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made.1 -5 Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigations are dissimilar. Edmondsonl found that in Berea sandstone a temperature-dependent effect was present, while Shilobod,2 using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A&M U.3-5 found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75OF to 540°F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study. It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system. Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75OF to 500°F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effect6 to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated7). Evidence for a similar source of temperature dependence in superheated steam-white oil experiments

Jan 1, 1970