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Jan 1, 1908

Dr. Oldshue has provided a useful summary of a voluminous subject and my task will be to select and direct attention to those areas of mixing theory and practice which are germane to mineral processing in general, and to fine particle treatment in particular. Pulp mixing in impeller actuated reactors occurs in mineral processing in several different applications: (1) emulsification of reagents; (2) mixing pulp with 'reagents as in conditioning for subsequent operations (such as flotation, flocculation or agglomeration) ; (3) high intensity agitation, as in (a) disintegrating and dispersing aggregates, and (b) aggregating particles as in shear flocculation or in selective agglomeration; (4) hydrometallurgy; (5) hydrometallurgy with gas phase (e.g., Arbiter process); . (6) flotation in sub-aeration machines. Attention is invited to 3 above in which two opposite effects can be induced by proper choice of chemical treatment and hydrodynamic conditions. Successful processes for treating mineral fines require excellent aggregate dispersion in order to fully accomplish the liberation stage. Some processes depend further upon selective aggregation following dispersion. The term “dispersion” is often used in different senses which for present purposes will be clarified at the bottom of the next page.

Jan 1, 1979

By P. A. Witherspoon, Y. W. Tsang

Normal stress-fracture closure variation and stress-dependent fluid flow rates were calculated for rock fractures of different aperture distributions. This study shows that both the mechanical and hydraulic properties of the fracture are controlled by the large-scale roughness of the rock fracture. Hence the typical large-scale undulation wavelength of the rock joint dictates the suitable sample size to be used in normal stress and fluid-flow measurements, if results due purely to sample size are to be avoided.

Jan 1, 1982

By H. L. Overton, J. B. Lipson

The concept of sodium single-ion equivalent activity as developed by Gondouin, Tixier and Simard,' was used to determine the filtrate resistivity-activity relationships for 150 laboratory and 49 field drilling muds. With the exception of the native and phosphate high-resistivity muds and the calcium-treated muds, the filtrate resistivity-activity relationships were found to be within 20 per cent of that for pure sodium-chloride solutions. Gondouin, et al,* previously suggested a method of treating the high-resistivity muds in quantitative electrical log analysis. A new treatment is presented which uses the P-alkalinity of the filtrate as a correlating parameter in handling the calcium-treated muds in quantitative electrical log analysis. INTRODUCTION Gondouin, Tixier, and Simard in 1957 introduced new interpretive procedures for analyzing the self-potential curve of electric logging. They re-emphasized the previous work of the Schlumberger brothers, Wyllie and others, and re-defined the activity concept in terms of a number which they termed the effective resistivity. Their procedures are particuarly effective when the connate-water resistivities are less than 0.08 ohm-m or greater than 0.3 ohm-m. For gyp muds where the calcium content is known, a procedure was presented which allows calculation of the connate-water resistivity with improved accuracy. These procedures assume that one of the fluids in the system is a pure sodium-chloride solution, but they are not limited by the assumptions. For the fresh and saline connate waters, for instance, it is assumed that the drilling mud filtrate is a pure sodium-chloride solution. For the gyp mud interpretive procedure, it is assumed that the connate water is a pure sodium-chloride solution. Brown,' on the other hand, has suggested that it would be extremely fortuitous if drilling mud filtrates could all be treated electrochemically as sodium-chloride solutions, and he cites some examples where discrepancies exist. A study has been made of the deviations of sodium single-ion equivalent activities, an of drilling mud filtrates from that of pure sodium-chloride solutions. Drilling fluids in common use on the Texas and Louisiana Gulf Coast and laboratory-controlled muds were investigated. Using a cell patterned after Gondouin, et al, (Fig. I), the equivalent activities were measured. It should be remembered here that the activity measured is merely an index which uses numbers that represent the sodium single-ion equivalent activity a,., of the mud filtrate. The membrane potential developed across the cell was determined with a null-type potentiometer. The resistivities of the solutions were measured by the four-electrode method. The resistivity system was calibrated by using saturated KC1 solution as a standard. Chemical properties of the drilling fluids studied were measured with standard API-approved equipment for the particular property in question. For the activity measurements, two shale discs were chosen to serve as cationic membranes. These two discs were both 1 1/4 in. in diameter and, respectively, 1/4 and 1/8 in. in thickness. The membrane potential, Em, was determined using the shale discs as cationic selective membranes separating two standard sodium-chloride solutions of known mean activity. Then by comparing the constant Km in the following equation, with the theoretical value of — 59 mv at 75OF, the perfection of the membrane was determined. The variation of Km for the two membranes used in this experimental work, as well as one of the many unsuitable membranes, is shown in Fig. 2. The measurement of the activity of mud filtrate involves the balancing of its combined individual activities against a standard solution of known mean activity. At the point where there exists zero potential across the membrane cell, the activity effects may be assumed equal for all practical purposes. The mechanics of making a null reading of this sort requires having a large number of different mean activity solutions. A more practical method involves

By R. A. Generes, H. C. H. Darley

Laboratory tests showed that at elevated temperatures a reaction takes place between all metal hydroxides and clay muds, which results in a thickening or solidifying of the mud, the extent of which depends on the nature of the ingredients. Calcium hydroxide gave the strongest solidification whereas barium hydroxide only caused a mild thickening, indicating that the use of barium hydroxide muds instead of lime muds would be a good way of preventing high-temperature solidification. It was found possible to prepare barium mud in the laboratory with caustic soda and a thinner in the same manner as lime muds, and these barium muds had the same or better toleration of high solids content, resistance to salt contamination, and low gel strengths as the corresponding lime muds. Three field trials have been made with barium mud. The principal difficulty encountered was in determining the correct proportions of the tourly treatments required to maintain low gel strengths. A satisfactory systern was finally developed, and low gels were maintained throughout the third test. The wells on which the trials were made were not carried deep enough to test the resistance to solidification adequately, but oven tests at 350°F were made periodically and no tendency to solidification was noted except immediately after severe cernent contamination had introduced excessive amounts of calcium into the system. Although barium hydroxide costs considerably more than lime, the total mud costs were as low, and on the last well significantly lower, than the average cost of lime mud wells drilled in the vicinity. INTRODUCTION The advantages of repressing dispersion and hydra-tion of clay cuttings carried in the mud, particularly when drilling through thick clay formations, are well recognized. This repression is generally achieved by the use of lime, and lime muds have in consequence the desirable characteristics of high toleration of solids, low thixotropy, and good resistance to contamination. They have, however, the disadvantage of high-temperature solidification. This phenomenon has been described in detail by Gray et al, who have shown that it is the result of a chemical reaction between the hydroxides and the clay minerals. The work described in this paper was undertaken to find a substitute for lime which would not cause this solidification. LABORATORY EXPERlMENTS The principal positive requirement for a substitute for lime is that it should repress the hydration and dispersion of clay. It is well known that monovalent cations promote hydration while polyvalent cations repress it. Therefore, a few representative polyvalent salts and hydroxides were tested to determine whether they could be used as substitutes for lime. Their efficiency at repressing hydration and dispersion was measured by means of the clay-volume test. It has been shown elsewhere' that this test is a good measure of degree of dispersion of clay in suspension and that hydration accompanies and correlates with dispersion, so that measuring one measures the other. The test is made by centrifuging a 1:100 mixture of mud and 1-N NaCl and observing the volume of sediment—the greater the volume, the greater the dispersion. The tendency to caux solidification was measured by heating the muds in pressure vessels for 16 hours at 150°F and 370°F. An approximate quantitative

Jan 1, 1957

For the year ending February, 1919 PRESIDENT SIDNEY J. JENNINGS, NEW YORK, N. Y. PAST PRESIDENTS L. D. RICKETTS, NEW. YORK, N. Y. PHILIP N. MOORE, ST. Louis, Mo. FIRST VICE-PRESIDENT C. W. GOODALE BUTTE, MONT. TREASURER GEORGE D. BARRON, NEW YORK, N. Y. SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 2, 1919

For the year ending February, 1920 PRESIDENT HORACE V. WINCHELL MINNEAPOLIS, MINN. PAST PRESIDENTS PHILIP N. MOORE ST. Louis, Mo. SIDNEY J. JENNINGS NEW YORK, N. Y. FIRST VICE-PRESIDENT A. R. LEDOUX, NEW YORK, N. Y. TREASURER GEORGE D. BARRON NEW YORK, N. Y SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y

Jan 7, 1919

For the year ending February, 1920 PRESIDENT HORACE V. WINCHELL MINNEAPOLIS, MINN. PAST PRESIDENTS PHILIP N. MOORE ST. Louis, Mo. SIDNEY J. JENNINGS NEW YORK, N. Y. FIRST VICE-PRESIDENT A. R. LEDOUX NEW YORK, N. Y. TREASURER GEORGE D. BARRON NEW YORK, N. Y SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 12, 1919

By C. F. Floe, N. J. Grant, A. Joukainen

A CCORDING to Guertler,¹ Smith and Hamilton were the first to study the Cu-Ti alloy system, but because of the presence of large amounts of impurities their data are inconclusive. Hensel and Larsen² in 1930 and Kroll³ in 1931 determined the high copper end of the diagram. In 1939 Laves and Wallbaum,4 in a short summary of compound determinations in titanium binary alloys, mentioned the existence of a face-centered cubic compound, Ti2Cu, with 96 atoms per unit cell, and also a compound, TiCu3, which was said to have a deformed hexagonal close-packed structure in which ordering had been observed. The existence of a compound, TiCu, was also found but the crystal structure was not determined. Craighead, Simmons, and Eastwood determined the effect of copper on the allotropic transformation in titanium. The investigation was limited to alloys containing from 0 to 5 pct Cu, using titanium of fairly high impurity content. Experimental Procedure The methods used for determination of the diagram included metallographic examination and X-ray and thermal analyses. The system was first worked out using the higher purity "Process A" sponge titanium and oxygen-free copper. The high titanium region was next determined more accurately using iodide titanium and vacuum-melted, oxygen-free copper. Preparation of Alloys: The alloys were prepared by arc melting under prepurified helium atmos- pheres in water-cooled copper crucibles. The high purity iodide titanium alloys were prepared by melting three compositions along with a specimen of unalloyed titanium in a single charge. A multiple crucible was used which consisted of a copper plate with four cup-like depressions. The unalloyed titanium was melted first and acted as a getter for any oxygen and nitrogen in the melting chamber. Since these elements harden titanium, the hardness of the standard specimen was an index of the highest probable contamination of the alloy melts. The sponge titanium alloy melts weighed from 100 to 200 g each and the iodide titanium melts from 20 to 25 g. In order to insure greater homogeneity most of the alloys were melted, turned, and remelted twice. The larger buttons made from sponge titanium were sectioned or crushed before remelting. These alloys up to 30 pct Cu were further homogenized by forging at 925°C. They forged readily up to 20 pct Cu but numerous cracks were formed in the alloys containing from 20 to 30 pct. Above 30 pct Cu the sponge titanium alloys were homogenized by heating for 200 hr at 850°C under prepurified helium. Similarly, the iodide-grade titanium alloys containing up to 3 pct Cu were homogenized at 1000°C for 24 hr and all others at 880°C for 200 hr.

Jan 1, 1953

By R. W. Bond

The gas-lift is a comparatively recent development in the Oklahoma and Kansas fields. It was used to some extent in the old Dilworth field several years ago, but the first extensive installations were made in the Tonkawa and Garber fields in Oklahoma early in the year 1926. Compressor Equipment During the early development of the system, the equipment used generally consisted of small tandem compressors of about 250 cu. ft. per min. displacement, driven by automotive-type gas engines, using a short belt drive. These compressors were first installed at the individual wells largely as an experiment. After the experimental installations had proved the method a success, it was considered economically advisable to centralize the compressor equipment in strategically located stations. However, as the information in regard to "gas-lift flowing life" was anything but definite, and the most optimistic estimates in regard to it did not exceed six months, portability of equipment was still the first consideration in the minds of many operators, who continued to install srnall semi-portable com-pressors in their centralized stations. As electric power became available in the fields, the electric motor came rapidly into use as the prime mover for the small compressors. The operating cost of this motor is greater than that of the automotive-type gas engine for the same power output, but the greater continuity of service tends to balance the extra cost. Aside from the semi-portable units, a number of strictly portable compressors were used. These consisted of automotive-type gas engines direct connected to vertical compressors. The unit was assembled on one base and could be mounted on wheels or skids as desired. The chief objection to these, in the writer's opinion, was their small capacity— approximately 150 cu, ft. per min.—which made it necessary to use two, three, and sometimes more units per well, thus making the installation rather costly. However, they have been found valuable for test purposes and emergencies, where installation time is an important factor.

Jan 1, 1928

By H. C. Theuerer

EVEN the highest purity silicon available for semiconductor use contains significant amounts of donors and acceptors, usually aluminum, phosphorus, and boron. Aluminum and phosphorus can be removed from silicon by adaptations of the zone refining techniques' widely used with germanium. Removal of boron, however, has been a difficult problem. The approximate distribution coefficient for boron in silicon is 0.8, so that while zone refining is possible, it is not very effective in any reasonable number of passes. It has been found, however, that boron can be effectively removed from silicon by treatment of a liquid zone with hydrogen and water vapor. Starting with 40 ohm-cm, n-type silicon, use of zone refining coupled with hydrogen

Jan 1, 1957

By W. Rostoker, S. A. Spachner

FOLLOWING the discovery of the w transition phase in certain titanium-chromium alloys by Frost, Parris, Doig, and Schwartz, much interest has centered on the alloys in which this phase is found and its mode of precipitation. The w phase has been found in alloys of Ti-Cr, Ti-Fe, Ti-Mn, Ti-MO,2 and Ti-v.3 The temperature-time-transformation characteristics have, as yet, not been determined for most of these. In this study, such transformation characteristics have been investigated for two heat-treatable titanium alloys known to exhibit transition phase phenomena. The alloys chosen, Ti-8Cr and Ti-13M0, are representative of two classes of binary equilibrium systems. In the

Jan 1, 1959

By Carolyn Barnes

The Offshore Technology Conference, the world's largest technical conference and exhibition on the development of offshore resources and protection of the ocean environment, is sponsored annually in Houston, Texas, by 12 international engineering and scientific societies. This year's OTC, the seventh, will be held May 5-8 at the Astrodomain, and will be the largest in its history. The technical program for the first meeting in 1969 consisted of 100 papers, an exhibit display of 380 booths, and an attendance of 4300. This year. 280 technical papers are to be presented, and more than 2800 exhibit booths, representing some 1200 companies and nine countries, will be on display for an anticipated audience of 40,000.

Jan 4, 1975

OFFICERS AND DIRECTORS For the year ending February, 1935 PRESIDENT AND DIRECTOR HOWARD N. EAVENSON PITTSBURGH, PA. PAST PRESIDENTS AND DIRECTORS SCOTT TURNER WASHINGTON, D. C. FREDERICK M. BECKET NEW YORK, N. Y. VICE-PRESIDENT, TREASURER AND DIRECTOR KARL EILERS NEW YORK, N. Y. VICE-PRESIDENTS AND DIRECTORS EUGENE MCAULIFFE OMAHA, NEB. PAUL D. MERICA NEW YORK, N. Y. HENRY KRUMB SALT LAKE CITY, UTAH EDGAR RICKARD NEW YORK, N. Y. LOUIS S. CATES NEW YORK, N. Y.

Jan 1, 1934

By Edel Moldenke

Burma has long been known for its ruby, tungsten, and tin deposits, and, lately, for having the largest lead-zinc mine in the world, the Bawd-win mine of the Burma Corpn. All the coal used, however, is imported from Calcutta; this is a bituminous coal of about 11,000 B.t.u., 24 per cent. ash, and costs about $8 per ton. Bituminous coal has not, thus far, been found, but many lignite deposits are known. The most promising lignite deposits are in the Namma field, Fig. 1, situated in the Northern Shan States of Upper Burma, about 30 mi. south of Lashio, the terminus of the Burma Railway, 750 mi. north of Rangoon. The

Jan 1, 1922

By W. Rosotoker

Using an expression for the free energy of a homogeneous phase as a function of composition, a relationship is derived which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. Comparisons between observed and calculated phase boundaries in the systems Fe-Ni, Fe-Mn, Fe-W, Ti-Mo, and Ti-Cb are presented. IT is the purpose of this paper to illustrate how the general free energy equations for two phases in equilibrium may be used to derive an expression which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. The free energy per gram atom of a disordered solid solution may, for many purposes, be represented by the equation:' F = ½NZ [C-V,, + (1-C) VbB + 2C (l-C)V] + K(T) +RT[C-lnC+ (l-C)ln(l-C) ] [1] where N is Avogadro's number; Z, the coordination number; C, the concentration of the solute element in atomic percent; the subscripts refer to concentrations at phase mixture boundaries; VAA, VBB, and V,, are the bond energies between like and unlike adjacent atoms, respectively, at the interatomic spacing characteristic of the phase. The bond energies are usually assumed to be independent of small changes in the lattice parameter occasioned by solute additions and variations in temperature; V = VAB ---------------—— ; K(T) is the sum of the heat con- tent and heat entropy; R, the molar gas constant; and T, the temperature in degrees Kelvin. The free energy of a homogeneous phase is there- fore the sum of an internal energy, a specific heat, and a configurational entropy term, respectively. The compositions of two phases in equilibrium at a given temperature are governed by the minimum total free energy principle. Graphically, this is represented by the points of tangency of the tangent common to the free energy vs. concentration curves of the two phases. Analytically, this may be expressed as: ( df) = (df) [2] dc dc Expanding both sides using eq 1, the following equation is obtained after convenient readjustment of the terms: RT In[(ca)(1-c)]-½N (Vaa-Vbb)(Za-Zb) +NV [Za(l-2Ca)-Z,(l-2C,)] [3] The following assumptions have been made at this point: 1—The specific heats of the two phases are independent of composition variations within the range under consideration. Accordingly, the K(T) terms disappear on differentiation. 2— (Vaa)o = (VAA); (VBB). = (VBB); Va = V, Theyjustification for these assumptions can lie only in the successful application of the resultant equation. It may be noted that Zener2 has used assumption 1 in the calculation of the boundaries limiting the (a+j3) phase mixture in the Cu-Zn system.

Jan 1, 1952

By O. U. Bradley

The methods of handling the oil output of the Mid-Continent fields are not unlike those practised in other oil fields of the United States, and it is not expected that this paper will present any entirely novel ideas. Some features of the practice of handling this oil may be of interest, however. Wooden Gaging Tanks Practically all of the oil sold to pipe line? and other purchasing agencies throughout the Mid-Continent field is gaged from wooden tanks. Steel gaging tanks are slowly coming into use, and are preferable in many ways—leakage and evaporation are reduced, and the strapping and recalculation of capacities are unnecessary. The wooden tanks are slightly coned to facilitate tightening the hoops. The sizes in common use are 250, 500, 800 and 1600 bbl. The number and the capacity of the gaging tanks upon any producing oil property depend upon its production, and the facilities for disposing of the output. The 1600-bbl. size was the most common in the Cushing field, particularly during the period of flush production. The tanks are distributed over the leased premises in groups of two, three, and four tanks each, and these are filled from flow tanks, or through direct pipe connections with the heads of the wells. Flow tanks are merely temporary reservoirs to facilitate the transfer of oil from the wells to the gaging tanks. They diminish fire risk, and are considered indispensable on small producing properties where water is pumped with the oil, as they permit the refuse and water to 'settle out before the production is run to the gaging tanks. strapping and Calculations After a gaging tank has been strapped (measured) and its contents computed, a deduction of 3 per cent. is made from its computed volume. The strapping of a tank requires four steps: (1) The outer circumferences

Jan 1, 1920

By Brian F. Dyson

The surface tensions at 1550°C of some Fe-S alloys (in the range 0.008 to 0.052 wt pct S), Fe-Sn alloys (0.31 to 48.4 wt pct Sn), Fe-P alloys (0.038 to 2.38 wt pct P), Fe-Cu alloys (2.15 to 22.8 wt pct Cu), and Fe-1 pct C-S alloys (0.005 to 0.076 wt pct S) along with the surface tension of the base iron have been measured by the sessile-drop method. A mean value of 1754 dynes per cm was found for the surface tension of the base iron. Sulfur was found to be highly surface-active, the surface-tension results being in quantitative agreement with existing data. Tin and copper were found to be less surface-active than sulfur while phosphoms was completely nonsurface-active. The surface tensions of Fe-1 pct C-S alloys were found to be lower than those of the Fe-S alloys containing the same sulfur content. This was shown to be a mmzifestation of the increase in the thermodynamic activity of suZfur by carbon. It is only in recent years that attempts have been made to measure the surface tension of liquid iron of known high purity.1-3 Earlier measurements4-7 were made on liquid iron containing variable amounts of what are now known to be surface -active solutes. The exact value of the surface tension of liquid iron is still, however, open to some doubt. Halden and Kingery' reported a value of 1720k 34 dynes per cm at 1570°C, Kozakevitch and Urbain8 gave 1790k 25 dynes per cm at 1550°C, while Van-Tszin-Tan et al. obtained a value of 1865k 37 dynes per cm at 1550°C. The first systematic investigation into the effect of controlled solute additions on the surface tension of iron was made by Halden and Kingery.' They showed that sulfur and oxygen were highly surface-active, whereas nitrogen was only slightly active, and carbon inactive. A subsequent investigation by Kingery indicated that two other group-6B elements, selenium and tellurium, were also surface-active. This highly surface-active nature of sulfur and oxygen has recently been substantiated by Kozakevitch and Urbainla and Van-Tszin-Tan et al. l1 Kozakevitch and Urbainl2 have also conducted an experimental survey of the effects of a number of metals on the surface tension of liquid iron. Their surface-active nature was, in all cases, less than that of the group 6B elements. The present investigation was undertaken to study in more detail the surface tensions of dilute Fe-S alloys and to measure the surface tensions of binary alloys of iron containing phosphorus, copper, and tin. The effect of sulfur additions on the surface tension of Fe-1 pct C alloys was also determined. EXPERIMENTAL PROCEDURE The sessile-drop method was employed in the present investigation. An apparatus was built similar in principle to that described by Humenik and Kingery.lS It consisted of a horizontal silica tube, which could be evacuated to pressures less than 10-5 torr, with its central portion surrounded by a water jacket within which was a high-frequency coil. This generated heat in a tantalum susceptor placed inside the silica tube, which in turn radiated heat to the specimen mounted on a recrystallized alumina plaque. Temperatures were measured by an optical pyrometer and photographs of the molten drop were taken on a fixed-focus plate camera giving a magnification of X2. Surface-tension values were determined from the resultant drop using the method described by Baes and Kellogg.l4 The high vapor pressure of molten iron made it necessary to conduct all the experiments under a 1/4 atm of argon (greater than 99.995 pct purity). The analysis of the base iron used in the investigation is given in Table I. Each sample was approximately 3 g in weight and had a hemispherical base to ensure a uniform advancing contact angle on melting. The iron alloys were prepared individually in the sessile-drop apparatus by drilling a hole in the top of each sample and adding the required amount of solute, the drops being analyzed after the experiment. This method of preparation had the advantage of ensuring a consistent minimal contamination by oxygen due to refractory attack and also allowed surface tension to be measured at the same time. Every precaution was taken to ensure that the specimen was not contaminated by grease when it was introduced into the apparatus, the samples being cleaned in acid, dried in alcohol, and rinsed in petroleum ether. All handling was done with tweezers. Once the specimen had been placed inside the susceptor, the furnace was evacuated and the Sample leveled. The furnace was then degassed at approximately 1000"C before the argon was introduced. In every case the surface tension was determined at 1550" C.

Jan 1, 1963

By E. S. Anolick, Joseph Singer

The magnetic after-effect, in the form of time decay of permeability (l/µ), has been used to obtain independent data on the solubility of' carbon in pure iron. The results differ slightly from the solubilities obtained through internal -friction experiments. The mechanism of the time decay being the magnetic analogue of internal friction, it appears necessary to explain the observed discrepancies, and some suggestions are made. THE purpose of this work was to establish the reliability of the time decay of permeability as a measure of dissolved interstitial in the body-centered-cubic lattice, and further, to establish techniques suitable for such measurements with samples of a form convenient for various other measurements. This particular sample form was the "epstein" strip, i.e., 25 cm by 3 cm by 0.035 cms. While the general conclusions are not limited by this geometry, there are two aspects of the samples that may be relevant: a) texture, and b) grain size, which ranged generally from 1 to 10 mm. Effects due to these two possible parameters were thought to be small and were not investigated. Calibrating the time decay technique and the other experimental procedures by measuring the solubility of carbon in pure iron suggested itself because of the accumulation of data on this subject through the related technique of the internal friction'; The essentials of this report have been published in a somewhat condensed form.5 Since then some additional data have been taken. It is the purpose of this paper to add these data and to provide more complete description of the experimental techniques than was possible then. The time decay of permeability is a form of the magnetic after-effect.6,7 Permeability is measured immediately after demagnetization (µº) and also long after (µ8). The time decay, ?(l/µ), is the difference 1/µ8 - 1/µ0 and has been considered to be proportional to the concentration of a dissolved interstitial6,8,9,12 The relaxation time! 7, is characteristic of a particular diffusion, and affects the permeability as follows: where he being the activation energy for diffusion of the interstitial. Reference is made to the works of snoek6 and Neel7 for a complete discussion. A brief exposition of the principal ideas may be in order here, as follows. On the basis of the simplest model, resistance against domain wall motion increases with time after demagnetization due to the diffusion of interstitials to preferred sites created by the magnetostrictive tetragonolization under the strong magnetic field. Thus permeability, measured with a small field after the abrupt removal of the large field, will continuously fall with the process of diffusion of the interstitials, and the total "time decay" (or "time decrease") should be proportional to the amount of interstitial in solid solution. In the present report, use is made only of the total time decay rather than of the nature of the progress of the decay; the only problem involved in this approach is the need for assurance that only one interstitial is contributing to the effect as used. It is felt that the special use made here of the total time decay warrants the conclusions. Other work has been going on elsewhere on the detailed study of the nature of the time decay.8'9 EXPERIMENTAL A) Materials—12-lb ingots were made in a vacuum furnace from high-purity iron and by a series of hot and warm reductions were brought down to 14-mil strip. This was cut into 25-cm epsteins. The pure iron was decarburized at 750 °C by hydrogen. The time decay measurement for the decarburized iron (see below) indicated a satisfactorily low starting level of interstitials. Grain growth to grain sizes of 1 to 10 mm was produced in the pure iron by a 700" anneal in hydrogen after a critical reduction of about 7 pct as suggested by previous trials. No measurement of texture in the pure iron was made. The grain size was taken to be large enough to be beyond any sharply critical size regarding solubility. B) Infusion of Carbon—Since the permeability measurement required about two dozen epsteins, a special method of carbon infusion had to be developed to ensure homogeneity of infused carbon. This was accomplished by setting the samples edgewise in a

Jan 1, 1961

By L. R. Raymond, J. L. Hudson

This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well-bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time. Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed pertneability value. From the slope of the injection-rate curve. a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result. Graphs of pressure and injection rate us functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can he used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested. The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility. INTRODUCTION To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimu- lation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists. Several techniques for determining reservoir transmissi-bility from well tests have been presented in the literature. 1,2,3,4 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry Out. and this paper contains the first available method for the analysis of constant-pressure well tests. Determination of wellbore damage from transient well tests has been the subject of several papers."" From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage. All previous studies of well testing to determine wellbore damage have been based on the two-zone perrneability model. In this model the damaged zone has a permeability k,, extending to a radius r,,, and the formation permeability k obtains from r, to the drainage radius r,.. Consequently, there is a discontinuity in permeability at r = r,,. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests. ANALYSIS OF CONSTANT-PRESSURE WELL TESTS The mathematical analysis associated with the injection of fluid at constant wellbore pressure into a single-zone, horizontal reservoir completely filled with a fluid of small and constant compressibility and constant viscosity is given in Appendix A. In this analysis it is assumed that the well is located at the center of an undamaged, circular drainage area. From this analysis, the formation permeability can be obtained as follows. 1, Estimate a value for the formation permeability k. 2. Prepare a plot of injection rate q vs

Jan 1, 1967