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By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

Extremes in temperature and weather, along with the highly corrosive nature of acid leach solutions used at open-pit copper mines, necessitates the use of pipeline systems that are both corrosion resistant and impervious to the environment.

Jan 6, 1976

By W. C. PAGE

AS the pioneer operation treating the mixed lead- zinc-iron ores from the district tributary to the Salt Lake Valley, the International Smelting Co.'s plant has offered an extremely interesting and instructive opportunity to study some phases of this problem. Basically, there were two main reason for our attempting to work out a successful operation for the separation and concentration of the values contained in the rather widespread deposits of these so- called lead-zinc ores. In the first place, the time was ripe and demanded some method of curtailing the economic waste resulting from the costs of past and present practice of smelting ores of this character, or rather, those ores which could stand the charges inherent with smelting them. Secondly, but rather primarily with us, we believe that such a solution would greatly in- crease in general the production of lead in the district tributary to the Salt Lake Valley. It is generally known that there were and are three relatively large lead smelting plants in the Salt Lake Valley and the decreasing production of correspondingly clean lead ores was not efficient to justify the existence of all three. We could not hope for better lead smelting metallurgy nor more efficient business management than was being practised, so the only prospect was to at- tempt to work out some way to increase the primary production and thus widen the scope of operations.

Jan 1, 1926

By C. A. Stickels

A heat of electrolytic iron, to whzch alunzinutn and nitrogen had been added, was hot-rolled, cold-rolled 90 pct, and recrystallized at temperatures from 500" to 700°C. Primary recrystallization textures appear to arise from competitive growth of two types of nuclei: 1) those having orientations belonging to the "usual" primary recrystallization texture found in riming steel, and 2) those with the {111} (110) ovientation. Development of a (111}(1 10) component in the primary recrystallization texture occurs only over a certain interval of isothermal recrystallizatzon temperatures when the material is supersaturated with respect to the precipitation of AlN. Lowering the degree of supersaturation depresses the temperature interval in which a (111)(110) component occurs. An elongated, 'pancake-shaped" recrystallized pain structure and a marked delay in the start of recrystallization were found in all specimens which were supersaturated with respect to A1N precipitation after cold work, regardless of their recrystallization texture. ONE of the consequences of killing low-carbon steel with aluminum is a significant change in recrystallization behavior. About 15 years ago, Solter and eatttiel showed that this behavior was largely controlled by aluminum and nitrogen in the steel. If complete precipitation of A1N was prevented before cold rolling, an increased "recrystallization temperature" was observed in subsequent. annealing, and the recrystal-lized grains were not equiaxed. Leslie et a1.2 studied this phenomenon in some detail and clearly demonstrated the relationship between A1N precipitation, recrystallization kinetics, and the development of "pancake-shaped" grains. It has also been known for some time that aluminum-killed steels, processed to produce elongated "pancake" grains, develop a (11 I}( 110) primary recrystallization texture. This texture has not been found in iron or low-carbon rimming steel as a primary texture4j5 but has been observed following grain growth in electrolytic iron.5 The present work was undertaken to study in more detail the effect of A1N supersaturation on recrystallization textures in iron. LITERATURE REVIEW The deformation texture in heavily rolled iron has been studied in detail by Bennewitz.~ The texture consists primarily of a partial fiber texture about a (110) axis in the rolling direction, designated here as fiber texture A. It includes the range of orienta- tions (111)[110] - (001)[ 110] - (11l)[110]. A weak secondary texture also is present.6 This is a duplex partial fiber texture about two (110) fiber axes located 60 deg from the rolling direction and 30 deg from the sheet normal. The range of this texture, designated here as fiber texture B, about the [101} fiber axis is (112)[110] - near (545)[252] - (211:1[011] *The range given here follows Bennewit~.~ A few pole figures from re-crystallized material indicate a broader range than this.' However, the components which are strongest in the recrystallization texture are in this range.'________________________________________________________ Primary recrystallization textures in unkilled steels can be accounted for by growth of members of fiber texture B present in the deformed metal.5 However, while members of fiber texture B dominate the primary texture, other orientations survive primary recrystallization as well. In particular, some {111}(110) members of fiber texture A must also grow during primary recrystallization, because a well-defined {1ll)( 110) texture develops during subsequent grain growth at 700°C.5 The unusual recrystallization behavior of deformed supersaturated solid solutions has been attributed to: 1) retention of the solute in solution,' 2) formation of coherent, preprecipitation solute clusters prior to and during re~r~stallization,~ and 3) formation of a precipitate prior to and concurrent with recrystallization.'~-'~ When aluminum is supersaturated with iron, the difference in grain boundary mobility between general high-angle boundaries and certain special coincidence site boundaries is apparently eliminated.' In aluminum-killed steels, precipitation of A1N can take place at ordinary subcritical recrystallization temperatures. The rate of precipitation increases with increasing aluminum or nitrogen contents.2'13 There is some doubt, however, as to whether true precipitates form during the time at temperature needed to complete recrystallization. Leslie ef a1.2 found that precipitation in one steel was complete after about 100 min at 700GC, or after about 1000 min at 650GC, as measured by chemical analysis for AlN. Aoki et a1.,13 using internal friction for dissolved nitrogen, showed that a large fraction of the dissolved nitrogen was removed from solution within a few minutes annealing time at temperatures from 400" to 800°C. However , the rate of formation of AlN, as detected bv chemical analvsis. was much slower than the apparent rate of nitrogen removal. Hasebe,'~~ using carbon extraction replicas, has identified A1N precipitates by electron diffraction in a 0.2 C steel, solution-treated at 1300°C and annealed 2 hr at 700°C. Borchers and kim,I6 also using a replication technique, observed precipitates after annealing treatments as short as 2 min at 640°C. However, Leslie et a1.' state that no A1N precipitate can be seen while recrystallization is being inhibited in aluminum-killed steel.

Jan 1, 1967

By J. F. Smith, J. E. Davison

A value for the enthalpy of formation of z2 of -3.14 i 0.21 kcal per g-atom has been measured by the technique of acid solution calorimetry. This result is in quite good agreement with two earlier determinations by tin solution calorimetry and by direct reaction caloriinetry, and averaging of values determined from the three independent calorimetric techniques gives enhanced precision and accuracy with AHh8 (CaMgZ) = - 3.15 i 0.05 kcal per g-atom. For comparison with experimental data, values for the enthalpies of formation of CaMgz, SrMgz, and BaMgz of -9.8, -7.9, and -2.8 kcal per g-atom were estimated from a calculation based on the LVigizer-Seitz approximation as modified by Raimes for polyvalent elements. While complete quantitative accord between these calculated talues and available experimental data is lacking, nonetheless numerical accord is better than might be expected and, more importantly, parallel numerical trends are observed between experimental and calculated vnlues. WITHIN the past decade the enthalpy of formation of CaMg, has been determined a) from measurement of magnesium vapor pressures over binary Ca-Mg alloys,' b) by solution calorimetry with liquid tin as the solvent,' c) from measurement of hydrogen vapor pressures over ternary alloys of calcium, magnesium, and hydrogen,3 and d) by direct reaction alorimetr. The value from tin solution calorimetry is the most precise and is probably the most reliable, and this value is within the quoted uncertainties of the other three experimental results. The overall agreement among the four independent investigations is quite good, particularly so when the diversity of techniques is noted. On the basis of this agreement, CaMgz was chosen as a test material to evaluate the operation of a newly constructed apparatus for the determination of enthalpies of formation of intermetallic phases by acid solution calorimetry. This was believed to be a severe test because of the high chemical reactivity of both calcium and magnesium which reactivity presumably accounts for the fact that an early determination5 of the enthalpies of formation of Ca-Mg alloys by acid solution calorimetry yielded values significantly more negative than the four recent determinations. EXPERIMENTAL APPARATUS AND MATERIALS Experimental Apparatus. The enthalpy of formation of CaMg, was determined by measuring the difference between the heat evolved when dissolving the metallic compound and the heat evolved when dissolving equivalent amounts of unreacted metallic elements in hydro- chloric acid. This was done differentially with an apparatus consisting of twin calorimeters which were constructed to be as nearly identical as possible. The advantage of differential calorimetry is that systematic errors arising from the individual calorimeter design tend to cancel. A schematic representation of the apparatus is shown in Fig. 1. A dead air space around both calorimeters was provided by a large, thermally insulated jacket. Each calorimeter consisted of a 2-liter Dewar flask which was completely enclosed in a copper container. Each Dewar contained 1600 g of 2.5hr HCl to act as the solvent, and thermal effects resulting from solvent evaporation were minimized by covering the acid with 50 g of mineral oil. There was no detectable reaction between the acid and the mineral oil. Equivalent amounts of mechanical energy were added to the calorimeters through twin stirring rods which were driven at the same rpm by a single motor with the intent of the stirring being to maintain thermal equilibrium throughout the solvent. To calibrate the heat capacities of the calorimeters, known amounts of electrical energy could be added by passing measured voltages and currents for known times through submerged heaters, approximately 20 ohms, which were wound noninductively from Manganin wire. A 6-v storage battery was used as a power source, and a dummy heater was used as an exercise circuit to allow the battery to stabilize at a constant electromotive force before energizing one or the other of the calorimetric heaters. A type K-2 potentiometer was used to measure the potential drop across an energized heater while the current was determined from the potential drop across an external standard resistor. Times of energization were measured with an electric timer, and the electrical energy supplied to a heater

Jan 1, 1969

By E. L. Tucker

PREVIOUS investigations of E. L. Tucker and R. E. Head' related in particular to the effect of cyanogen compounds on galena, sphalerite, and pyrite, and their behavior in the presence of such com- pounds. The present contribution deals with the float- ability of the copper minerals and of pyrite. All experiments were performed on minus 200-mesh material, the method of preparation being the same as that described in the previous article. Flotation tests were made in a small mechanically agitated machine of 50-g. capacity designed in this laboratory by Gates and Jacobsen." General Naval Stores pine oil No. 5 and potassium xanthate were used in constant amount in all of the experiments; these agents were selected because of their present wide use in the flotation of copper minerals. Lime additions were varied to secure four 'final hydrogen ion concentrations, namely, neutral, 0.0005 per cent CaO, 0.003 per cent CaO, and 0.02 per cent CaO. The variation in lime addition was introduced to include the range of alkalinities employed in actual flotation practice.

Jan 1, 1926

By W. R. Hibbard

Evidence is presented which confirms previous findings that models of solution strengthening depending solely on lattice parameter changes are incomplete. Direct evidence for the Suzuki interaction of chemical effects was obtained from alloys with constant lattice parameter, for which solution strengthening was nearly independent of temperature from 300° to 20°K. SOLUTION hardening principles have been reviewed recently by Parker and Hazlett.' In addition, the interactions of dislocations and solute atoms were reviewed by Cottrell.' It is not proposed to review this information again here, but to refer only to those details which are pertinent to the developments which have occurred since these papers were published. Literature Survey To set the stage, it has been known for some time that solid solutions are stronger than the pure parent metals, and that the strength increases with increasing amounts of alloying element. One of the most extensive earlier investigations was that of Lacy and Gensamer,3 who reported that the solid solution strengthening of iron is a power function of the composition, that the relative strengthening is a function of the solubility limit, and that the rate of strain hardening is a function of the amount of solution hardening. Thus, the slope of the plastic portion of the stress-strain curve increases with increasing yield strength. An approach to the development of principles resulted from work by Gulyeav,4 who reported that the strengthening effect of solid solution alloys is periodic in character when plotted as a function of the atomic number of the solute. A more quantitative approach was to relate the amount of solution hardening to the lattice parameter of a solid solution. This was done quite early by Norbury,5 and later by Brick, Martin, and Angier,6 Frye and Hume-Rothery,7 and French and Hibbard. This relationship is only approximate in character. The next development was to relate the amount of solution hardening to lattice stress, as proposed by Frye and co-workers.9 They calculated what they called ionic overlap from the lattice parameter changes represented as a change in volume, using Bridgman's hydrostatic compression equation. The resulting correlation was somewhat improved as compared to the simple correlation with lattice parameter. The next step was carried out by Dorn, Pietrow-sky, and Tietz,10 who suggested an effect of valence differences in addition to the effect of lattice parameter. Their proposed parameter shows flow stress as a single valued function of the concentration and a relationship involving these two atomic variables. In addition, they contributed new data on the temperature dependence of solution hardening which indicated that it was a strong function of temperature for aluminum alloys. Allen, Schofield, and Tate11 carried the valency effect even further by reporting data indicating that with a given solvent element the stress-strain curve is a function of electron density, entirely neglecting the size factor, which varied by a factor of two. This evidence led to a quantum mechanical calculation by Cottrell, Hunter, and Nabarro,12 based on the formation of a dipole around an edge disloca-

Jan 1, 1959

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.

Erwin S. SperRy, Bridgeport, Conn.: The analysis of refined copper is a subject of great importance, and has not received the attention it deserves. Copper metallurgists, therefore, will welcome the paper of Mr. Heath with satisfaction. The state of the art of the chemical analysis of copper has been such that consumers, if they could not afford to run any risk, have been obliged to buy copper from the smelter having the best reputation, and a specification for copper to meet certain requirements could not be drawn up by the mere giving of the chemical constituents. Mr. Heath has brought the analysis of the copper to such a state that when a specification calls for copper " equal to Lake copper " one will know immediately what percentage of the pure metal to expect. It seems to be a pretty well established fact that the copper of Lake Superior is practically free from antimony and bitmuth ; and, with the exception of arsenic, the other elements are easily separated from copper by electro-deposition in an acid solution. The authorities differ in regard to the question whether antimony is deposited with the copper in an acid solution. Classen* recommends the employment of a solution containing 10 per cent. of free nitric acid, sp.gr.1.21, and the strength of the current from 0.3 to 0.4 ampere, in order to prevent the other metals from being deposited with the copper; and for this reason, I presume, the method has been generally used. I, myself, have been accustomed to use such a solution for the analysis of copper-alloys, but have found that for such alloys only a small quantity of nitric acid is necessary, if sulphuric acid is present in sufficient amount to give the solution the required conductivity.

Jan 1, 1898

By E. F. Johnson, F. H. Brinkman, H. J. Welge, S. P. Ewing

This paper presents a method for predicting the manrler in which oil will be displaced from a porous body by enriched gas. The calculations apply to a gas rich enough to give a partially, but not a completely, misci-ble displacement. The method — a three-component, two-phase analysis — takes into account condensation of some of the intermediate hydrocarbons from the injected gas into the oil, as well as enhanced volatility of heavier hydrocarbons at elevated pressures and temperatures. The condensation swells the oil and decreases its viscosity, thus aiding in its recovery. The calculations have been extended to apply to actual crude oil-natural gas systems by arranging the components into three groups according to their volatility. As an approximation, each group is then treated as a single component in the analysis. The influence of an angle of dip for an inclined displacement is also taken into account. The recovery predictions are corroborated by experiments which used both consolidated sand cores and un-consolidated glass beads. In some of these tests, actual live crude oil was displaced by a multicomponent gas typical of enriched gases used in oil fields. INTRODUCTION This paper presents a method for predicting the amount of oil that can be displaced from a homogeneous, linear, porous body at various stages during the injection of enriched, or "wet", gas. The porous body can be in either a horizontal or an inclined position. 'This type of displacement is sometimes known as condensing gas drive The method is developed especially for the case in which the injected gas is enriched enough to be partially, but not completely, miscible with the reservoir oil. The need for a calcula-tive procedure for this type of operation is emphasized by the number of field projects where completely miscible drives are not practical, but where near-miscible conditions are feasible. The factors taken into account in the predictive calculations include: (1) the condensation of gas components into the oil, with a resulting increase in oil volume; (2) the lowering of oil viscosity by the addition of lighter ends from the gas; (3) the increase in oil volatility at high temperatures and pressures; and (4) the physical displacement of the oil by the gas. The techniques developed in the paper can be extended to other nonequilibrium displacement processes. Other such processes that we have analyzed include a displacement by lean gas which stripped intermediates from the oil, and a water flood in which the water con. tained in solution a substance somewhat soluble in the oil. ANALYSIS OF ENRICHED-GAS DRIVE GENERAL PRINCIPLES Our method for predicting the amount of oil that can be displaced by an enriched gas uses an analogy between a three-component and a multicomponent system.' The predictive method is based on these assumptions: (1) constant, or nearly constant, pressure; (2) complete equilibrium by diffusion perpendicular to the main direction of flow, but no significant mixing along the direction of flow; (3) constant injection velocity; and (4) flow in a linear porous body. The composition of a liquid or a vapor with respect to three components can be plotted on a three-component, or ternary, diagram like that in Fig. 1. Let Point A represent the composition of the oil originally in place. In this case, Oil A is undersaturated with gas. If Point A lay on the equilibrium Curve BF, the oil would be saturated. In the extreme case where the original oil contained no intermediates or dissolved gas, Point A would lie at the lower left-hand corner of the ternary diagram. In a displacement of Oil A by Gas D, there will be a progressive change in the composition of the oil phase as more and more gas is brought into equilibrium with the oil. The end result of this progressive change is an oil having the composition represented by Point F. This oil is richer in intermediate hydrocarbon and methane than the original oil and, therefore, has a greater forma-

By Strathmore R. B. Cooke

That calcium will activate quartz for flotation with anionic collectors such as soaps has been known for a number of years,1 2 3 and the method has been applied to the concentration of various iron ore 4 5 6 as well as to other materials. Clemmer gives the permissible pH range for the activation of quartz by calcium as between 9.5 and 12.5 with an optimum value of 11.0, and Hertzog7 has determined the calcium abstraction of iron ores and of Ottawa sand, but otherwise little quantitative data are available. The purpose of the present investigation was to determine those conditions under which dilute solutions of calcium chloride will activate quartz for anionic flotation and to determine the amount of calcium ion adsorbed by quartz. Those variables, the influence of which was primary, such as calcium, sodium, and hydrogen ion concentrations, were studied. Other factors which influenced the results are discussed in the description of the experiments. Three different experimental methods were used to determine the activation of the quartz. The first method was to treat a sample of ground, deslimed quartz with solutions of calcium chloride and sodium hydroxide, and to determine the calcium adsorbed by chemical analysis of the solution. Ad- vantages are that a direct value for the

Jan 1, 1949

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi's solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith' have applied Raimondi's solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,' Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By Gill Montgomery

At this moment in the history of the world, the all- pervading and universally most important fact is that the world population is beginning to outgrow its food supply, and the United States has suddenly lost its ability to give away huge food surplus to any nation in the world with a food shortage problem. This, of course, means that, all of a sudden, our government must completely reverse its former bureaucratic stance regarding crop controls and agricultural price supports, to out-right incentives to increase farm production and bring more idle land into food-growing use.

Jan 2, 1967

By H. A. BURK

THE ores of the Tonopah, district are hard, compact and' highly siliceous. They contain from .1 to 2, per cent. of sulfide material, of which argentite is the valuable mineral; occasionally pyrargyrite is found in the richer ore. The sulfide is, chiefly pyrite with small amounts of chalcopyrite,. and sometimes sphalerite. The ore also contains a small amount of gold-about 1 per cent. by weight of the silver present. The major gangue constituent is quartz but frequently considerable rhodonite-called by the miners pink manganese-is present. For primary crushing, jaw and gyratory crushers are used. These crushers are of such capacity that, in most cases, one 8-hr. shift will supply the mill for 24 hr. The Extension Co., at the Victor ore house, passes the ore through a 13 by. 24-in. Blake type McFarland crusher set at 13 in., and at the No. 29 re house, a 14 by 24-in. Blake type Traylor crusher is used. The ore is thus crushed to stamping size in one reduction. The capacity of each crusher is about 40 tons per hr.; the power consumption is 0.6 kw. per ton.

Jan 1, 1921

By B. H. Kear, S. M. Copley

A dynamic theory of precipitation hardening in alloys containing cohevenl, stvess-.free, ordered particles is developed. The yield stvess is predicted from the stress dependence of the plastic strain vale, which is related to a derived dislocation velocity-stress function. The theory is shown to predict the magnilude and temperature dependence of the yield stress of a commercial nickel-base superalloy as well as many details of its slip structure. GLEITER and Hornbogen have developed a theory of the yield stress in alloys hardened by coherent, stress-free ordered ptrticles based on the observation that dislocations (b = a/2 (110)) glide in pairs.' When a dislocation pair shears through an ordered particle, the glide motion of the leading dislocation is impeded since it must create antiphase boundary (APB), whereas the motion of the trailing dislocation is assisted because it annihilates APB produced by the first one. Taking into account the APB energy, the size, and spacing of the particles, G-H predict the observed yielding behavior in Ni/18.8 Cr/6.2 A1 alloys composed of a matrix phase y '(nickel-solid solution) and particles of y' (basically Ni3A1). The G-H theory, as well as all previous theories of hardening by coherent ordered particles, do not include the details of dislocation motion; the present dynamic theory is an attempt to overcome this limitation. In the dynamic theory, the yield stress is predicted from the stress dependence of the plastic strain rate, which is related to a derived dislocation velocity-stress function. This function can be evaluated if the structure of the alloy, the APB energy of the ordered phase, and the characteristic drag or frictional stresses of the matrix and precipitate phases are known. The theory is shown to account for the observed temperature dependence of the yield stress in a commercial nickel-base superalloy. 1) NICKEL-BASE SUPERALLOYS Although their compositions are complex, the nickel-base superalloys have remarkably simple structures. A detailed examination of the commercial superalloy

Jan 1, 1968

By CHARLES R. KETES

I. INTRODUCTORY. Lake Valley, New Mexico, has long been one of the most widely known mining districts of southwestern United States. For many years its silver-mines have been among the most famous of the country, visited by many mining men and geologists; yet little information regarding the origin of the ore-deposits and the influencing geologic conditions has found its way into print. With the recent revival of public attention, after a decade and a half of utter stagnation, to the mining of silver in the Southwest, special interest attaches to the genesis and geologic disposition of the ore-bodies which are so finely open to inspection in the Lake Valley district. Moreover, the local features here described are typical of the conditions existing over a much larger field. The fact that the ores are chiefly the chloride and the chloro-bromide of silver adds further interest. Data bearing upon the genesis of haloid ore-deposits are, at the present time, very much sought. Arid regions offer particularly favorable conditions for the formation of such ores. This New Mexican district appears to supply solutions to many problems concerning this class of ores, which have long vexed the student of ore-deposits. II. LOCATION AND HISTORY. The town of Lake Valley is situated in Sierra county, in the southwestern part of New Mexico, and 100 miles northwest of El Paso, as the crow flies.From a mining standpoint, the location of the place is itself suggestive, as it lies on the southeastern slope of the great quaquaversal arch of the Colorado plateau. The center of this vast dome is in north-central Arizona, and radii about 150 miles in length reach its foot in all directions. Around its basal margins runs the broad mineralized belt containing most of the great mines of the Southwest, which extends from south-central Colorado southward and southwestward through New Mexico, thence westward through Arizona, northwestward and northward through southeastern California and western Nevada, and, finally, eastward through Nevada and Utah into Colorado again. This great mineralized belt is important as geographically limiting profitable mining over the greater part of five States.

Jan 1, 1908

By P. L. Hendricks, J. W. Spretnak

The interstitial atom principally responsible for the yield point and strain aging in electron-beam-melted tantalum is identified by analysis of the kinetics of the return of the yield point after an increment of plastic deformation. Two sets of specimens contained two levels of oxygen with very low hydrogen contents and the third set had comparable oxygen and hydrogen contents. The activation energy for the return of the yield point agrees well with that for diffusion of oxygen for the first two sets of specimens. For the third set of specimens, the activation-energy value lies between those for diffusion of hydrogen and for diffusion of oxygen. The advent of the dislocation model of plastic deformation in metals has revitalized interest in the yield point and strain aging in bcc metals containing a certain minimum content of interstitial solute elements. Much theoretical and experimental work has been performed in recent years to elucidate the detailed mechanism of these phenomena. The purpose of this investigation is to attempt to identify the principal interstitial element responsible for the yield-point phenomenon in electron-beam-melted tantalum by analysis of the kinetics of the return of the yield point after an increment of plastic deformation. Some of the earlier theories of the yield-point phenomenon proposed a grain boundary film of iron carbide. Such models could not satisfactorily explain all features of strain aging and the yield-point phenomena. The most widely accepted explanation is that of Cottrell,1 later extended by Cottrell and Bilby.2 Strain aging is ascribed to "locking" of dislocations by interstitial solute "atmospheres". The yield-point phenomenon results when the dislocations are torn away from their atmospheres. The strain-aged condition is re-established after sufficient time to allow the interstitial atoms to diffuse to the dislocation lines and re-establish the locking atmospheres. Clearly, the Cottrell-Bilby model is concerned with the bulk of the grain and does not specifically involve the grain boundary. The recent modification of the Cottrell-Bilby model is a redirection of attention to the role of the grain boundary and the possibility of multiplication of a limited number of free dislocations rather than unlocking all of the dislocations. Theories have been advanced by Hahn3 and conrad4 which are modifications of the Cottrell-Bilby theory. The model proposed by Hahn indicates that, although the possibility of un- locking anchored dislocations is not excluded, it implies that unlocking is not necessarily required to explain yield drop. Locking of dislocations during the aging treatment is a necessary part of the theory; however, it assumes that dislocations once locked remain locked. It is suggested that the yield drop observed is a result of the following factors: 1) the presence of a small number of mobile dislocations initially, 2) rapid dislocation multiplication, 3) the stress dependence of dislocation velocity. In the case of bcc metals, locking is considered to be the means by which dislocations are immobilized. Cold working of the metal results in the generation of larger numbers of new dislocations and the stress dependence of the dislocation velocity accounts for yield drop observed. Conrad' has proposed a model similar to the one just described which applies to strain aging of iron and steel and which logically could be extended to other bcc metals. This model also does not require large-scale unlocking of dislocations. It is proposed that, during initial loading of a specimen below the upper yield stress, a few dislocations are torn free of their Cottrell atmospheres at regions of stress concentrations. With an increasing stress, some multiplication of dislocations occurs by a double cross slip mechanism, thus giving a preyield microstrain. At some critical stress represented by the upper yield stress, sudden profuse multiplication of dislocations occurs, enabling plastic flow to proceed at a lower stress. In this model, microstrain, preyielding, and flow represent the movement of free dislocations. It should be noted that this model also requires the locking of dislocations by interstitial solute atoms for the occurrence of a yield point; however, unlocking of large numbers of dislocations is not required. If it is assumed that the yield point will return when some fraction of free dislocations produced during pre-straining are pinned, the number of solute atoms required to pin unit length of a dislocation line can be calculated when prestrain and reloading are done at the same temperature and strain rate. Since the migration of solute atoms back to the stress fields of dislocation lines is controlled by the diffusion rate of interstitial solute atoms, it is to be expected that the activation energy for strain aging would be identical to the activation energy for diffusion. It would also be expected that the strain aging observed will be controlled by the fastest diffusing species capable of producing locking over the temperature range investigated. The rate of yield-point return has been found to be adequately expressed by an empirical rate equation of the form: rate=Ae-Q/RT [1] where A = constant, Q = activation energy, R = gas constant, and T = absolute temperature. Cottrell and Bilby2 have expressed the number of atoms per unit length of dislocation line which arrive

Jan 1, 1967

By C. Chamberlain

The Telfer Project, Australia's newest, largest, and most remote gold mine treats 480 kt of ore grading 9.33 g/t derived from open pit mining operations. Coarse gold is recovered by gravity concentration with jigs and further upgraded wing a continuous strake launder table, and by amalgamation. Remaining gold is recovered in a cyanide circuit and incorporates flat bottom air agitators, counter current decantation (CCD) and stellar filters for clarification and precipitate removal. Overall recovery into a bullion averages 98%. The mill incorporates a number of design features that allow for maximum efficiency and security wing a minimum number of operation personnel.

Jan 1, 1983

By D. Turnbull, H. N. Treaftis

Precipitation of tin from Pb-Sn alloys (lead-rich) occurs by the nucleation and growth of hemispherical cells which consist of tin lomelloe interspersed in the depleted solid solution. Nucleation and growth of these cells and the tin interlamellar spacing at various compositions and temperatures have been investigated. The interlamellar spacing increases approximately as the reciprocal of the logarithm of the supersaturation ratio. For constant initial tin concentration the concentration of cell nuclei increases with decreasing temperature to a limiting temperature-independent value. The kinetic results support the view that the cell growth rote is governed by the diffusion of tin along the cell boundary. In the main, the results confirm the authors' earlier deductions, drawn from resistometric and calorimetric data, about the precipitation mechonism. IT has been shown1, 2 that tin (ß) precipitates from lead-rich (a) PbSn solutions by the nucleation and growth of cells (cellular or discontinuous precipitation). These cells consist of tin lamellae, with a spacing 1, interspersed in a depleted a solution. Reorientation of a also accompanies cell growth. The kinetics of cellular precipitation of tin from lead have been measured by resistometric2, 3 and ca1orimetric1, 3 techniques. The time-transformation isotherms (t equals time; x, volume fraction of specimen transformed) of the initial rapid precipitation, which drains about 60 pet of the tin from solution, have been described by a kinetic law having the form x = 1 —exp (—bt n) [I] where n usually has the value 3.0. It was shown" that this law and the other kinetic facts can be explained satisfactorily if it is assumed that the cells grow at a constant rate and that all the cells nucleate in a time negligible in comparison with the period of cell growth before impingement. Thus, for hemispherical cells b = (2/3)pNG3 [21 where G is the rate of cell growth in cm per sec, and N is the number of cell nuclei per unit volume. The rapid rate of cell growth at low temperatures can be accounted for"' if it is assumed that the dissolved tin drains to the lamellae edges by diffusion along the sweeping cell boundary rather than by diffusion through the a crystal (volume diffusion). For cell growth governed by cell boundary diffusion it was shown, approximately G=2(X° - X° / X° ) DBA / l2 where A equals the thickness of the cell boundary; D R, the coefficient of diffusion of tin atoms within the boundary; and X° and X, are the atom fractions of tin in the supersaturated and saturated solutions, respectively. Zener8 had already shown that, where

Jan 1, 1959