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By H. A. Wahl

This paper presents methods of designing hydraulic fracture treatments in formations saturated with slightly compressible liquids. Howard and Fast describe the fluid-loss control resulting from the viscosity and compressibility effects of the reservoir fluid in terms of a fracturing fluid coefficient. However, for horizontal fractures, this coefficient is applicable to infinitely thick reservoirs. These methods of evaluating fluid loss from horizontal fractures during treatment differ from previous methods in that: (I) formation thickness is incorporated in the velocity function describing the rate of fluid loss to the formation; and (2) for a given thickness the relative position of the fracture to the horizontal boundaries of the reservoir or any interrnediate permeability barrier is incorporated in the design procedure. This theory is applied to several actual and hypothetical field cases. The results of these calculations demonstrate that the eflect of formation thickness on fluid loss from horizontal fractures may result in fractures several times larger than predicted by other methods. INTRODUCTION Hydraulic fracturing has been the dominating well-stimulation technique during the last decade. From the time it was commercially available, fracturing has had a very favorable success ratio compared to other stimulation methods. However, numerous wells that were successfully stimulated remained economic failures. Only in the last few years has the oil industry recognized the importance of designing treatments for each well which will yield the maximum profit. This implies that for a given set of treatment conditions the size and general physical characteristics of the fracture can be determined. One of the outstanding contributions in the field of fracture design was presented by Howard and Fast.' In their paper, three flow mechanisms that control fluid loss from the fracture to the formation are defined: (1) viscosity effects of the fracturing fluid, (2) viscosity and compressibility effects of the reservoir fluid, and (3) wall-building effects of a treated fracturing fluid. The rate of fluid loss to the formation adjacent to a fracture is shown to be a function of time. For each flow mechanism the velocity function v(t) is expressed as a constant or fracturing fluid coefficient divided by the square root of time. This form of v(t) can be used in the Carter equation, as developed in the Howard and Fasc paper, to estimate the areal extent of fractures. This equation may be written as In the following sections the effect of formation thickness on fluid loss from horizontal fractures is evaluated when the controlling flow mechanism is the viscosity and compressibility of the reservoir fluids. The major assumptions inherent in the Carter equation are brought out in subsequent mathematical developments. THE EFFECT OF RESERVOIR FLUIDS ON FRACTURE EXTENSION When a fracture treatment is performed using a fracturing fluid identical to the reservoir fluid, the only flow mechanism controlling fluid loss is the viscosity and compressibility effects of the reservoir fluids. In developing a fracturing fluid coefficient for this mechanism, Howard and Fast considered a segment of the formation bounded by a unit area on the fracture face and extending to infinity in the direction of leak-off as shown in Fig. 1(a). The direction of leak-off z is normal to the fracture face. The equation governing the linear isothermal flow of fluid into this segment is where a = Eq. 2 is a form of the diffusivity equation. It is derived from the equation of continuity, Darcy's law and Eq. 3

By A. M. Gaudin, D. W. Fuerstenau

IN concentration of certain ores by soap flotation, prevention of quartz flotation is desired; the contrary is true in treatment of some oxide iron ores. Experimental study of the flotation of quartz goes back at least a quarter of a century.' Clean quartz does not float with fatty acids or soaps but does float when activated by one of many metallic salts. Control of pH is important. Broadly speaking the problem of quartz flotation has been approached from the empirical side, as was the related topic of flocculation or dispersion of quartz suspensions? Empirical studies indicated the existence of critical relationships between the additions of collector and activator. These additions were not stoichiometric for the formation of soaps of the activator cation. For example, Gaudin and Rizo-Patrona found optimum quartz flotation at pH 10.6 using barium activation and oleate collection when the molar ratio of oleate to barium was 1 to 1 instead of 2 to 1, as would be called for formation of Ba(OL),. Cooke and Digre" ' found that if calcium is the activator, a minimum quantity of that agent is required for effective flotation when the pH is 11.5. In other words, if the concentration of Na' exceeds 10 -2.5 mols per liter or if the concentration of H exceeds 10-11 mols per liter, the concentration of Ca++ in solution required for quartz activation is increased. This suggests that H+ is much more effective than Na+ on 10-2.5 quartz, perhaps in the ratio ofp or 108. Schuh- mann and Prakash6 studied anew the activation of quartz by barium, calcium, aluminum, and ferric iron. Salts of these metals are activators provided they are in stoichiometric excess over the collector used with them. Alkaline-earth salts are effective only in alkaline circuits. Important as they are in giving data on the effect of various agents on quartz, all these studies fail to give information on the detailed structure of the quartz-solution interface. A beginning in this direction was made by Gaudin and Chang,? who measured the adsorption of radioactively marked barium and laurate ions at quartz surfaces, and by Gaudin. Spedden, and Laxen,8 ho measured the adsorption of radioactively marked sodium at quartz surfaces. Work has also been done by Bell0 n measurement of the adsorption of sodium ion and chloride ion at quartz-solution interfaces. In all these experimental measurements of adsorption, the solid was centrifuged or filtered from the bulk of the liquor with which it had been associated; and the composition of the solid surface was ascertained by analysis, after allowance was made for the ionic composition of the liquor included with the centrifuged solids on the assumption that it is identical to the bulk liquid. Adsorption measurements give only the total amount of collector adsorbed at the quartz-solution interface; they give no indication of the distribution of these adsorbed ions at the interfacial layer. It is the ionic structure of the solid-solution interface and its importance to flotation that is the subject of this paper. The structure of this interfacial layer can be investigated by means of electrokinetic methods so that by combining electrokinetic studies with adsorption measurements, a more complete picture of the quartz surface may be obtained. The following studies were made to ascertain how electrolytes used in the soap flotation

Jan 1, 1956

By D. H. R. Price

This paper presents two tentative models of the use of a notional metal in a country like Britian, which have been developed using the System Dynamics modelling method. Computer simulations have been carried out using one of the models. These show the effect on the recycling of the notional metal of a wide range of possible future values of world market price and demand for the metal.

Jan 1, 1977

By David L. Thompson

The Alumet Company, a partnership of National .Steel Corporation, the Southwire Company, and Earth Sciences, Inc., is in the final phase of its feasibility study for an alunite plant. To be located in southwestern Utah, it could be the first commercial-scale operation in the Western Hemisphere to recover alumina from an ore other than bauxite. Sulfuric acid and sulfate of potash are by-products of the process. Alumina production level will be set at 500,000 tons p

Jan 1, 1976

By L. S. Austin

Our SUCCESSFUL plants in the West were at first erected on a small scale, and as their business has been built up, have been added to gradually as their limitations permitted. They have had to adapt themselves later to their circumetances, making the best of drawbacks, and putting up with much which, had it been originally allowed for, would not now impede them.

Jan 1, 1897

By Leslie C. Richards

The competitive position of producers of industrial minerals depends upon the delivered price of their product. Freight charges are a major factor in the sales to consumers. A comparison of freight rates on movements of limestone and silica rock in the Pacific North-west shows a wide variance in mills per ton mile for like hauls, thereby favoring some localities over others.

Jan 2, 1950

By A. V. Deforest, A. R. Anderson, C. W. MacGregor

ONE of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing of the A.S.T.M., 1938. The work of Mann,1 Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserve especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by plotting [So = ooT as a function of eo =o] where A o and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors? It was shown that the true physical behavior of the material in the tension test could best be represented by plotting the average true stress, [S = P] as a function of [e = q' = log A-le = log Lo] where P, A, L, S, [e], and q' refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximum load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain difficulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece

Jan 1, 1941

NOMINATIONS FOR OFFICERS. In accordance with the Constitution, Article VII., the following nominations have been prepared by the Nominating Committee, submitted to the Board of Directors at its October meeting, and are hereby published for the information of the members. For Director and President: Benjamin B. Thayer, District 0 For Directors and Vice-Presidents: Herbert C. Hoover, District 6 W. L. Saunders, District 0 For Directors : Reginald W. Brock, District 11 Charles W. Merrill, District 6 Albert R. Ledoux, District 0 Henry L. Smyth, District 1 D. C. Jackling, District 7 The Constitution further provides that " Any complete or partial ticket of nominees signed by any twenty-five Members or Associates of the Institute and transmitted to the Secretary by December 15 shall also be printed and circulated with the official ticket and over the names and with the recommendations of the nominators, together with an expression of opinion of the Board thereon if deemed expedient.

Jan 11, 1913

By William G. Pariseau

The extraction ratio approach to pillar design in flat seams is based on a mathematically exact analysis that is a reasonable physical approximation to room-and-pillar layouts in many instances. The essentials of the approach are reviewed and then mathematically approximate formulas for pillar design in inclined seams of arbitrary dip are proposed. Detailed numerical analysis of stress about a typical 5 entry, 4 pillar panel at dips of 0, 15, 30, 45, 60, 75 and 90 degrees at low and high extraction ratios show that the proposed inclined seam extraction ratio formulas for pillar normal and shear stresses, although conservative, have an accuracy quite adequate for engineering purposes. Appropriate pillar safety factors for compressive and shear failure and a safety criterion for overturning are specified.

Jan 1, 1982

By John W. Cloud

THE delivery of blows upon roadway structures by the locomotive engine at high speed, although long recognized, has, perhaps, not been a generally understood in severity, relation to speed, and cause as is desirable in matters of such importance. Some points of explanation, with illustrative diagrams, are, therefore, submitted to your attention, preparatory to a note on "Steel for Bridges," also submitted. In order that a locomotive may run at high rates of speed with-

Jan 1, 1881

By Telfer Norman

THE use of cadmium as a base for bearing metals is one of the most interesting recent developments in this field. It has caused a strong demand for cadmium and a marked rise in its price. It appeared to the authors, therefore, that the situation might be relieved for users if accept-able substitutes could be developed. A preliminary investigation has revealed that to some extent mercury may be substituted for cadmium. Whether its use is justified cannot be stated at this time. Most of the authors' work has indicated that the addition of mercury to alloys of cadmium and nickel detracts from their desirable physical properties; but this work has not been extended to cover service tests, which might reveal that the addition of low percent-ages of mercury to the cadmium-base alloys would improve their per-formance. The results of tests made by the authors are therefore briefly summarized for this paper. Table 1 gives the proportions of the metals

Jan 1, 1937

'The Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties. United Engineering Trustees, Inc. When Mr. Carnegie made his gift which made possible a home for the engineering societies, a separate corporation was organized to act as a holding company and to manage the common property. This was long known as the

Jan 1, 1932

By D.E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size. IN order to determine the relative wear rates of several sizes of grinding balls, groups of 4, 31/2, 3, and 2 in. balls were marked individually and were charged, all at the same time, into each of two production mills grinding copper ore. The remainder, and vast majority, of the ball charge consisted of 2 in. diam, and smaller, white, cast iron balls. The original weight of each test ball was determined and recorded. Some of each group of test balls were recovered from the mills periodically, individually reidentified, and reweighed. The test balls were recovered during regular maintenance shutdowns, at approximately thirty-day intervals, so as to avoid disrupting operations. As soon as the weights had been recorded, each marked ball was recharged into the mill from which it had been taken. The test units were mechanically the same and theoretically received equal tonnages of feed. All of the test balls were of forged, alloy steel composition with only slight variations in chemistry that would not be expected to affect the physical properties. All were heat treated in the same manner to produce a high hardness, as equal as possible for all sizes and as uniform as possible from surface to center. Generally speaking, the hardness of the portion worn from the balls during the test ranged from 62 to 65 Rockwell C. The microstructure was, therefore, predominately martensitic. The method of marking the test balls consisted of forming a small, round hole, 3/16 or 1/4 in. diam, into the center of each test ball with a Thomas Metal Master disintegrator, which produces a hole in fully hardened steel without affecting the hardness of the surrounding metal. After the hole was formed, each test ball was individually weighed to the nearest gram and the weight was recorded. The balls were grouped as to size and each group assigned a code letter. The individual balls within the various groups were then assigned a number. A small copper disc was stenciled on one side with the group letter and on the other side with the individual ball number and dropped into the hole in the corresponding test ball. The hole was then plugged with a low-melting-point metal alloy, which could be melted out in boiling water. Half of the test balls in each group were charged into one mill and the other half into another mill, so that all test balls in each mill would be subject to, as nearly as possible, identical conditions for an equal length of time. Previous testing had indicated that the wear rates on balls of different sizes could not be accurately compared if weight loss, or percentage weight loss, were used as a basis for comparison. Fig. 1 is a graphic record of the average weight loss for each size group in mill No. 1, and it becomes readily apparent that the larger balls lose substantially more weight in a given length of time. Fig. 2 is a graphic record of the average percentage weight loss for each size group in mill No. 1, illustrating that the smaller balls definitely lose a greater percentage of their original weight in a given length of time. It was, therefore, decided to convert the actual weights of the test balls to diameter and follow the diameter losses periodically to see if the wear rates

Jan 1, 1951

By M. T. Hepworth, W. B. Sample

HYDROGEN solubility and linear contraction measurements were made at constant temperature on an alloy of titanium of constant oxygen-to-titanium molal ratio but variable hydrogen content. A cylindrical specimen of titanium (0.25 by 1.6 in.) containing 0.75 at. pct 0 and less than 0.03 at. pct N was cast from a master button of iodide process titanium which had been alloyed with titanium dioxide. Four vacuum fusion analyses, which were made along the length of the cylinder after the hydrogen solubility studies were made, revealed a variation of oxygen content of less than 0.02 at. pct. The specimen was introduced into a quartz furnace tube, annealed and outgassedat 1050"~ for about 1 hr, and then held at 800" * 0.5" for about 30 hr, during which latter time experimental data were taken. The leak rate to the furnace chamber was not sufficient to contaminate the specimen during the run as determined by leak-rate studies and vacuum fusion analyses for oxygen and nitrogen before and after the runs. The furnace chamber was attached to a modified Sieverts apparatus used to introduce measured quantities of purified hydrogen to the specimen. A quartz pushrod transmitted changes in length of the specimen to a Chevenard dilatometer. The push-rod passed through a vacuum grease seal to the dilatometer which amplified motion of the rod by a factor of 319. During hydrogen addition, the pushrod did not contact the specimen. Measured quantities of hydrogen were added to the specimen and equilibrium hydrogen pressures recorded as a function of hydrogen content. The solubility data, which appear in Fig. 1, agree well with a separate investigation made with a different apparatus. The solubility limit of the hcp a phase appears as an abrupt discontinuity in slope at 3.4 at. pct H. The solubility plot has been extended as a dashed line at this discontinuity in order to emphasize the discontinuity. The hydrogen content at which bcc P appears is not clearly defined. An arrow indicates solubility data were taken upon hydrogen addition. Upon reaching the arbitrary maximum hydrogen content of the run, the quartz pushrod was pressed against the specimen in order to record the change in length with hydrogen removal. A pressure of about 100 g per sq cm was required to overcome the friction of the vacuum seal in order to obtain reproducible linear contraction data. The contraction ratio ~2/1", change in length divided by original length, was set equal to zero for the maximum hydrogen content. The relative contraction of the specimen was observed upon removal of hydrogen in the following manner. The system was opened to the pumps for a few seconds and an unknown quantity of hydrogen was removed. The system was then isolated from the pumps by closing a stopcock and allowed to return to equilibrium. When the temperature returned to 800°C, the pressure stabilized, and contraction ceased, measurements of contraction and pressure were made. The hydrogen content of the specimen was then deduced by measuring the equilibrium PIydrogen pressure and referring to the solubility plot. Linear contraction was then plotted against interpolated values of atomic percent hydrogen. The justification for this procedure is the established reversibility of the hydrogen equilibrium.' Uniaxial compression was assumed to have no effect on hydrogen pressure. The isothermal linear contraction data are plotted on Fig. 1. An arrow indicates data were taken upon removal of hydrogen. The solubility limits of the two phase a i /3 region can be identified by discontinuities ill slope of the dilatometric plot at 9.1 and 3.4 at. pct H, agreeing well with other studies.' Dashed extensions of the plots emphasize the discontinuities. Isothermal studies of expansion made upon hydrogen addition gave curves of much smaller slope and less pronounced discontinuities. A uniaxial compressive stress tends to accentuate volume changes in going from the more open bcc phase to the hcp phase.2 Incomplete data on ex-

Jan 1, 1962

By D. E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size. IN order to determine the relative wear rates of several sizes of grinding balls, groups of 4, 31/2, 3, and 2 in. balls were marked individually and were charged, all at the same time, into each of two production mills grinding copper ore. The remainder, and vast majority, of the ball charge consisted of 2 in. diam, and smaller, white, cast iron balls. The original weight of each test ball was determined and recorded. Some of each group of test balls were recovered from the mills periodically, individually reidentified, and reweighed. The test balls were recovered during regular maintenance shutdowns, at approximately thirty-day intervals, so as to avoid disrupting operations. As soon as the weights had been recorded, each marked ball was recharged into the mill from which it had been taken. The test units were mechanically the same and theoretically received equal tonnages of feed. All of the test balls were of forged, alloy steel composition with only slight variations in chemistry that would not be expected to affect the physical properties. All were heat treated in the same manner to produce a high hardness, as equal as possible for all sizes and as uniform as possible from surface to center. Generally speaking, the hardness of the portion worn from the balls during the test ranged from 62 to 65 Rockwell C. The microstructure was, therefore, predominately martensitic. The method of marking the test balls consisted of forming a small, round hole, 3/16 or 1/4 in. diam, into the center of each test ball with a Thomas Metal Master disintegrator, which produces a hole in fully hardened steel without affecting the hardness of the surrounding metal. After the hole was formed, each test ball was individually weighed to the nearest gram and the weight was recorded. The balls were grouped as to size and each group assigned a code letter. The individual balls within the various groups were then assigned a number. A small copper disc was stenciled on one side with the group letter and on the other side with the individual ball number and dropped into the hole in the corresponding test ball. The hole was then plugged with a low-melting-point metal alloy, which could be melted out in boiling water. Half of the test balls in each group were charged into one mill and the other half into another mill, so that all test balls in each mill would be subject to, as nearly as possible, identical conditions for an equal length of time. Previous testing had indicated that the wear rates on balls of different sizes could not be accurately compared if weight loss, or percentage weight loss, were used as a basis for comparison. Fig. 1 is a graphic record of the average weight loss for each size group in mill No. 1, and it becomes readily apparent that the larger balls lose substantially more weight in a given length of time. Fig. 2 is a graphic record of the average percentage weight loss for each size group in mill No. 1, illustrating that the smaller balls definitely lose a greater percentage of their original weight in a given length of time. It was, therefore, decided to convert the actual weights of the test balls to diameter and follow the diameter losses periodically to see if the wear rates

Jan 1, 1951

By John J. Van den Broek

As the established tailings disposal techniques do not meet the requirements of today, alternative methods of disposal are explored. McIntyre Mines Ltd., Coal Div. found a solution in the construction and operation of a tailings dewatering plant. The solids are recovered from the tailings slurry by means of mechanical dewatering equipment and are then dried in a unique drying system to provide an excellent thermal fuel for a power generating station.

Jan 1, 1983

LET us return and follow our first intention of discussing the art of melting. Since I have demonstrated to you how large works are made, you may have thought that the way to the small ones was also open to you, and you would not have been mistaken. But in order to avoid work and expense there are shorter and easier ways to be used, both because the things can be handled more easily and because it is not necessary to have so much regard for the forces of small materials. Therefore, wishing to make a distinction for you, I shall call this the small art of casting. Before speaking of this, I shall tell you of several methods of making powders for moulding. Then I shall also tell you of the methods of moulding in boxes and in frames, and how the said powders are to be prepared for casting either dry or green. Then I shall tell you some methods that are held as secret by the masters for handling the metals in melting and making them flow readily, so that you may easily fill the cavities of your moulds.

Jan 1, 1942

By The Staff of Dames & Moore

Five factors are required for the formation of uranium deposits: a source, transporting medium, host, trap, and preservation. Locating and evaluating uranium deposits requires ail integration of methods and techniques to determine if the above factors are present. A typical exploration program consists of selection of a favorable area, field reconnaissance, land acquisition, and target definition and evaluation. Target definition and evaluation utilizes a combination of geologic mapping, geochemical surveying, geophysical surveying, and drilling and logging. Each overlaps the others to some degree.

Jan 10, 1978

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

US 4,185,872-In the solution mining of uranium values from a subterranean uranium ore deposit, a lixiviant comprising sodium sulfate or other alkali metal sulfate and optionally minor proportions of an alkali metal carbonate or bicarbonate and an alkali metal hypochlorite is introduced into the ore to solubilize uranium therein. The pregnant lixiviant is recovered for processing. E.T. Habib, Jr., assigned to Mobil Oil Corp. Jan. 29, 1980. 5 pp (299-4). Filed- 8-18-78 (934,933).

Jan 1, 1982