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Jan 1, 1968

By Herty, C. H.

Iron oxide (FeO) plays an extremely important part in the manufacture of iron and steel. In the three major processes- blast-furnace, open-hearth, and Bessemer converter-iron oxide is the chemically predominant compound and controls to a large ex- tent the operation of the furnaces and the composition and quality of their respective products. In order to emphasize the importance of iron oxide in each process, they will be considered individually in some detail. THE OPEN-HEARTH FURNACE. Iron oxide is introduced into the open-hearth furnace in four ways : 1. The scrap charged into the open hearth is oxidized by the furnace gases, the amount of oxide formed depending primarily on the amount and type of scrap charged. It has been found' that with large scrap, 1.7 Ib. of FeO is formed per 100 Ib. of scrap charged, whereas with scrap of medium size about 5.3 Ib. of FeO is formed per 100 Ib. of scrap charged, when the period between the charging of the scrap and the addition of hot metal is 3 hours. 2. The decomposition of the limestone sets free CO, by the reaction

Jan 1, 1957

By W. A. Hockings, D. W. Fuerstenau, A. L. Mular

This paper briefly describes a simple air pycno-meter and its use for rapid determination of the composition of mixtures of solid particles. Research on such problems as the pelletizing of solids, the mixing of solid particles, and the comminution of mixtures can be simplified by means of this analytical tool. THEORY OF OPERATION Liquid pycnometers1 are commonly employed to measure volumes. These devices are time consuming and sometimes give inconsistent results. The liquid used in the pycnometer may have an undesired influence on the material to be measured; moreover, complete displacement of air by the liquid is seldom

Jan 1, 1963

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962

By P. van Meurs, C. van der Poel

From observations of the linear displacement of oil by water from a porous medium as visualized in transparent models, new insight into the mechanism of vircous fingering, as occurring in the case of unfavorable oil-water viscosity ratios, has been obtained. A mathematical description of the observed phenomena leads to formulas. expressing both oil production and pressure drop across the formation as a func-tion of cumulative water injection with the oil-water viscosity ratio as a parameter. Theoretical results are compared with those obtained from scaled laboratory experiments in sand-filled rubes in which water was injected at the one end and production was obtained from the other end. In the second part of the paper the same principles are used to calculate a more realistic production scheme in which production of oil and water is obtained from wells regularly distributed over the field. Results show satisfactory agreement with production data of an actual oil field. Application of the theory is extremely simple as only a limited number of readily available parameters have to be known and results are presented in an analytical form. INTRODUCTION When oil is displaced from a porous medium by water having a viscosity lower than the oil. the oil-water interface is essentially unstable and has the tendency to break up into what are called "fingers" or "streamers". This Viscous fingering has been noted before by Engelberts and Klinkenberg&apos; and has recently been demonstrated in transparent models by van Meurs-. It is highly questionable whether it is at all possible to perform relative permeability measurements In the laboratory reproducing the same distribution of water and oil in the cores as Present in practice. Therefore, we based our descriptive theory on an idealized model which was "tailored" to the fingering mechanism as observed in transparent models under scaled conditions. This approach was the more attractive, as a highly simplified model had already yielded an adequate description of the process. Though we are aware our theoretical approach can be extended in several ways, it is given here in its simplest form to explain the fundamental principles and to avoid complicated formulas. SIMPLEST CASE OF A LINEAR DRIVE Observations and Theoretical Model In Fig. 1 a series of photographs shows how water penetrates into a formation saturated with an oil which is considerably more viscous than the water. The technique for obtaining these photographs, using transparent models, has already been described?. The fingers can be clearly observed and are seen to be mainly parallel to the flow direction. Note that the contours of these fingers are not smooth but show protrusions of water enclosing oil pockets.

By NONE N

Jan 1, 1963

By E. Northcott, F. N. Oberg

By electrostatic separation, course Florida pebble phosphate, too lou-grade to find a ready market, can be upgraded to a satisfactory saleable product. Pebble running from 60 pct bone phosphate of time may be upgraded to 73 to 77 pct BPL depending on the mineralogical. structure of the pebble and the nature of the silica innpurity. High-grade concentrates from Florida pebble phosphate deposits have long been recovered by wet methods. When work was begun in the field, only the coarse pebble (generally +1 mm) was re- covered. In the 1920&apos;s a froth flotation process was developed to separate quartz from the finer phosphate fractions, but this method proved unsatisfactory for treating the intermediate fraction (—1 mm +35 mesh). Consequently various other processes were adapted, including agglomerate tabling and spiral separation of reagentized feed. Today the three processes are used—washing and screening for coarse pebble, tabling or spiraling for intermediate sizes, and flotation for —35 mesh material.

Jan 1, 1959

By Y. C. Liu, G. A. Alers

The anisotropy of Young&apos;s modules has been measured in a series of Cu-Zn alloys containing from 1 to 28 wt pct Zn and cold-rolled to 97.5 pct reduction in thickness. These modulus data show a transition in texture as a function of zinc content. In alloys containing 3 pct Zn or less, the texture is essentially that of copper. A transition is clearly seen to develop in 5 and 8 pct Zn alloys, and to have been completed in a 12 pct Zn alloy. Increasing the proportion of zinc to 28 pct does not produce any further changes in texture. The ease and clarity with which this texture transition can be seen in the modulus data is in great contrast with the inccertainty in the visual detertiination of the range of texture transition from a series of pole figures. It is also shown that the rolling texture of the high zinc content alloys cannot be a one-COIIIponenl texture, characterized by the (110)(112) ideal orientations, as usually assumed. A second, quite important component must also be present. Furthermore, the present data are inconsistent with matrix orientations on which the "oriented growth" hypothesis of the Formation of recrystallization textures is based. THE rolling textures of binary fcc alloy systems have generally been considered to lie between two terminal textures. One of these terminal textures is the copper type and the other is the 70:30 brass type. Alloys of intermediate solute content exhibit a texture which is said to be a transition between the two terminal textures. On the basis of efforts to correlate rolling and recrystallization textures, two concepts have been advanced in the literature on the nature of these transition textures. One school1 suggests that the addition of alloying elements, e.g., zinc, causes a gradual rotation about one of the (111) poles from the (358)( 523) ideal orientation of the copper-type rolling texture to the terminal {1 10)( 112) ideal orientation used to describe the rolling texture of 70:30 brass. This concept is depicted in Fig. 1 with the angle of rotation corresponding approximately to the zinc content and is designated here as the "rotational concept", since the ideal orientation of the transition textures varies continuously with alloy content. The other concept,&apos; the "mixture concept", suggests that the copper-type rolling texture is a two-component texture. {358) (523) and {110)(112). The addition of alloying elements affects only quantitatively the relative amounts of these two components—a decrease in the amount of material in the {385}(523) orientation and an increase of that in the {110)(112) orientation with increasing solute content. An experimental distinction between these two concepts is essential to a better understanding of both the mechanism of formation of rolling textures and the subsequent formation of recrystailization textures in fcc metals. Because of the lack of resolution inherent in pole figures, it has not been possible to differentiate between the two concepts on the basis of this data. Both concepts, in fact, make use of the same set of pole figures but interpret them in a manner acco-rding to the view held.&apos;" Experimental results obtained from inverse pole figures or selected-area electron diffraction3j4 simply -yield more refined pole figures but do not eliminate the ambiguity of interpretation. Quantitative measurement of an entirely different, orientation-dependent property must thus be considered

Jan 1, 1967

By Gerald Greene

Tan various lead producers have given the subject of lead drosses much attention in recent years but the problem of their economical treatment is yet to be solved. Formerly the copper in the furnace feed was removed from the furnace in the form of matte. The speiss at that time consisted principally of the iron arsenide. The practice today is to roast off most of the sulfur and the copper in the feed forms a dross in the furnace, which is removed from the furnace with the lead. This material is poured into the drossing kettles and allowed to cool down to but slightly above the freezing point of lead. The copper dross, containing almost all of the arsenic and part of the antimony, is skimmed off and treated in a small reverberatory furnace at most plants. This is essentially a liquation process. The skimmed dross contains from 70 to 80 per cent lead, and much of this lead is liquated out. The products from this treatment are: (1) impure lead, (2) speiss and (3) matte. The speiss from the reverberatory furnace was studied in this research. The literature on the subject is of very little assistance, as almost no work has been done on the problem of establishing the exact identity of the various phases present. One author(1) states that speiss consists of a series of isomorphous compounds of the general formula FexAsy in which the Fe may be replaced by Ni, Co, Cu, Pb, Ag, Au, Pt, Zn, Cd and the As replaced by Sb, S and Bi. Hofman(2) states that the iron arsenide present is Fe5As.

Jan 1, 1935

By M. R. TECK, N. Rudd, L. K. Thomas, D. L. Katz

The authors are to be congratulated for presenting the first comprehensive paper on the theory and practice of threshold pressure determination in connection with underground gas storage. It is of particular value since most previous experimental work on this subject has been proprietary to the commercial laboratories engaged in such testing and to their clients. This dlscussion is presented in amplification of the subject paper, not in criticism, and is based upon our experience with approximately 5,000 threshold pressure determinations. Our comments are directed primarily to the experimental procedures as described by Thomas et al. It should be noted that, while clay mineral-rich lithologies are the most common caprock materials, the samples used (Table 1) include low permeability sandstones and carbonates, but do not include shales or other formations in which clav minerals exert a dominant effect. While our experience on samples analogous to those investigated by the authors generally confirms their findings, we have found that even more rigorous experimental conditions must be imposed where clay minerals are the controlling factor. These additional conditions result from the well-known molecular character of the clay minerals themselves in which water is interlaminated with, and bonded to, silicate sheets, thus becoming an essential component of the molecule. In many clay minerals the character of the intersheet bonding, and thus the dimension of the lattice, is strongly affected by variations in the identity and concentration of cations present in the intersilicate water. On a supermolecular scale, adsorbed water films on particle or "flakes" of shale provide much of the cohesive force necessary to maintain mechanical strength. The thickness of these films is variable and inversely proportional to intergranular pressure within the dimensional limits involved in caprock investigation. The thickness of the intersilicate water layers may also be subject to pressure under some conditions. These considerations are reflected in several necessary modifications of the experimental procedures described by the authors. Two of these are, in our judgment and experience, of such importance that they cast real doubt on the validity of data obtained on argillaceous materials without their application. The very careful resaturation procedures proposed by the authors should give good results in connection with the relatively "inert" lithologies used in their experiments. Our experience suggests, however, that they would create more problems than they would eliminate if applied to argillaceous materials. 1. Drying of the sample at the temperature and for the duration indicated by the authors not only will dessicate the sample with consequent shrinkage cracking, parting along bedding planes, and even total disassociation in the case of fissile shales, but it may also alter the character of the clay minerals themselves — in some cases irreversibly. 2. Prolonged evacuation to 2 microns Hg further dessicates the sample and is even more effective in reducing the intersilicate water content. 3. Resaturation with water differing in pH or chemical content from that existing originally in the sample also serves to alter the nature of the sample, particularly its structure and strength. 4. Our experience has been that, even with the thorough precautions proposed by the authors, complete resaturation of very fine grained materials is rarely obtained. Yet our experience confirms the

Jan 1, 1969

By M. Prats

Most of the information available on the heat efficiency of hot fluid injection processes, both water and steam, has been obtained from calculated temperature distributions in the pay zone and adjacent formations. The usual approach has been to write the heat balance equations in terms of the temperatures, and then to introduce whatever simplifications are necessary to help obtain an analytical or a numerical solution. In either case, the assumption has often been made that the vertical thermal conductivity in the flooded interval is infinite, so that the temperatures within the flooded interval are then independent of vertical position. Because it was first made by Lauwerier,l and has been used extensively since, this assumption will be referred to as the Lauwerier assumption. Excellent reviews of the literature on the heat efficiency of hot fluid injection processes have been given by Spillette,2 Flock et al.,3 and Ramney.4 Of course, the most significant contributions take into account the effect of a finite vertical thermal conductivity on the vertical temperature profile. The most general analytic expression for the heat efficiency of a hot fluid injection process is that of Antimirov5 who considers injection of a heated incompressible fluid into a reservoir through an arbitrary number of wells. The rate of heat injection into the reservoir, as well as the injection temperature, is an arbitrary function of time. The geometry of the horizontal flow is arbitrary, although the reservoir is considered to be of uniform thickness and properties and to be of infinite areal extent. Heat transfer within the reservoir is by horizontal convection and conduc- tion, and by vertical conduction. In the formations adjacent to the flooded interval, heat transfer is by conduction in any direction. Thus, the available expression for the heat efficiency due to hot water injection has been developed for rather general conditions. This degree of applicability has not been obtained for other thermal recovery processes. By making the Lauwerier assumption we have been able to obtain expressions for the heat efficiency that are essentially independent of the thermal recovery process, be it steam, hot-water, or underground combustion. Clearly, then, the approach followed here is more restrictive than that of Antimirov5 in that it uses the Lauwerier assumption. At the same time less restrictive assumptions are made about the horizontal heat transfer mechanisms, either in the flooded interval or in the formations adjacent to it. The main difference between our approach and that of other investigators is that the heat balance in the pay zone is expressed for the pay zone as a whole rather than for a volume element within it. The Lauwerier assumption is introduced after the problem is developed along these lines as far as possible. The details of the development of the heat efficiency are given in the Appendix, while the main features of the model are discussed in the next section. Results and their implications are discussed later in a separate section. The Model Certain assumptions have been made to determine

Jan 1, 1970

By E. L. Affleck, W. G. Stevenson

In both Canada and the United States, a company making a public offering of securities must comply with regulations which have been passed by Federal, State and/or Provincial Legislatures. These regulations usually require the distribution of an acceptable prospectus which provides essential background information about the issuer, the project and the share offering. when the public offering has been accepted, the unlisted company may then seek a listing of its shares for trading on a Stock Exchange. Once listed, the company will be subject to rules of the Stock Exchange. This paper will deal with the specific information required for inclusion into a prospectus being submitted for a resource company and particularly those parts of concern to mining engineers and geologists.

Jan 1, 1985

By L. T. Stanley

A method is described whereby the behavior of the front is approximated when gas is injected into a thick reservoir having reasonably homogeneous properties. The method is applied to the Abqaiq field of Saudi Arabia. The producing member is the Arab-D, a high-permeability calcarenite which has no continuous betlding planes. Field performance indicates the injected gas to be partially miscible with the reservoir oil because gas volume factors experienced are lower than those predicted by the gas law. Eqlrilibril~m calculations confirnz ihis and also show that the volume factor may vary appreciably, depending on the relative quantities of oil and gas in contact in the reservoir; consequently, volutnetric balances are made for the purpose of determining the behavior of the gas volume factor during injection history. The effect of gravity segregation on position and shape of the gas front is approximated by dividing the producing section into three zones vertically and tracing the movement of the average interface in each zone, with counterflow of oil and gas taking place betweell zones behind the front. This results in a gas front that advances more rapidly along the top of [he formation than along the base, producing an "umbrella" effect in cross section that becomes more pronounced as the front progresses. The calculations cover the gas-injection period of Abqaiq field history through 1958, and the position of the gas front is plotted at one-year intervals. Finally, some comparisotls between the calcrlated fronial position and the gas-oil contact as Measured by neutron logs are made. INTRODUCTION Fig. 1 is a structure contour map of the Abqaiq field. For analytical purpcses, the field has been divided into two areas designated A and B, as shown on the map. Gas injection into Area A was begun in early 1954 into two wells located near the crest of the structure on the north-south axis of the anticline. During the period covered by this paper, the average injection rate has been 122 MMscf/D with a maximum sustained rate of 160 MMscf/D. The reservoir pressure has been maintained at 2,450 psig since start of gas injection. The reservoir originally was undersaturated but, prior to pressure maintenance, the pressure was drawn below the bubble point in most of the Area A section, creating an in-place free-gas saturation of 8 per cent at the crest of the structure. The average critical gas saturation is 13 per cent established by laboratcry core tests. That the entire reservoir remained below critical gas saturation prior to gas injection is borne out by the fact that none of the crestal wells have exhibited high gas-oil ratios during production history. The Area A reservoir is a carbonate section about 200-ft thick having average porosity and permeability of the order of 22 per cent and 500 md, respectively. The productive horizon is the Arab-D member of Jurassic age and is encountered at an average depth of

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 28 Montreal, Canada Sept, ?79 8

Jan 1, 1923

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8

Jan 1, 1923

By W. T. Bell, M. P. Lebourg

The perforating of multiple tubingless completions, in which two or more strings of 27/8-in. OD casing are installed in the same borehole, presents two basic problems. First, good completion practices require an eficient perforator that leaves no debris to interfere with subsequent completion operations. Second, and of more complicated nature, a system is needed for controlling the direction of fire so that adjacent strings are not damaged. Development of of a 2-in. OD, steel retrievable, shnped-charge gun has solved the first problem. The second was resolved through development of three different devices to provide directional perforating for the two types of completion methods being employed today. These include a mechanical orienting device and two self-orienting radiation devices. Conceivably, the latter methods could be adapted to the directional perforating (of .upper zones) of conventional dual and triple completions without removing production tubing and packers. INTRODUCTION The recent trend to multiple tubingless completions,&apos; wherein two or more strings of 27/8-in. OD casing are installed in the same borehole, has presented two basic perforating problems. The first problem to be overcome was the design of a gun that would result in efficient perforations without causing debris to bridge in these small-diameter casings. The second problem was, of course, to devise a system for controlling the direction of fire such that adjacent strings would not be damaged. The problem of gun debris in slim-casing completions has been well defined in the numerous 27/8-in. single tubingless completions which have been effected during recent years with the expendable-type perforators. Failure of expendable-gun debris to settle out properly, even with good gun break-up, has resulted in bridging inside these small-diameter casings. This, in turn, has interfered with completion and re-conditioning operations. The past two years have clearly shown, in fact, that debris problems are not confined to this small range of casing with most designs of expendable-type guns. A high incidence of bridging has even been reported in 4%-in. OD casing. The perforating of multiple tubingless completions has entailed, therefore, the development of a completely debris-free gun of adequate performance, as well as the necessary devices to provide positive directional perforating in the two completion methods presently being employed. THE GUN —DESIGN CONSIDERATIONS The design of a shaped-charge gun for slim-casing perforating has presented a maze of interrelated prob-lems. Since the primary specification has been leveled at efficient charge performance with complete elimination of gun debris, it has been necessary to develop a retrievable steel-carrier gun of tubular construction to house the charges. The carrier must be retrievable through 2.29-in. API pump-seating nipples which are usually installed in 2 7/8-in. strings. To provide for recovery of the gun from the well, swelling of the carrier on firing must be carefully controlled. Control of swelling automatically means control of explosive weight in the shaped charge which, in turn, influences charge performance. Carrier swelling also depends upon the confinement pressure at the level being perforated, which imposes a hydrostatic pressure-depth limitation. Burr interference on the wall of the carrier, resulting from passage of the jet through the carrier wall, must be eliminated by suitable design. Clearly then, a satisfactory shaped-charge gun design for slim-casing operations represents a fine balance between carrier swelling, hydrostatic pressure, explosive weight and charge performance. Additionally, to lend itself to directional perforating, the gun design must provide a positive locking mechanism for individual charges within the gun carrier. This fixes charge orientation within the carrier and prevents

By Herbert K. Kutter

This paper is concerned with the physical phenomena in the fracture process of presplitting and only indirectly with the establishment of the optimum presplitting parameters. Its nature is therefore qualitative, rather than quantitative.

Jan 1, 1968

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 27 Montreal, Canada Sept, ?79 8 28 New York, N.Y. Feb, ?80 9 29 Lake Superior, Mich Aug, ?80

Jan 1, 1923

By R. A. Wattenbarger, H. J. Ramey

The trend in gas well testing has been to rely more on the early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modern gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks. It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore. Russell and Truittl published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark2 applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis. The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz3 presented the drawdown equations for *Now with Scientific Software Corp., Denver. ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice. Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore. The Mathematical Model The geometry of our mathematical model is similar to that used by Prats.4 The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through the wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model. The equation for the flow of real gas in a porous medium with uniform porosity, permeability and thickness is5-7

Jan 1, 1970