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By V. Maazallahi, A. Rouleau, A. Saeidi

"The geometry of the terrain topography before and after the failure are the essential factors for analyzing a landslide and for the design of remedial works. This paper presents a method to determine these factors, considering that the determination of the slide surface profile is difficult and costly using traditional methods and the pre-slide topography data is often not available. The presented method to locate the 3-dimensional geometry of the slide surface is based upon determining the slide surface in 2- dimensional vertical sections. This method utilizes post-slide topography of the area to determine the pre-slide topography and uses equations to estimate the pre-slide situation using a statistical process applied to points located on the sliding mass. This method is tested on the Maskun landslide in Iran. The results indicate the applicability of the proposed method to obtain the key factors for the back analysis of a landslide in a cost effective manner.INTRODUCTIONProbably the most reliable method of determining the strength of soil and rock mass is to back analyze a failed or failing slope (Caia et al. 2007; Wyllie & Mah, 2004). This method is used in geotechnics for estimating geotechnical parameters of the rock and soil mass (Sakurai et al., 2003; Frayssines and Hantz, 2009; Cepuritis et al. 2010), but it requires that the failure mode is well established and that there is complete and precise information available on the slide surface and the sliding mass (Sjöberg, 1996). Measurement of the slope profile before failure provides the basic information required for a back analysis (Hock & Bray, 1981). The post-slide topography is another key factor. The back analysis process for determining the actual strength parameters of soil or a decomposed rock mass after a landslide requires knowledge of the sliding mass geometry, both before and after the sliding event. Many studies are reported in the literature about the application of back analysis for determining geotechnical and geomechanical parameters of rock and soil mass (Sakurai et al., 2003; Cepuritis et al. 2010; Frayssines and Hantz, 2009, Hussain and Stark, 2011), but they generally present little information about the geometry of the slide surface, and the weight of rock and soil mass that slid, although these factors are the most important parameters for back analysis process. Liang and Xue-song (2012) determined the slip surface having the minimum factor of safety (called critical slip surface in deterministic analysis of slopes) and the slip surface with the minimum reliability index (called critical reliability slip surface), but they have not considered the actual profile and geometry of the slide surface. Rocscience (2013) proposes the back analysis option in the Slide software for slope stability study, but it requires an imposed slide surface as input; alternatively, one can estimate by a finite element analysis the surface with the minimum factor of safety. However, this estimated surface is very likely different from the actual sliding surface, considering the uncertainties in input data of the finite element method."

Jan 1, 2015

By Michael Rieber

This study is an extension of our previous work in the area of coal transportation Its subject is the comparative costing of competing transport erodes. A wide range of costs and aspects of costs are dealt with in terms of engineering - economic analyses of the cost of the components which make up the facility and operating system descriptions of each coal transport mode. The cost comparisons, though analyzed, are not meant to be statements of policy but, rather, an input to decision making. The technical material presented in the succeeding volumes, alone with the earlier work cited above, forms the basis for the analyses. This material may also broaden the general understanding of coal transportation issues and problems. The project is divided into two main sections: (1) lone distance coal transport and (2) gathering and distribution systems. Within each section economic and technological comparisons are made of the available modes. These are used as the basis for comparisons among the modes. Inter-modal compatibility is studied with respect to both mixed trunk line shipment anti with respect to feeder to trunk line and trunk line to distribution systems. The engineering and technological data form the bases for the costing and economic analyses.

Jan 1, 1977

By C. F. Jackson

This paper has been prepared as a progress report in connection with the series of articles on mining methods and costs which are being published by the U. S. Bureau of Mines in the form of information circulars. When enough circulars have boon completed it is planned to publish a more complete and comprehensive paper in bulletin form dealing with the subject of underground transportation. Progress reports, followed b., bulletins, will be prepared from time to time dealing with other subjects included in the general study of mining methods at individual nines, such as mine development, drilling, and blasting; stoping methods (each principal stoping method to be summarized in a separate paper); Ventilation; wage, contract and bonus systems, etc.

Jan 1, 1931

By J. O. Lewis

The operation of gas-condensate fields is comparatively new and involves physical principles with which the industry was not prcviously familiar. It has been necessary to devise methods for testing gas-condensate wells and to correlate laboratory and field data. In this paper new methods are advanced for interpreting well G.P.M.† tests whereby dilution by dry gas can be estimated and information supplied on revaporization of condensates by dry gas. Inaccuracies in well test data are discussed. Changes in flow rates can cause changes in the G.P.M. of the effluent and it may take some time for a well to become stabilized after an important change in flow rate. Retrograde tests as usually conducted cannot be directly compared with field G.P.M. data, because the retrograde tests usually include solution gas in the condensates, which are reported On the cumulative basis whereas field data (G.P.M.) usually report pentaneS PlUS on a rate or instantaneous basis. Introduction Though long known to physicists, the phenomena Of retrograde condensation became known to the oil and gas industry Only in recent years, when deeper drilling disclosed that the behavior of vapors under changing pressures was different in high-pressure reservoirs than under the low-pressure operations with which the industry was familiar. These deep, high-pressure reservoirs in which condensation and vaporization behaved inversely to the accustomed manner became known as "gas-distillate," or preferably "gas-condensate" fields. Partly to prevent precipitation and retention of liquids in the reservoir, but still more to prevent the waste of residue gas, the operation known as "recycling," or preferably "cycling," was instituted, in which the residue gas is reinjected into the reservoir, thus maintaining pressure and driving the wet gas to the producing wells. For lack of field experience to serve as a guide, the industry had to assume that theory and laboratory experiments could accurately forecast retrograde behaviors in operating these gas-condensate fields, but it is obvious that these assumptions should be checked at the first opportunities against actual field experience. To make such checks, it is necessary to accumulate a large quantity of reliable field data, but experience has shown that it is difficult to obtain reliable field data and that the laboratory data as usually presented are not in directly comparable form. The problems of correlation involve the complex phase behavior on the one hand, and a knowledge of field data and a visualization of underground conditions on the other hand. This paper is an approach from field experience, The purposes of this article are to discuss the sources of uncertainty in the data and to present methods of analyzing, interpreting and correlating laboratory and field data. Data mostly from lower Gulf Coast fields are presented, from which some conclusions can be derived, but better data from more sources than those available to the writer will be required before satisfactory answers to many questions can be obtained. This paper is presented to stimulate the analysis and publication of data from other fields, the reexamination of field and laboratory methods, and the taking of more complete and reliable field tests. For these purposes, the writer presents some speculations that otherwise would not be appropriate.

Jan 1, 1947

By J. O. Lewis

The operation of gas-condensate fields is comparatively new and involves physical principles with which the industry was not prcviously familiar. It has been necessary to devise methods for testing gas-condensate wells and to correlate laboratory and field data. In this paper new methods are advanced for interpreting well G.P.M.† tests whereby dilution by dry gas can be estimated and information supplied on revaporization of condensates by dry gas. Inaccuracies in well test data are discussed. Changes in flow rates can cause changes in the G.P.M. of the effluent and it may take some time for a well to become stabilized after an important change in flow rate. Retrograde tests as usually conducted cannot be directly compared with field G.P.M. data, because the retrograde tests usually include solution gas in the condensates, which are reported On the cumulative basis whereas field data (G.P.M.) usually report pentaneS PlUS on a rate or instantaneous basis. Introduction Though long known to physicists, the phenomena Of retrograde condensation became known to the oil and gas industry Only in recent years, when deeper drilling disclosed that the behavior of vapors under changing pressures was different in high-pressure reservoirs than under the low-pressure operations with which the industry was familiar. These deep, high-pressure reservoirs in which condensation and vaporization behaved inversely to the accustomed manner became known as "gas-distillate," or preferably "gas-condensate" fields. Partly to prevent precipitation and retention of liquids in the reservoir, but still more to prevent the waste of residue gas, the operation known as "recycling," or preferably "cycling," was instituted, in which the residue gas is reinjected into the reservoir, thus maintaining pressure and driving the wet gas to the producing wells. For lack of field experience to serve as a guide, the industry had to assume that theory and laboratory experiments could accurately forecast retrograde behaviors in operating these gas-condensate fields, but it is obvious that these assumptions should be checked at the first opportunities against actual field experience. To make such checks, it is necessary to accumulate a large quantity of reliable field data, but experience has shown that it is difficult to obtain reliable field data and that the laboratory data as usually presented are not in directly comparable form. The problems of correlation involve the complex phase behavior on the one hand, and a knowledge of field data and a visualization of underground conditions on the other hand. This paper is an approach from field experience, The purposes of this article are to discuss the sources of uncertainty in the data and to present methods of analyzing, interpreting and correlating laboratory and field data. Data mostly from lower Gulf Coast fields are presented, from which some conclusions can be derived, but better data from more sources than those available to the writer will be required before satisfactory answers to many questions can be obtained. This paper is presented to stimulate the analysis and publication of data from other fields, the reexamination of field and laboratory methods, and the taking of more complete and reliable field tests. For these purposes, the writer presents some speculations that otherwise would not be appropriate.

Jan 1, 1947

By J. S. Ll. Leach, L. R. Rubin, M. B. Bever

The energies of formation of ordered and disordered solid solutions of composition CusAu and the energy of ordering in this alloy were determined by tin solution calorimetry. The degree of order was measured by X-ray diffraction and electrical resistance and microhardness measurements were made on ordered and disordered specimens. AMONG the phenomena associated with the order-disorder transformation of a solid solution, the change in internal energy is of special interest because of the part it plays in the various theories of ordering. Published values for the decrease in internal energy accompanying the formation of a superlattice from a disordered solid solution of composition CuAu range from —370 to —2260 cal per gram-atom. Some of these values represent calculations based on theory and others are the results of experimental measurements. The distinction between the change in internal energy, AE, and the change in enthalpy, AH, can here be neglected, because they are approximately equal for solid-state reactions at normal pressure. An analysis of ordering by Bragg and Williams' predicts an energy change of —605 cal per gram-atom for the formation of a superlattice in the alloy Cuau from a completely random solution. Peierls" application to Cuau of Bethe'sb earest-neighbor theory yields —560 cal per gram-atom for the formation of a superlattice from a matrix which initially contains short-range order. Cowley' extended the nearest-neighbor approach to include as many as five shells of neighbors; on this basis a change in energy of —500 cal per gram-atom is expected. Eguchi," using a quantum-mechanical treatment, calculated a value of —2260 cal per gram-atom for the difference in the energy of completely disordered and completely ordered Cu,Au. Sykes and Jones- eated a completely ordered alloy and measured its heat capacity as a function of temperature. This measured heat capacity agrees closely with the corresponding value found by the Kopp-Neumann (or mixture) rule up to about 250°C and above this temperature exceeds it, especially near the critical temperature for ordering. The difference between the integrals with respect to temperature of the observed and the Kopp-Neumann heat capacities was considered to be the energy of ordering. By this method Sykes and Jones found a value of —530 cal per gram-atom. This value is not adjusted for the short-range order remaining above the critical temperature. The pres- ence of such short-range order is suggested by the difference between the measured heat capacity and the extrapolated Kopp-Neumann heat capacity immediately above the critical temperature. Values reported by Weibke and von Quadt' and by Hirabayashi, Nagasaki, and Maniwaa were obtained in the course of investigations primarily aimed at other objectives. Weibke and von Quadt measured the temperature coefficient of the electromotive force of a Cu-CuAu cell. They obtained a value of —1010 cal per gram-atom for the heat of formation of the alloy at 500°C, at which temperature there is no long-range order. They also obtained —1380 cal per gram-atom as the heat of formation of the ordered alloy at 370°C. Considering the heat of formation of the disordered alloy to be independent of temperature, they estimated the energy of ordering at 370°C as —370 cal per gram-atom. At this temperature long-range order is incomplete and the degree of order changes rapidly with temperature. Hirabayashi, Nagasaki, and Maniwa," using an annealing calorimeter, investigated an alloy containing 23.4 rather than 25.0 atomic pct Au and thus could not obtain complete order. Thelr value of the energy of ordering was —490 cal per gram-atom. Orianis has recently investigated the Au-Cu system by the galvanic emf technique. He reports values for the heats of formation of Cu-Au alloys, from which the heat of formation at 427 OC of an alloy of composition CuAu may be found by interpolation. This value is —1080 cal per gram-atom. In the work here reported, disordered and ordered alloys of composition CuAu and corresponding mixtures of gold and copper were dissolved in liquid tin and the heat effects measured. These heat effects are small, since the dissolution of gold in tin is exothermic and the dissolution of copper is endothermic. The method, therefore, yields fairly precise values of the heats of formation of disordered and ordered alloys and of the energy of ordering. Experimental Procedure The calorimeter consisted of a long-necked Dewar flask immersed in a constant temperature salt bath and has been described by Ticknor and Bever." The chief changes in this equipment were an improvement in vacuum and the replacement of the mercury thermoregulator by a resistance thermometer control circuit. The solvent, which was maintained at a constant temperature near 350°C, consisted of 500 grams of 99.99 pct pure tin. The solute samples were mixtures of gold and copper in the proportion corresponding to the composition Cu,Au or solid solutions

Jan 1, 1956

By Andy Cole

Barrick Gold recently implemented an oxygen roasting process to treat carbonaceous ore from its Goldstrike property in Nevada. One of the key project challenges was the design of the roaster gas cleaning system, which was driven by the requirements of a strict air permit and the need to achieve very high reliability. The roaster gas systems include multiple stages of wet particulate collection, a dual-alkali SO2 scrubber, mercury scrubbing, CO oxidation and NOx reduction. This paper describes the gas system, the influence of regulations on project implementation, and performance of the system.

May 1, 2002

By Steve Vaughan

Canadian Regulation and Reporting Requirements High reporting standards are essential in developing and sustaining a strong confident capital market. As of February 1, 2001, technical reports on mineral exploration and mining work, must conform to the standards of the Canadian Securities Administrators (CSA) National Instrument 43-101. Only a ‘qualified person’ may supply the technical information on which a news release is based and must verify that the final version of the release is accurate.

Jan 1, 2003

By A. L. Jones

The subject assigned to me of "The Power" Problem of the Mine" is so broad that I have decided to confine myself to the question of the power supply itself, rather than the application of electricity throughout the property. We will look over certain economic aspects of the problem, particularly in the way it affects the mine manager or executive and his attitude toward the power plant. The accepted method of power application to the mine is by electric power, and the experience of each of you is that the job is never complete as you are always undertaking some further electrification which necessitates the stiffing up the power house to care for the additional load. The mine executive, then, is wrestling almost continuously with the problem of his power plant. Either it is overloaded and must be enlarged and rebuilt; or its operating costs are excessive; or it breaks down and limits coal output; or some one wants to sell new and improved machinery, until the manager almost hates the thought of such a restless part of his property. If he purchases power, every day new uses for it seems to be found. In many ways this unrest is due to short-sighted policy toward the problem, and the tendency when the problem of extension has to be met, to dispose of it in the cheapest way and without thought as to where the future is leading. The day when each opening had its own boiler plant, steam hoist, steam driven fans, steam pumps, steam loaders, etc., seems to be far behind us. The recognized method of power distribution today is by electric power, except for rather limited applications of compressed air; most of which is electrically compressed. During fifteen years contact with mines of Colorado and Wyoming the writer has seen nearly every mine power house double or triple in capacity or abandoned in favor of purchased power, worn. out and inefficient machinery thrown out, isolated boiler plants dropped, seam pumping at great depth changed to electric drive, all resulting in greatly reduced labor and fuel costs. Power costs, which in such isolated plants were considered normal, would be unthinkable today. One property where the main power supply was by compressed air from steam driven com¬pressors used under boilers 8.35 per cent of all the coal mined. The cost of power was 12 1/2 cents per ton of coal mined. Another property of four openings, each with its own boiler plant and usual equipment of hoists, pumps, etc., had a power cost of 10.3 cents for each ton mined; and these were days when you did not get very high prices for coal. Another property operating two mines mostly by steam used 11.1 per cent of the coal output under their own boilers and the power cost was 19.45 cents for each ton mined. Each of these properties is now electrified and power costs are from 3 to 4 cents per ton, and the fuel burned runs from 1 to 2 per cent of the output. With the broadening market and high prices for slack coal and the high prices for labor in boiler and engine rooms, the cost of steam is reaching a high figure, and efforts must be made to keep this down, by more efficient steam production and by utilizing this steam in better machinery which will increase the work done by each pound of steam. It must not be overlooked either, that the plant which is very wasteful of fuel is usually a pretty old one and one far from reliable. In a general way the more efficient the plant, the greater its reliability. Ample and reliable power supply means ability to get out coal when there is a market. The increasing use of purchased power is largely due to changing conditions which are tending constantly to push up the cost of power, unless the most efficient machinery is used and large scale production possible. The

Jan 1, 1923

Gaby Copper Mining?s Gabriela Mistral property is located in the Antofagasta region of northern Chile, at an altitude of 2,660 m (8,727 ft) above sea level. The reserve contains an estimated 562 Mt (620 million st) of oxide ore with an average grade of 0.41 percent total copper. The mine went into production in 2008. Gaby Copper faced the problem of having no reliable way to measure the solids level. This is a challenge that exists throughout the mining industry, where dust in the air and accumulation of solids on a sensor make accurate measurements difficult in areas such as transfer chutes, the rock box underneath crushers, silos and anywhere else that information is needed on the level of solids. The next-generation technology in the Sitrans LR560 radar from Siemens addresses this challenge. With a frequency of 78 GHz ? higher than previous generations of radar ? it provides a more robust signal for measuring in areas where there are high levels of dust accumulation. The Sitrans LR560 provides a signal beam angle of four degrees, significantly narrower than any other product on the market can offer.

Jan 1, 2014

By A. Cole, F. Porretta

Barrick Gold recently implemented an oxygen roasting process to treat carbonaceous ore from its Goldstrike property in Nevada. One of the key project challenges was the design of the roaster gas cleaning system, which was driven by the requirements of a strict air permit and the need to achieve very high reliability. The roaster gas systems include multiple stages of wet particulate collection, a dual alkali SO2 scrubber, mercury scrubbing, CO oxidation and NOx reduction. This paper describes the gas system, the influence of regulations on project implementation, and performance of the system.

Jan 1, 2002

By J. Koster

[In lQ jG thc E'lcct,ro:~(: L7.l :~u..-ic:ll S;%cti ?n of t?c :I. tcIl~tr,-;lcal 3:vi cioa, ?U~CE~U of lv!irtos, bc,~m an 9.ct iv.t In-:?*t ik7;5i GI of r.:ct.l-;c?;is for rccovcrin,; niclrel, cop?ir, an2 ?? cciou:; ~ot-1 c 1;-on or; :; of tile 3unl~crvi~.l~~ tiistrict in C1ni.k Coult:r, !Icl.r. ]

Jan 1, 1939

By Chas. F. Jackson

During the past 5 years the Bureau of Mines has published information circulars dealing with mining methods and costs at 78 ore mines; 7 circulars, each of which is devoted to a discussion of one of the principal mining, methods; and 23 circulars dealing with special phases of mining, such as ventilation, shaft sinking, tunnel driving, the cost of equipping and developing prospects and small mines, underground transportation, diamond drilling, and ground support. These circulars were written by many different authors, and in order that the method of presentation and the basis for compilation of data might be the same in all the papers the Bureau drafted an outline to be followed in their preparation. To clarify the data in these circulars, which are in the libraries of many engineers and mining companies, and the summarized data presented in this paper, that portion of the outline dealing with cost and labor-performance data is reproduced below.

Jan 1, 1934

By J. Koster

[In 1178 thn S-00n of thr !~Viluralcal Divicion, pur--'11 cf Mines, bcran an o. 't iv in': n-t!Y_Vnn of vothod; for recoverin'-1, Achol, copp~r, nK precioun notnin Zycn o;. -z of tic Bunkcrvillo KOH& in Clark County, Tcv. Tho Bunkcrvillo ran arc of t,-j)(,e of -iincrilization similar to that of 02 SWbury, Ontario, CannO, nichvl dc-?o?-:.t,. At prcoont, only n anall tonnes? p of ore has loan cxDr)scd in t*ic' :hui:er7ilIp rc: inn, ann. there is decided nce! for orjn: izod OrospectiAg ina drvclo-nnnt "crk there. It wann believod, howevar, t4it the dc,cuits varo 3ilficUntly siSnIficant to warrant an investigation iito their]

Jan 1, 1939

By Norman G. Foster

The mass spectra of 14 previously unreported alkylthiophenes are pre-sented. Low ionization voltage data of selected compounds from these 14 and 23 previously reported alkylthiophenes are presented and discussed for their value in supporting fragmentation mechanisms analytical correlations. A comparison with and corroboration of earlier correlations is made. Additional correlations concerning detection of side chain branching and the detection of ethyl-alkyl and propyl-alkylthiophenes are made. A discussion of the possible fragmentation routes and mechanism of fragmentation is given. Speculative structures are inferred s out some of the ions and hence this work provides a basis for suggesting fation mechanisms for the alkylthiophenes according to modern theories ass spectrometry. Verification of these mechanisms must await the availability of isotopically labeled molecules which are labeled in specific lotions that permit the definition of the paths of frag-mentation. Some suggestions for further work to generalize on the correlations and studies made to this point are presented.

Jan 1, 1965

By Martin A. Elliott

The Bureau of Mines began its investigation of the use of Diesel engines underground to provide technical information necessary to assist this development in the United States. It was considered desirable to furnish such assistance because successful European developments/ in this. field had indicated that Diesel mine locomotives might be safer than electric trolley locomotives. The Bureau has recognized for some time the importance of eliminating the hazards associated with underground haulage systems using bare trolley wires. For example, each year 30 to 40 fatalities occur as a result of electrocution by contact with bare trolley wires. In 1943 and 1944, 101 men were killed and extensive property damage occurred as a result of mine fires started by falls of roof grounding the bare trolley wires.

Jan 1, 1948

By AIME

IN the parlance of Hollywood, it was a super-colossal meeting. In the more restrained language of engineers, the Institute's 75th Anniversary Celebration attracted the largest crowd ever; was the longest Annual Meeting ever held, occupying a full week; had more important papers, more important people, more of an international flavor, and more glamour than ever before. And in the minds of those who came to the big city from the wide open spaces, one other record should be mentioned: for those not on an expense account, it was the most expensive affair ever staged by the Institute! To state the attendance down to the last digit for a meeting such as this is impossible. The total names registered on cards, plus those who attended the Annual Banquet but were not otherwise registered, came to 3149. But a few were registered twice, and probably a still larger few did not register at all, but just dropped in for a session or two in which they were interested. It would appear that 3200 would be about as close an estimate of attendance as could be made, and that is some 300 more than came to the biggest Annual Meeting of the past-in 1944. A considerable number of members brought their wives, but most were delegates at large.

Jan 1, 1947

By G. Pizzi, G. M. Ciucci, G. L. Chierici

The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and produclion measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available. INTRODUCTION A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows. 1. A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.'-' 2. A reliable value for the reserves can be obtained only if reservoir data are very accurate'- or if past production performance has been subjected to abrupt variations in the production rate."' 3. No unique value for the reserves can be obtained from reservoir past production performance. This conclusion has been based upon theoretical considerations" and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented. THEORETICAL CONSIDERATIONS As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gp, Wp,) and n output variables (p,), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multi-variable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production G,(t) and W,(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "black-box It has been demonstrated" that for a blackbox the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance. When W,(t) is known, the determination of G from

By O. G. Kiel, G. W. Swift

The concept of "a continuous succession of steady-states", which has been applied successfully by Aromfsky and Jenkins to obtain a solution for the nonlinear partial differential equation describing the transient Darcy flow of gas through porous media, is demonstrated to be equally valid for transient non-Darcy flow. A mathematical model, which numerically solves the partial differential equation, is used to check the validity of the succession of steady-states solution. Comparison of sand-face pressure histories compelted by the two methods shows excellent agreement. The utility of the succession of steady-states solution in predicting performance of gas wells rests in the fact that no special computation equipment is required. The development of the succession of steady-states solution leads also to a practical method for determining and analyzing field test data. A method for taking gas-well test data under constant-rate conditions is presented. Experimental data obtained in the field by employing the constant-rate method are presented and analyzed in accordance with the succession of steady-states solution. Analysis of data in this fashion is demonstrated to give direct "in situ" information for reservoir permeability, porosity and turbulence or non-Darcy coefficient. INTRODUCTION The economics of gas production are dependent upon the transient behavior of flow within the reservoir. For production from a finite reservoir, the transient flow behavior can be subdivided into two parts. At first, the transient caused by the movement of the pressure "wave" into the reservoir is of importance. Later in the production history, the pressure-wave movement ceases and the second transient stage of material depletion becomes controlling. For reservoirs of relatively high permeability, it can be shown that the pressure wave moves into the reservoir and stabilizes quite rapidly. In the case of relatively impermeable reservoirs, quite the opposite is true. Although it is theoretically possible to compute the production capability of a well from the properties of the reservoir as determined by static tests and core analyses, more reliable information is obtained by conducting flow tests on the well and thereby obtaining some measure of "in situ" formation properties. For gas wells, there are two basic types of tests in existence: the flow-after-flow method,' and the isochronal method.' Both of these techniques are tailored to obtain data that can be analyzed in accordance with the empirical performance equation: In addition, the isochronal method makes provision for the sluggish nature of pressure-wave movement in "tight" formations by requiring pressure build-up between flows and by stipulating that data obtained on successive flows be analyzed at equal elapsed flow times. It can be demonstrated that either test is valid for reservoirs of high permeability. Further, since it has been pointed out that the pressure wave stabilizes rapidly for reservoirs of this type, tests of relatively short duration will give stabilized information on the performance of a well. Further decline of sand-face pressure and/or production rate may be determined by employing material-balance techniques. Cullender' points out that for relatively impermeable reservoirs the flow-after-flow method gives invalid results. (See Appendix C.) If the isochronal method of testing is used, there are two alternatives: (1) the tests must be conducted for a sufficient length of time to obtain stabilized information (which may require months to accomplish); or (2) some method for extrapolating the results of short-term isochronal tests must be employed. The first alternative is impracticable because of manpower, conservation and economic considerations. Recourse to the second alternative requires some assurance regarding the reliability of the extrapolation technique. Poettmann and SchilsonJ present an empirical method for predicting stabilized performance. The present investigation was originally initiated to determine the reliability of this technique. To do this, a mathematical model was developed to simulate the Darcy and non-Darcy flow of gas through porous media. The model consisted of a finite-difference approximation of the nonlinear partial differential equation which was solved on an IBM 7090 computer. Long-term production histories were simulated by the model and compared against predictions obtained from the Poettmann-Schilson method. As the work progressed, it became apparent that a straightforward predictive equation could be developed by utilizing the concept of a succession of steady-states. As a result, the emphasis of the work was redirected to exploit the advantages of the new method.

By H. P. Rassbach, E. R. Saunders

MUCH progress has been made in recent years in the theory and practice of making stainless steel. By effective utilization of oxygen for decar-burization and more suitable alloying agents, it has been possible to attain consistent production of very low-carbon stainless steel. In order to facilitate economical production of stainless steels, the Electro Metallurgical Co. has carried out an extended experimental program that has clarified some of the complex interrelations of temperature and composition under decarburizing and reducing conditions. These results'-:' have been founded in large part on small experimental heats, and in order to confirm their validity and significance under commercial conditions, a survey of stainless steel melting practice has been made with the cooperation of stainless steel producers. Conditions required for decarburization and associated oxidation of chromium, manganese, and iron have been fairly well established in relation to the beneficial effect of the highest practicable temperature. The recovery of chromium and manganese from highly oxidized slags by reduction with silicon has been indicated with somewhat less precision and this study has shown significant deviation in large commercial heats from the small experimental heats. In spite of an unsatisfactory degree of accuracy in estimating the conditions affecting reduction of metallic values, it has been possible to calculate a slag weight in reasonably good agreement with the results observed in large heats. While there still is much to be learned about both the qualitative and quantitative aspects of stainless steel melting, this survey has indicated the manner by which the efficiency of the production process may be measured. Oxidation Period In order to establish practices for the recovery of chromium and manganese from the slag the amounts of these metals oxidized should be known. Moreover, since reduction of oxidized chromium and manganese must necessarily be accompanied by similar reduction of iron, knowledge of the total quantity of metallics oxidized is essential. The relations between carbon, chromium, and temperature under oxidizing conditions were developed by Hilty in 1948.' While it had been realized previously that retention of chromium in the metal during carbon oxidation is favored by high temperatures, the Hilty relation provided quantitative information useful for evaluating melting procedures. For example, it was shown that decarburization to moderate carbon levels can be achieved while retaining substantial amounts of chromium. However, in decarburizing to the low-carbon level necessary for producing 0.03 pct maximum carbon stainless steel, very little chromium remains in the bath at the temperatures generally employed. For this reason, Hilty, Healy, and Crafts' later projected an extension of the chromium-carbon relation to the low-chromium region. Although this chromium-carbon-temperature relation defined the composition of a chromium steel bath at the end of the oxidizing period, it did not provide a direct means for estimating the total amount of metallic oxidation occurring during decarburization of a stainless steel heat. This subject was investigated by Crafts and Rassbach³ and, later, by Hilty, Healy, and Crafts" who demonstrated that metallic oxidation is a function of the chromium content of the initial furnace charge, the minimum carbon content attained, and the temperature. It was further demonstrated from data on 1-ton heats that an empirical relationship exists between the ratio of chromium plus manganese to iron in the slag (S) to the corresponding ratio of these components present in the metal bath. The following expression was derived to permit the calculation of the amount of metallics oxidized during decarburization of a given charge: W-2000 (Cr1 + Mn1)-(Cr2 + Mn2) 1 100s/s+1-(Cr3 + Mn2) where W is the pounds of chromium, manganese, and iron oxidized per ton of charge; Cr1, the percentage of chromium in the charge; Mn1, the percentage of manganese in the charge; Cr2, the percentage of chromium in the bath after oxidation; Mn2, the percentage of manganese in the bath after % Cr + % Mn oxidation; and S =%cr+ % Mn/%Fe in the slag after %Fe oxidation. In order to establish whether the slag ratios of commercial heats are consistent with those found in the experimental heats, the slag and metal analyses shown in Table I were evaluated. These data represent samples taken after the oxidation of two 1-ton and seven 15 to 25-ton heats of types 303, 304, and 304L stainless steel made in chromite, acid, and basic hearths. Fig. 1 illustrates that the results for the commercial heats correlate reasonably well with the relationship originally established for experimental 1-ton heats. It will be noted that in the range of metal composition of these heats, the slag values generally lie above the line. As was suggested by

Jan 1, 1954