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By B. L. Landrum, J. Simmons, J. M. Pinson, P. B. Crawford

Patentiometric model data have been obtained to estimate the effect of vertical fractures on the areas swept after breakthrough in water flooding and miscible displacement programs such as gas cycling where the mobility is near one, The data are presented for the case of the fire-spot pattern in which the cemer well is fractured various lengths and orientations, the data indicate that for 10-acre spacing, fractures extetidirrg over 1300 ft in either directior1 from the fractured well may re.srrlt in reductions in sweep efficiencics from 72 to approximately 34 per cent. However. the area swept after break through may be quite largr and only 10 or 12 per cent 1ess than would be obtained if the reservoir were trot fractured. For the specific case when the volume of fluid injected is equivalent to 100 per cent of the pattern vol-unie, the swent area may vary from 80 to 88 per cent, depending on the lenght of the fracture. The former value is that which occurs when the break through or sweep efficiency was orrly 34 per cent and the latter figrrre of 88 per cent is that which is obtained if the reservoir were unfrac-ttm'd. It is pointed out that although the sweep efficiency may he very low in vertically fractured five-spot patterrz.s, the area swept at low water-oil ratios may be only 5 to 10 per cent less than those achieved if the reservoir were unfractured. INTRODUCTION Since the initiation of commercial reservoir fracturing techniques it has been desirable to determine the effect of fractures on the areas swept after breakthrough. Most water flooding or gas cycling projects are continued for substantial periods after the brcakthrough of the injected fluid. Although the sweep efficiency serves as one criterion for rating various flooding patterns. the area swept after breakthrough for various water-oil ratios or percentage wet gas, if cycling. is of perhaps more importance than the sweep efficiency alone. Sweep efficiency data on the vertically fractured five-spot have been presented3. Previous work on the line-drive pattern has shown the effect of vertical fractures on the area swept after breakthrough for the case in which the distance between injection and producing wells divided by the distance between adjacent input wells was equivalent to 1.5 (see lief. 2). The data indicated that for the line-drive pattern it may be desirable to flood or cycle substantially perpendicular to the fractures in order to achieve the greatest recovery for the smallest volume of fluid injected. For this study the center well of a five-spot is assumed as the fractured well. All fractures were assumed to originate at this well and extend into the reservoir for various distances and orientations. All the fractures are straight and are of large permeability compared to the matrix proper. These data are presented to aid the engineer in estimating fractured five-spot pattern performance. ANALOGY The potentiometric model was used in making this study. The model used was 20 20 in. by approximately 1-in. deep. For certain portions of the study one corner of this model was considered to be an injection well and the opposite corner a production well. To simulate vertical fractures a copper sheet was soldered to the wire well and made to conform to the desired length and orientation. In other studies the same model was used except that the four corners of the model might be considered as the corner wells of a five-spot pattern and a fifth well was placed in the center of the model. The well placed in the center of the model was fractured. The total fracture length is L and the well spacing. d. The complimentary fracture angles will be obvious from Figs. 3 and 4. The data obtained on the potentio-metric model assumes the pay to be uniform and homogeneous, the mobility ratio is one, steady-state conditions exist and gravity effects arc neglected. The permeability of the fractures is very great compared to that of the matrix proper. The po-tentiometric model has been used widely both in water flooding and gas cycling projects, and may be used for miscible displacement; how-ever. it is believed that the poten-tiometric model data are more properly applicable to gas cycling than water flooding because the model as-

By E. C. Pechin

The attention of the members of the Institute of Mining Engineers is asked to a description of the minerals of Southwestern Pennsylvania, as representing the minerals of an enormous area, stretching continuotisly, with local variations, along the western slopes, and at the base of the Alleghany Mountains, through Western Pennsylvania, West Virginia, and Kentucky, and destined to play no mean part in the future of the iron trade of the country. The particular locality is at and near Donbar, in Fayette County, where the most careful examinations and extensive developments have been made. The deep gorges cut by the Youghiogheny and Monongahela Rivers, in their passage through the mountains and lower lands, give admirable facilities for observing the measures lying between the sandstones of No. 11 and the upper coal measures. Apart from its varied mineral and agricultural resources this section of country has great historic interest attaching to it. It was down the Monongahela that Braddock led his ill-fated army to its defeat under the wails of Port Duquesne, and it was up the Youghiogheny River and Dunbar Creek that the shattered remnants hastily fled to gain the camp of Colonel Dunbar, the second in command, who was entrenched upon a high knob, at the head of the creek which bears his name, and which is still known and visited as Dunbar's Camp. Numerous streams, runs, and localities preserve the names of the guides and pioneers who accompanied, in early colonial times, young George Washington, who was pushing his surveys into the trackless and hostile wilderness, and many of them taking up large tracts of

By J. E. Warren

The mathematical problem considered by the author1 can be given another physical interpretation which is of some practical significance. The alternative physical problem involves the approximate behavior of a single well which is producing at a constant rate through an axially symmetric, horizontal fracture of infinite flow capacity which is located at the center, top or bottom of a uniformly thick, horizontal, homogeneous, anisotropic reservoir of infinite lateral extent which contains a single, slightly compressible fluid. Using Coats' asymptotic results, the wellbore pressure in the fractured system is given by the following equation.

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Clayton A. Signor

Abstract: Expansive soils cause more damage to structures annually than a combination of other major natural disasters. Because of the cost to our society, all means and methods need to be fully explored to mitigate the problems associated with expansive soils. This study will present a foundation design approach that is underutilized in this application, driven piles. The main objective of the study is to present pile test results and analysis from four driven pile project sites in three types of expansive soils found in central Texas: Del Rio formation, Taylor/Navarro formation, and expansive alluvium. High strain dynamic pile tests were conducted on each of the four studies with rigorous signal matching analysis from the CAse Pile Wave Analysis Program (CAPWAP). Ultimate pile capacities ranged from 73 to 311 kips with an average of 61% of the total capacity coming from the pile shaft and were two to six times the structural capacity needed. Allowable loads calculated from Modified Gates dynamic formula best modeled allowable test results. Average unit skin frictions ranged from 0.50 to 4.71 ksf. Restrike pile tests of 1 to 17 days after initial driving reported 30 to 100% shaft capacity gain. All open-ended pipe piles driven produced soil plugs ranging from 4 to 14 feet thick. Small diameter, thick-walled, open-ended pipe piles reached penetration of twice the depth of designated zone of seasonal moisture change without problem. The observed production rate of the driven piles was on average 8 minutes, which implied daily production of 15 to 40 piles. Predrills or augered holes should be specified for underground obstructions found in soil investigation.

By J. Davies

This paper describes the successful management and construction of the 5.18 m (17 ft) diameter, segmentally lined, North Dorchester Bay CSO storage tunnel in Boston, MA. This 3,300 m (10,830 ft) long tunnel was mined through variable soft ground with only 6 m (20 ft) of cover, using an earth pressure balance tunnel boring machine. These extensive data collected from the projects unique automated and internet accessible geotechnical and TBM monitoring system, will be examined and used to explore the relationships between geological conditions, TBM operating parameters and measured settlements. The paper will also discuss the use of screw revolutions as an indicator of muck volume.

By Youn-Bae Kang

Evaporation mechanism of S from liquid Fe–C–S alloys at 1873 K was proposed by analyzing available experimental data. It has been known that increasing C content in liquid alloy increases activity coefficient of S ðfSÞ, and it could raise driving force for the evaporation reaction S = S(g). However, experimental data of the evaporation of S in the Fe–C–S alloys could not be accounted for only by considering the increases of fS. In the present study, formation of carbosulfides, CS(g) and CS2(g), was additionally taken into account in order to explain role of C for the accelerated S evaporation. Surface adsorption of S was also taken into account, which retards the evaporation rate of S. An evaporation model equation was formulated. It can be applied to calculate the evaporation rate of S over wider C content (from zero to its saturation to liquid alloy).

By B. Manana

In heap leaching, the oxidative dissolution of value minerals encapsulated deep within large particles cannot be fully understood on the basis of the bulk solution conditions relative to variable solution conditions near the mineral surface. In the present study, the diffusion of the oxidising species through inner particle pores is simulated in a model apparatus that separates an inert platinum electrode under controlled reduction potential from the bulk solution through narrow pores of varying length. The Cu-NH3 system was selected as a model system and Cu(II)/Cu (I) as the redox couple of interest. Platinum probes inserted in the pores allowed the measurement of varying redox potentials along the pore length. Results showed that in a 10 mm pore, there exists a narrow (0.5 mm) zone near the reduction surface that is depleted of the oxidant and in which its supply is strongly diffusion limited, even if it is in abundance in the bulk solution. The consistent presence of this narrow diffusion region across all experimental results indicated that the transportation of the reduced species away from the reaction surface had the most significant influence on the potential variations within the pore. This was further supported by the minimal effect of varying concentrations of both Cu(II) and dissolved oxygen on the solution potential within this region.

By C. R. Boyd

Without attempting to do more than give a preliminary or skeleton report upon the geology and minerals of Southwestern Virginia at this time, I am led to hope that the great commercial importance of the sixty miles of cross-section here crudely treated of

By E. R. Spencer, E. Reeves

National Institute for Occupational Safety and Health (NIOSH) researchers conducted an investigation to quantify sound levels and to determine the amount of sound reduction provided by engineering noise controls installed in a talc processing plant. Baseline sound level and sound intensity measurements were performed at the plant and the measurement locations were recorded for comparison to post-control measurements. Follow-up measurements were then made at the same locations after the initial noise controls were installed. The plant subsequently decided to implement additional noise controls and the researchers returned to conduct measurements for a final analysis of all noise controls. The most significant results showed a sound level reduction in the main mill area from a range of 93-104 dB(A) down to 90-94 dB(A), and a total sound power level reduction of 21 dB(A) for air classifying mill 3.

By A. A. Hazell

Mine management by objectives by A. A. Hazel The procedure of setting production targets is illustrated in Appendix I of the paper. This procedure is intended only as a guide although the standards on which it is based were established by work studies and found subsequently to be well within the limits of a trained crew.

By Albert L. Brautigam, Michael R. Yenchek, Jeffrey Shawn Peterson, James C. Cawley

The National Institute for Occupational Safety and Health investigated how the starting of induction motors may cause nuisance tripping of short-circuit protection on coal mine power systems. This research had a dual purpose: 1) to identify how motor-start waveforms differ from those for short circuits and 2) to devise a method to provide short-circuit protection without intentional time delays to account for motor starts. This technology will help ensure that surface temperatures of energized electrical apparatus will not exceed gas or dust ignition thresholds when short circuits occur.

By R. G. Hawthorne

This report is concerned with fluid displacement in porous media, in those cases where viscous and gravitational forces control the displacement. Such a system would usually be found in a sand body of large physical dimensions such as an oil reservoir, although it is possible to create such a system in the laboratory. It is shown that the position of the fluid interface can be predicted by numerical calculations using a basic idea presented by Dietz. Fluid flow is considered in a vertical plane in a homogeneous, porous medium of sufficient thickness that the capillary transition zone is small in comparison with the total reservoir. A theory developed by Dietz' is used to make numerical calculations of the position of the fluid interface. The results for several conditions are compared with scaled model experiments. The results show that, for gas drive in a reservoir of steep dip, a relatively low flow rate can displace large volumes of oil before gas breakthrough. On the other hand, water injection at favorable mobility ratio and low dip may show best performance at high rates. Water tends to underride the oil and, given sufficient rime, will break through without much oil displacement. For certain conditions, which include relatively low flow rate, the interface is a straight line and its behavior is simple to calculate. At higher flow rates, the interface is unstable, and a numerical solution was programed for an automatic computer. In general, good agreement is shown between the fluid model and the computed results so long as gravitational forces have control. For a water drive at very unfavorable mobility ratio, many small water fingers appear. These viscous fingers are not controlled by the relatively small gravitational forces. When viscous fingering becomes the controlling factor, the mathematical model is oversimplified, and results do not check the fluid flow model. INTRODUCTION Present methods of reservoir analysis depend upon certain simplifying assumptions to obtain mathematical descriptions of practical use. Material-balance methods (Muskat2 or Tarner2) assume uniform fluid saturations in the entire reservoir, or in a few subdivisions of the reservoir. An unsteady-state flow calculation by West, er at considered pressure and saturation changes in flow to a well during solution gas drive, and neglected gravity effects. Results showed only a 4 per cent difference for ultimate oil recovery by the Muskat method, even though the case chosen for study was one in which unsteady-state effects should be high. The Buckley-Leverett5 method commonly assumes a one-dimensional flow system. It is applicable at high flow rates where viscous forces predominate over gravity forces. Simultaneous, parallel flow of the two fluids is assumed, and the concept of a fluid interface is not introduced. Permeabilities to each fluid for a given saturation must be known. The method is not applicable for a two-dimensional system where cross flow becomes possible. Less well known is the displacement equation derived by Dietz. This method is designed for two-dimensional flow systems and assumes a definable fluid interface within the porous medium. Dietz showed that, for a range of low flow rates, the interface would be stable. straight and at an angle of inclination which could be simply calculated. At a certain critical flow rate, the calculated interface tilt would equal the formation dip. For higher flow rates, a finger of displacing fluid would invade the displaced fluid. Dietz indicated that his method applied only to macroscopic reservoir behavior, while the Buckley-Leverett method applied to the small transition zone at the fluid interface. The examples worked out in this report are based on the fluid-displacement theory of Dietz. It is shown that the Dietz theory may be used to derive equations analogous to the Buckley-Leverett equations. In contrast to the Buckley-Leverett method, flow is considered in a plane rather than being limited to a line. Rather than a frontal advance, the movement of a fluid interface is followed. For flow rates substantially exceeding the critical rate and for high viscosity ratio, many fingers of invading fluid occur-—rather than the single finger assumed by Dietz. On the other hand, so long as some gravitational influence remains, the flow is not entirely parallel to the bedding planes as assumed by Buckley and Leverett; therefore, both methods fail to give an adequate descrip-

By A. J. Brown

The causes that have formed fissures in the earth's crust, and the agencies that have converted them into metallic beds, are amongst the most important and interesting subjects that can engage the attention of the mining engineer or the scientist. They lie at the very base of the whole system of vein geology, and until something like a correct theory can be arrived at with regard to them, the science as such is necessarily very incomplete. he data for such a theory, owing to a lack of careful and systematic observations in countries pre-eminently metalliferous, like Mexico and the States of Central and South America, are almost entirely wanting. Doubtless there has been abundant speculation on the subject, from the earliest times down to the present, in every country where mining has been one of the leading industries of the inhabitants. Perhaps the theory of Elie de Beaumont more nearly approaches a satisfactory explanation than that of any contemporary authority. The most recent investigations, both in Europe and on this continent, tend to produce the conviction that the phenomena of metallic fissure lodes are in some way connected with, and dependent upon, plutonic agencies— not, however, as the direct product of volcanic activity, but rather as the result of chemical agencies called into play through its aid. Active volcanoes generally produce only the well-known types of volcanic rocks, though, perhaps, well-marked cases can be shown where these contain ores of copper, etc., evidently derived from the same deepseated source as their hypogene gangue. To prove that there is a connection between metallic lodes and plutonic rocks, it is not necessary that the ores should in all cases occupy fissures within the limits of masses of propylite, rhyolite, or other like rocks, or be

By E. Charles Abbey

Manganese in electrolyte has both beneficial and detrimental effects in Zn electrowinning. Mn oxidizes to form MnO2 on Pb–Ag anodes, cell walls and pipes. MnO2 reduces anode corrosion but also leads to short circuiting and maintenance issues. MnO2 is thought to interact with chloride ions and produce oxidized chlorine species. The interactions between Mn and Cl are not well understood. Therefore, two sets of 45+ day bench scale experiments were conducted to investigate the effects of the manganese to chloride ratio on anode corrosion rate and electrolyte chemistry using rolled Pb–Ag anodes. Daily manganese and chloride losses from the electrolyte appeared to be correlated. Increasing the average Mn/Cl− ratio from ∼7:1 to ∼11:1 reduced the anode corrosion rate. Increasing the ratio above 11 did not reduce the corrosion rate further. Anode scales produced with Mn/Cl− ratios at and above 11:1 contained some γ–MnO2 while scales formed with ratios less than 11:1 did not.

THE Institute assembled in the Hall of the Boston Natural History Society on Tuesday evening. Dr. T. Sterry Hunt, of the Boston Institute of Technology, after a brief address of welcome to the Institute, read an introductory paper on the Geognostical History of the Metals. President Raymond responded to the welcome of Dr. Hunt. The following names were then presented to the Institute, with the recommendation of the Council, for election: Adams, J. M., . . . . . . Silver City, Idaho. Daggett, Ellsworth,. . . . . Salt Lake City, Utah. Geist, Alfred W., . . . . . Boston, Mass. Hays, Dr. S. Dana, . . . . . Boston, Mass. Heinrich, Oswald J., . . . . Midlothian, Va. Johnson, J., . . . . . . Braidwood, Ill. Leckie, Robert G., . . . . . Actonvale, Canada. Lyman, Edward, . . . . ' . Troy, N. Y. Maltby, William, . . . . . Braidwood, Ill. Nichols, Lyman, Jr., . . . . Bbton, Mass. Ordway, Prof. J. M., . . . . Boston, Muss. Rand, Theodore D , . . . . . Philadelphia, Pa. Richards, Prof. Robert H., . . . Boston, Mass. Roclrwell, Prof. Alfred P., . . . Boston, Mass. Roepper, Charles W ., . . . . Bethlehem, Pa. Schulz, A. von, . . . . . Central City, Colorado. Singer, William F., . . . . Pittsburgh, Pa. Spillsbury, E. G., . . . . . New York. Wells, Calvin, . . . . . . Pittsburgh, Pa. The session concluded with the reading and discussion of a paper, by Henry Engelmann, On the Mines and Ores of the Little Cottonwood Canyon, Utah. The second session was held on Wednesday morning, when the following papers were presented : On the Midlothian Coal Mines, by Oswald J. Heinrich. On the Probable Existence of Microscopic Diamonds in California, by Prof. Benjamin Silliman.

By H. M. Wells

The influence of economics on the design of mine shaft systems by H, M. WEI.LS, Pr. Eng., M.Se. (Fellow) The purpose of this paper is to review some of the more important economic criteria that must be taken into account when planning the number, type, size, and distribution of the shafts, or shaft systems, required to exploit a block of payable ore. The postulated philosophy governing the selection of design parameters is that of optimization of the financial return per rand of venture capital employed for the project as a whole. While this criterion may not necessarily satisfy the investment objective under all circumstances (as, for instance, where risk limitation is important), it does serve to place the relative economic advantages and disadvantages of specific design features, which may sometimes be in opposition, into correct perspective with respect to the overall economics of the project under the prevailing economic climate at the time of the investigation.

By C. S. Matthews, M. J. F. Rosenbaum

The purpose of thir work wax to lcarn it~lzut infori~lation could he obtained from various typs of pilot water floods and to attempt to find the optunum pilot patter11, for a revervoir which had previously been depleted by a solution gas drive. The study was made in the laboratory with mathemetical methods a dynamic analog and a potentiotnetric analog. Results werp tested against the field llistorics of a nrrnlber of pilot water floods. At a reasonable valrre of currzulative injection, the total production rate for the one-injector five-spot should reach about 6.5 per cent of injection rate, and for a four-injector five-spot, about 9 per cent. Accurate estimates of ultimate recovery cannot be made on the basis of such snzall prorluction rates. However, with a pilot composed of nine ir1jector.s and 16 producers the production rate is approximately 50 pcr cent of injection rate at a reasonable value of camulative injection. Sonle inforn~ation for extended performance predictions might he obtained from such a large pilot. These conclusions were drawn on the basis of results obtained for unit mobility ratio, and a sturly using tlre potentiometric analog was made of the effect of other mobility ratios to determine the range of applicability of these predictions. For the four-injector, five-spot pilot with the ratio of production to injection rate (before water breakthrough) is about twice that for with it is about two-thirds; and with M0= 10, it is about one-third For high mobility ratios, it was found that the production rate increased considerably as water-cut increased. These result can be used to modify, qualitatively, the inter.pretntions based on curves for the unit rnobilit\. ratio CaSeS. It was found that the maximum ratio of production rate to injection rate obseriled in field pilot floods was of rhe scime order as that prerdicted by these methods. The time required to reach thisr maximum did not generally agree with the time predicted for a homogeti~orir reservoir. The differcrlce between predicted and observed time of response gives an indication of the permeability profile and of the condition of the producin,g wells. Pilot water floods of the pattern type are generally carried out in reservoirs which have been depleted by solution gas drive and are at low pressure. Under these conditions, oil and water can be considered incompressible. It is assumed that, as the water is injected, an oil bank forms ahead of it and that there is a distinct interface between the water zone (or bank) and the oil zone (or bank) and between the oil zone and the region ahead of the oil zone. It is further assumed that only gas is mobile in the unflooded (gas) region, only oil is mobile in the oil bank and only water is mobile in the water bank. The saturations and the mobilities associated with each zone are assumed uniform. We idealize our reservoir to be homogeneous, horizontal and of constant thickness. Effects of gravity within the producing layer are assumed negligible. If the actual time-dcpendent flow problem is approximated by a acries of steady-state problems. the potential and stream function in the oil bank and water hank satisfy Laplace&apos;s equation in two dimensions. We can therefore use a poteiitiometric analog of this system. Potentiometric models have yielded uscful results in this laboratory&apos; and clsewhere in the study of a variety of secondary recovery problems. For the case where M = I, we generally prefer to use theoretical mcthods as well as a simpler dynamic analog. Except where otherwise noted, the ratio, side of five-spot/wellbore radius. is taken to be 3,600. a figure which corrcsponds to a normal-size wellbore in a 10-acre well spacing. THEORETICAL EVALUATION OF VARIOUS PILOT PATTERNS, Mw0 = 1 <&apos;he theoretical models which we used to examine the performance of various pilots are shown in Fig. 1. Image theory was used to determine the ratio of production rate to injection rate as a function of the volumc of the flood. The ratio of production rate to injection rate was chosen because this is an easily measurable quantity which is characteristic of a pilot

By J. E. Powers, T. D. Taylor, N. E. Wood

A computer program has been developed to simulate a gas transmission 1ine operating under transient conditions. The program was developed by application of the basic mass and momentum balance equations. The nonlinear equations thus obtained were transformed by the method of characteristics and finite-difference techniques to make them suitable for machine computation. Three tests of the computer program were made. In each of these, the initial condition was assumed to be steady-state flow, the inlet density was held constant at the initial condition, and the outlet mass flow rate was varied with time. One test was theoretical in nature, but the others were made for direct comparison with actual field data. Results of the tests are presented in graphical form. INTRODUCTION Theoretical investigations of the transient flow of gas in long pipelines have been limited in number. In 1951, Olds and Sage4 developed a gaphical method of solving the nonlinear flow equations describing transient gas flow in a long pipeline. Research in this field at the U. of Oklahoma was initiated by Nelson1 in 1956. Nelson utilized a computer to solve numerical equations involving a lengthy trial-and-error procedure, and his results have been reported in the literature? It does not seem likely that Nelson&apos;s method can be extended to the analysis of transient behavior of pipeline networks; therefore, the investigation to be discussed in this paper was undertaken to improve and extend the previous work. The following discussion presents, briefly: (1) the basic differential equations governing transient flow, (2) transformation of these equations into a form suitable for machine computation. (3) role of boundary conditions in the calculations, (4) a very brief description of the computer program which was developed to simulate the pipeline and (5) results of tests of the computer program.