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By T. Sterry Hunt

THE essential principle of this new process, now in operation in Chili and in North Carolina, for the extraction of copper from its ores, is the dissolving of the oxides of copper by a hot solution of protochloride of iron and common salt. In the action which takes place, the protochloride of iron is converted into peroxide, while the oxides of copper are changed into protochloride and dichloride, the latter of which, though insoluble in water, is readily soluble in a hot strong brine. From the solution thus obtained, metallic iron throws down the copper in a metallic state, regenerating the protochloride of iron; which is then ready for the treatment of a fresh portion of oxidized copper ore. In the case of slimy ores, the contact of the bath with the ore is effected by agitation in tubs; but when the ores are granular, lixiviation in large vats is equally efficient and simpler. The hot solutions, charged with chlorides of copper, are digested in tanks with scrap-iron, or better, are made to flow through covered channels containing the scrap-iron, and in their passage lose the whole of their copper; the reaction at the same time evolving so much heat as to keep up the temperature of the liquid. In order to prevent a certain loss of chlorine, which otherwise takes place from the production of some basic ferric chloride in the reaction between the ferrous chloride and the oxides of copper (both protoxide and dinoxide being generally present in calcined ores), a portion of sulphurous fumes from the roasting is made to pass through the regenerated bath before adding it to fresh ore. This has hitherto been effected by injection, with the aid of a jet of steam.

By C. Gatlin, N. E. Garner

Results of impulsive wedge penetration tests on two synthetic, plastically deforming rocks are presented. Basic data obtained were force-time, displacement-time, and force-displacement curves for the impacts, plus the crater geometry. Wedge geometry and blow frequency were varied over a considerable range. The synthetic rocks consisted of wax-sand mixtures; two waxes of diflerent ductilities were used to provide variable "rock" characteristics. Conventional triaxial tests showed that these synthetic rocks exhibited force-deformation curves and Mohr envelopes quite similar to real rocks, except that strengths were much lower. Measured forces from static penetration tests agreed closely with theoretical values; however, dynamic force values were much higher than the static. These latter disparities are attributed to the viscous nature of the waxes. Thus the utility of these or similar rock models must depend on the scaling of rock viscosity, which is as yet unknown for impulsive loadings at elevated stress states. It appears, however, that some macroscopic, static phenomena may be studied with wax-sand rock models. INTRODUCTION The resistance of solid materials to indentation or perforation by projectiles or other penetrators has been studied by workers in many areas. Despite these efforts no universally accepted laws or formulas are available for describing experimental observations. In the metals field the force-deformation behavior of impacting bodies is often analyzed by the Hertz law for elastic collisions, the Meyer law if plastic deformations occur, or some combination of both.' The similarities of these expressions to empirical drilling formulas of the oil industry are apparent. Beginning with the basic contributions of Simon and co-workers at Battelle,' a number of experimental papers concerning the reaction of rocks to vertical impact have appeared in the U. S. mining and petroleum literature.'-' Most published data have, to date, been obtained at atmospheric pressure, although some early high pressure information was reported by Payne and Chippendale.8 Maurer" has recently utilized available brittle impact data to develop a drilling rate equation based on the experimentally observed proportionality between crater volume and blow energy. His result agreed with earlier efforts by both Somerton, who used dimensional analysis, and Outmans, who used plasticity theory. It has long been known that rocks exhibit different modes of failure depending on the state of stress. The literature in this area is considerable; however, papers by Bredthauer, Handin and Hager,13 nd Robinson", are adequate to illustrate the point. Since rocks flow plastically at certain triaxial stress conditions, the mathematical theory of plasticity has been used to analyze the rock drilling problem. Cheatham'" has altered the wedge identation solution of Randtl to rocks, and has developed useful equations for penetrator forces under a variety of conditions. Outmans" has utilized Hill's solution in a similar manner to develop a drilling rate equation. Both Cheatham and Outmans used the linear Mohr-Coulomb rule to relate rock strength and confining pressure. The actual stress at the hole bottom is not easily ascertained, although photoelastic studies by Galle and Wil-hoit," plus the analytical treatment of Cheatham and wilhoiti8 provide some insight. Consequently it is not clear to what extent the highly idealized rheological model of a perfectly plastic solid can be realistically applied to the rock drilling problem. This paper is the first report on a long range experimental study of crater formation in rocks at elevated stress states. The data presented here are from the first phase of the project. Data obtained from impulsive wedge impacts on two synthetic, plastically deforming rocks are presented. MODEL ROCKS Geologists have long been faced with modelling the behavior of the earth and, as a consequence, have studied scaling problems in some detail.' In general, their main problem is handling the wide disparity between laboratory and geologic time. In our studies the time effects (blow velocity or rate of loading, blow duration, etc.) were essentiafly the same for both. model and prototype, as were were geometry and tooth penetration. Thus application of available scaling laws suggests that Similarity is obtained if the stress-strain curves of model and prototype are similar." For this reason Hubbert and Willis''

By H. T. Kennedy, S. G. Dardaganian, J. L. Clanton

This paper presents equilibrium ratios measured on oil and gas samples taken from the Kelly-Snyder field at the reservoir temperature of 128°F. From these data smoothed curves were constructed for the reservoir fluid up to the bubble-point, 1,874 psia. A material balance calculation, based on the use of equilibrium ratios instead of the usual solubility and shrinkage meayr~rements is made on the field and compared to the con\.entional method. DETERMINATION OF EQUILIBRIUM RATIOS The equilibrium ratios, or K values were obtained by recombining separator samples of oil and gas taken when the reservoir was above its bubble point, and thus represented the reservoir fluid before any change had occurred due to the evolution of gas. The well sampled had a gas-oil ratio of 617 cu ft of high pressure sepalator gas per barrel of separator oil. and a bottom-hole temperature of 128°F. Samples were brought to equilibrium by agitating for 24 hours in a thermostat, maintained at the proper temperature within 0.2ºF, mercury being added when necessary to maintain the pressure constant. Samples of oil and gas were then taken by constant pressure displacement, and analyzed by low temperature frac-tionation. Equilibrium ratios were determined at 128°F and 500, 800, 1,000 and 1,400 psig. At the latter pressure, there were indications that the gas samples were contaminated with small quantities of oil, and only data taken at the first three pressures were included in Fig. I. This figure has been extended to higher and lower pressures by the use of the Fluor charts for 3,000 psi convergence pressure, on which the experimental points fit well. MATERIAL BALANCE EQUATIONS The possible errors involved in conventional material balance equations have been analyzed by Muskat1. Where the errors occur in field measurements, or in obtaining effective averages from variables such as gas-oil ratio and pressure, they will evidently be involved in any attempt to estimate the content of the reservoir. On the other hand, substantial errors may be introduced in conventional material balance calculations by: (1) the neglect of the amount of oil dissolved in gas at high pressures and temperatures in the reservoir, but which condenses under separator conditions; (2) the assumption that the separation of oil and gas in the reservoir may be duplicated by a differential liberation in the

By B. Zondek, W. T. Cardwell, J. W. Sheldon

The fundamental equations that are used to describe two-phase fluid flow in porous media are Darcy's law for each phase and an equation of continuity for each component. The special case of one-dimensional, incompressible, two-phase flow has received much attention in the petroleum engineering literature.1-10 The basic paper on the subject is that of Buckley and Leverett.2 Buckley and Leverett showed that one could eliminate the pressure and obtain a single partial differential equation for the saturation. They solved this equation for the case when gravity and capillary forces are negligible. A frequently encountered property of the solution of the basic partial differential equation is that, as time progresses, the saturation becomes a multiple-valued function of the distance coordinate, x. Buckley and Leverett interpreted the formation of multiple values as an indication that the saturation-distance curve had be-come discontinuous. They developed a method of determining the position of the discontinuity from a material balance. We solve the Buckley-Leverett partial differential equation using the method of characteristics and the concept of shocks. Our treatment is analogous to treatments used in the theory of supersonic compressible flow." Although the numerical results obtained are the same as those obtained by previous methods, we believe that this approach is more logical and has broader applicability. It can, for example, be generalized to treat the case when the fluids are compressible. It is not clear how one would go about doing this using the method of Buckley and Leverett. To illustrate the power of the method of characteristics with shocks, we solve a problem in gravity segregation which has not been treated previously in the literature. A special case of the general method developed here was used by Welge, to solve a particular fluid displacement problem. We consider two-phase incompressible flow along the vertical direction x in a porous medium. We assume that there is no flow transverse to .x. We measure positive in the upward direction. The fundamental equations are obtained from Darcy's law and the mass conservation law. Since the two phases are incompressible, mass conservation is equivalent to volume conservation.

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By Richard Akerman, Frederick Prime Jr

[THE attention now being paid both in this country and Europe the greatest economy in the working of the blast furnace, and the eagerness with which all thoughtful men in the iron business look for any new information which will tend to throw light on this subject, is a quite sufficient excuse for presenting this paper to the American Institute of Mining Engineers.] I. It must be borne in mind that when two bodies unite to form a chemical compound, heat is almost always evolved. In order to

By Charles P. Williams

The successful production of zinc white or oxide on a commercial scale in this country dates from the issue of the patent of Samuel Wetherill, for the preparation of the material (November, 1855), and

By Oswald J. Heinrich

THE origin of spontaneous combustion in collieries is, of course, chiefly due to bad system in laying out the pits, unclean workings, insufficient ventilation, and neglect in damming off works after they are exhausted of the main coal. This is particularly indispensable in the Richmond field, because it is difficult and dangerous here, on account of the inferior roof, to remove the last vestiges of coal ; and we are compelled also to retain all the slates and bands, as far as possible, in the pit, to help fill up, although such material is liable to fire. This, however, can be prevented to a great extent, as mentioned below. I am satisfied that the only system of working this thick coal is by cross-cutting (Querbau, ouvrage & travers) or working in benches, as practiced in France (Creusot, Rive de Gier, St. Etienne), in Silesia (Kiinigsgrube), which I have used as far as it is practicable in an old pit, almost torn to pieces by former workings. Modifications may, of course, be needed, even in the same pit, on account of irregularities in the seam. I am also satisfied for economical reasons (on account of the heavy cost for timbering) that pits here ought to be worked upwards, even if it requires a longer period of time to win the coal, and a greater outlay of capital to commence with. The various saddle-shaped " troubles " making natural minor basins in the main basin aid in the execution of this plan. A pit worked once ought to be worked out clean, given up, and dammed off forever. If sections of proper height are assumed, according to the required amount of production for a certain period of time, they ought to be worked out and filled in as much as possible, dammed off, and ultimately allowed to fill up with water, in order to protect the upper works in future from fire in the gob below. This I consider indispensable, because we may not be able profitably to fill in all the ground. To do so we have to use the waste of the mine, although it is liable to fire in time. In using this stuff, it ought to be surrounded by walls of rock not liable to take fire, laid firmly in clay, the gob being in the middle, and firmly covered and packed with clay on top. In

By J. E. Berry

AII evaluation is made of the acoustic velocity log for measurement of formation porosity. Plots of field-observer1 velocities vs core-measured porosities of sandstones and limestotnes with inter intergranular porosity show that the velocity log gives a useful measure of porotity, in agreement with published data. A new method of plotting electrical and velocity log data makes it easier to recognize hydrocarbon-water coritnct~ from log darn and to make serni-quantitative estinlates of hydrocarbon saturation. Two examples of this interpretation technique are given. This paper also discusses the various factors that affect acoustic velocity and shows how corrections can be made for some of these factors. INTRODUCTION Although the continuous velocity log was developed primarily as an aid to seismic interpretation, it is finding widespread use for measurement of porosity. The purpose of this paper is to evaluate this use of the log. Results are presented for the velocity-porosity relationship in many sandstones and one limestone. Practical applications of porosity values derived from the velocity log to improve interpretation of electrical surveys are presented. Various parameters which affect velocity in porous media are considered. Porosity, composition, cementa-tion, pressure difference (overburden pressure minus fluid pressure), fluid saturation, and wellability are discussed. Some of the ideas are opinions based on general considerations of well logging problems while others are supported by published data and our own observations. Major conclusions from these studies arc given in the body of the paper and detailed discussions of some of the various factors affecting porosity are given in the Appendix. POROSITY Sandstones The primary factor affecting the velocity of sound in porous media is porosity. Wyllie, et al,1 have reported a time average equation for the relationship between velocity and porosity.* This has found considerable acceptance in the industry. Other relationships between velocity and porosity have been proposed, none of which are entirely satisfactory. It is doubtful that any one relationship will completely describe all situations. We have tried an empirical relationship based on correlating log velocities with core-measured porosities. Measured porosities were averaged over a depth interval equal to the spacing used in recording the velocity logs. The depth range for the information used was from 2,000 to 12,000 ft. Velocity measurements were normalized for the effects of depth and overburden pressure. A detailed discussion of the basis for this normalization is given in the Appendix. The change is usually insignificant and when working with individual formations it can be neglected. All velocity measurements were normalized to a depth of 10,000 ft. The velocity-porosity data for sandstones in Fig. 1 came from 20 wells scattered throughout the Mid-Continent and Gulf Coast areas. The scatter of the data points is attributed to three causes: 1. There is no theoretical basis for expecting an exact velocity vs porosity relationship and it is not possible to correct precisely for the effects of such factors as impurities, grain shape, manner of cementation, etc. Some of these factors are discussed in the Appendix. 2. Porosities measured by core analysis are not necessarily representative of what the velocity log "sees". 3. Inaccuracies appear in the velocity log reading. This is particularly true of velocities from one-receiver logging tools.*" A linear-time curve (time-average equation) is plotted in Fig. 1 along with the best straight line through the points. Velocities used for the linear-time curves were 19,500 ft/sec for the matrix velocity (zero porosity) and 5,500 ft/sec for fluid velocity. For clean sandstones with velocities greater than 10,000 ft/sec, there is little difference between the velocity-porosity and the time-porosity curves. Both curves are well within the scatter of data points. The data points in Fig. 1 were restricted primarily to clean sandstones, using the SP and/or gamma-ray logs as clues to the lithology. Where a lithologic de-

By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-

By W. S. Gatley, F. C. Appl

This paper presents a combined analytical and experimental study of chisel penetration vs time during chisel impact on rock, a problem of fundamental importance in improving the performance of roller-cone bits or percussion drilling toots. For a given force-time relationship between chisel and rock, the problem of determining the penetration (displacement) vs time of the chisel is formidable. This is so because the rock is a nonlinear system with distributed mass and distributed damping (friction, dissipation of energy due to rupture, etc.). Since the literature does not contain adaptable solutions, the rock behavior to impact was simulated approximately by an "equivalent" lumped system, that is, an "equivalent" mass, spring, dashpot system. With this assumption, an analytical solution was found for chisel penetration vs time due to a sinusoidal load between chisel and rock. From this solution were found curves, in terms of dimension-less variables, for the maximum depth of penetration vs the frequency of the sinusoidal loading and for the energy transfer vs frequency. The results of this analysis were used to predict the penetration rate of rotary rock bits us rotary speed. The curve indicated that an optimum speed exists. To verify this analysis, an experimental apparatus was constructed and used to apply a sinusoidal pulse to a chisel penetrating a rock specimen under atmospheric conditions. Strain gauges were mounted on the chisel shank and a velocity transducer was mounted between the chisel and the rock surface. The velocity was integrated electrically and picked up simultaneously with the strain gauge signal on an oscilloscope. Permanent records were made photographically to provide simultaneous records of force us time and penetration us time. In comparing the experimental results for limestone and dolomite with the theoretical results, good agreement was found in the frequency range of the experiments. Unfortunately, the inertia effect (peak penetration) indicated by the theory occurs at a frequency much higher than could be obtained experimentally with the apparatus constructed. A "rate-of-loading" effect is indicated theoretically, but has not yet been verified experimentally. INTRODUCTION The process of drilling with percussion tools or rotary rock bits is basically related to the transient response of rock to surface impact. Each time a bit tooth contacts the rock, high stresses are developed which result in penetration and rock removal. As the tooth moves on, stresses are relieved and a new cycle begins as the next tooth contacts the rock. Thus the drilling process, which consists of an endless succession of these cycles, can be studied in terms of a single cycle. It is apparent, therefore, that the study of single-chisel impact on rock is fundamentally important in improving the performance of roller-cone and percussive-type drills. Previous studies in this area have been conducted by Simon1 and Hartman2 by means of drop tests. In these tests a chisel was attached to a weight and allowed to fall, due to the force of gravity, so that the chisel was driven into a rock specimen upon impact. Strain gauges were attached to the chisel shank and the resulting force-vs-time curves were recorded photographically from an oscilloscope screen. The depth of penetration and crater dimensions were also measured. These tests have provided much valuable information but, as mentioned by the investigators, have not provided complete information on the effect of "rate of loading'! This is partly due to the fact that the chisel motion during drop tests is not a controlled motion which can be varied in form and frequency. Therefore, it seemed that additional information could be obtained by studying chisel impact under conditions where both the motion and the frequency of loading could be controlled. This paper presents a combined analytical and exper-

By T. Seldenrath

In the development of a fluid -operated hammer drill' for accelerated penetration of hard rock formations in oil wells, a research investigation was conducted to evaluate the percussion effects obtained with different design characteristics and to determine the possibilities of percussion in the low frequency range. Tests were conducted on granite blocks and comparable impact forces were measured with a load cell under selected test conditions. These full-scale laboratory tests provided an evaluation of the effectiveness of percussion which was further supported by actual downhole field performance. While much pertinent data have been presented by other investigators the method of evaluation described in this article resulted in good correlation between laboratory and field performance and may be applicable in other low frequency percussion developments. EXPERIMENTAL METHOD For these tests the bit was held stationary and the test block was rotated and forced upward against the bit by a hydraulically-lifted rotary table. "Weight on bit" was calculated from pressure readings on the fluid system of the lifting cylinders—corrected for tare and friction. Percussion was obtained with several tubular hammers of different weights up to 320 lb. These were lifted mechanically and allowed to drop by gravity from various heights onto a slidably-mounted bit sub or "floating anvil" for calibration of the load cell response with known kinetic energy of the hammers. During evaluation of percussion effects, the hammers were hydraulically operated to provide a range of percussion frequencies up to 1,020 blows per minute delivered to the anvil. To obtain comparable test readings, the load cell of the strain gauge type, was attached to the bottom of the anvil or bit sub in place of the bit. The load cell rested on a typical granite test block mounted on the drilling table. The latter was hydraulically supported as in the actual drilling operation. The effect of support resistance was the same for all tools when calibrating. Impact forces so determined werethusdirectly comparable with one another for the purposes of this investigation. When a roller bit was substituted for the load cell for actual drilling, the impact force would probably be reduced due to the resiliency of the bit body, legs. cones and teeth and the penetration of the teeth into the rock. However, since the bits and rock specimens were uniform in these tests, an evaluation of actual tool performance, in terms of parameters previously determined with the load cell at the selected standard conditions of calibration, proved satisfactory. Throughout these tests, 8¾-in. standard tricone, hard rock toothed roller bits and carbide-insert roller bits were used. Rotary speeds were 50 and 100 rpm; static weight on bit was applied up to 40,000 Ib, and percussion frequencies up to 1,020 blows per minute were available. During this investigation it was found that toothed bits on which the teeth had developed flat ends about 3/16 in. wide did not change appreciably for the duration of a test. Hence, all toothed bits used in this study were in this condition. Conventional reference curves obtained in these tests show that increasing weight on hit by 2:1 yielded an increased penetration rate of approximately 2.7:1, while an increase in rotary speed of 2:1 netted an increased penetration rate of roughly 1.7:l. Results are thus of the same order as those reported for hard rock drilling by other investigators." CALIBRATION Under the selected standard test conditions previously described, with the lifting table hydraulically supported, and the anvil interposed between hammer and load cell, the hammers were dropped from known heights. Thus, with the kinetic energy of the hammer known, the corresponding maximum impact force shown by the cell was determined. (It may be of passing interest to note here that special drop tests with the hammers showed that no appreciable reduction in impact force resulted from introduction of the anvil or hit sub.) From these calibrations, it was possible to determine the theoretical kinetic energy available in the hammer from the maximum impact force shown by the load cell while operat-

By H. O. McLeod, J. M. Campbell

This paper presents the results of the data obtained in the first stage of a long-range study at high pressures of the system, vapor-hydrate-water rich liquid-hydrocarbon rich liquid. The data presented are for the three-phase systems in which no hydrocarbon liquid exists. Tests were performed on 10 gases at pressures from 1,000 to 10,000 psia. One of these was substantially pure methane, and the remainder were binary mixtures of methane with ethane, propane, iso-butane and normal butane. Several conclusions may be drawn from the data. 1. Contrary to previous extrapolations, the hydrocarbon mixtures tested form straight lines in the range of 6,000 to 10,000 psia which are parallel to the curves for pure methane, when the log of pressure is plotted vs hydrate formation temperature. 2. The hydrate formation temperature may be predicted accurately at pressures from 6,000 to 10,000 psia by using a modified form of the Clapeyron equation. The total hydrate curve may be predicted by using the vapor-solid equilibrium constants of Carson and Katz' to 4,000 psia and joining the two segments with a smooth continuous curve between 4,000 and 6,000 psia. 3. The use of gas specific gravity as a parameter in hydrate correlations is unsatisfactory at elevated pressures. 4. The hydrate crystal lattice is pressure sensitive at elevated pressures. INTRODUCTION Prior to 1950 many studies had been made of the hydrate forming conditions for typical natural gases to pressures of 4,000 psia.""'"'"" Most of these attempted to correlate the log of system pressure vs hydrate formation temperature, with gas specific gravity as a parameter. One of the more promising correlations was made by Katz, et al, which utilized vapor-solid equilibrium constants. The only published data above 4,000 psia are those of Kobayashi and Katz7 for pure methane to a pressure of 11,240 psia. In the intervening years, most published charts for the high-pressure range have represented nothing more than extrapolations of the low-pressure data, with the methane line serving as a general guide. The reliability of these charts has become increasingly doubtful (and critical) in our present technology as we handle more high-pressure systems. The portion of our high-pressure hydrate research program reported here was designed to: (1) investigate the reliability of existing charts; (2) obtain actual data on gas mixtures to 10,000 psia; and (3.) develop a simple hydrate correlation that was more reliable than those which simply used specific gravity as a parameter. Binary mixtures of methane and ethane, propane normal butane, or iso-butane were injected into a high-pressure visual cell containing an excess of distilled water. Hydrates were formed and then melted to observe the decomposition temperature of the hydrates at pressures from 1,000 to 10,000 psia. EQUIPMENT The equipment consisted of a Jerguson 10,000-lb high-pressure visual cell, a 10,000-1b high-pressure blind cell and a Ruska 25,000-1b pressure mercury pump. The visual cell was placed in a constant-temperature water bath controlled by a refrigeration unit and an electric filament heater. A Beckman GC-2 gas chromatograph was used in analyzing the gas mixtures after each run was completed. EXPERIMENTAL PROCEDURE After evacuating the gas system, the heavier hydrocarbon was injected into the high-pressure mixing cell to that pressure necessary to give the desired composition. This cell then was pressured to 1,100 to 1,200 psia by methane from a high-pressure cylinder. The mixing cell holding the gas contained a steel flapper plate and was shaken intermittently over a period of 15 minutes. After mixing, the valve to the high-pressure visual cell containing excess distilled water was opened, and the gas mixture was allowed to flow into the cell. The temperature in the water bath was lowered 10" to 15'F below the estimated hydrate decomposition point. As a first check, the temperature was increased at a rate of 1°F every six minutes to find the approximate point of decomposition. It was again lowered 1.5° to 5°F to form hydrates. The temperature was raised to within l° of the estimated decomposition point and then increased 0.2F every 10 to 15 minutes until the hydrates decomposed. This procedure was repeated at various pressures to obtain 7 to 13 points for each mixture between 1,000 and 10,000 psia. After completion of the hydrate decomposition tests, the gas mixture composition was analyzed with a calibrated gas chromatograph. These gas analyses have an estimated error of ± .1 per cent.

By John R. Eckel

A Iaboratory drilling rig has been devised and placed in operation which permits the application of hydrostatic, terrastatic, and formation pore pressures to a rock sample for drilling under controlled conditions. Calibrated rests of this equipment in-dicate qualitative agreerment with field results on the effect of weight on bit, rotary speed, and rate of circ~~lation on drilling rate. Tests under pressure, using water and air as the drilling fluids, indicate that when drilling saturated limestone samples, a pressure differential between hydrostatic and formation pressure is the only pressure which affects drilling rate. A differential in either direction causes a reduction in rate, but the same diflerential from the wellbore into the formation causes the greater reduction. Also, in lime.stone, air favorably affected drilling rote only when compared to water at high hydrostatic pressurre, all other conditions remaining constant. Large increases in drilling rate with air could be obtained in the laboratory only while drilling a shale, which offered a limited permeability to nitrogen and which could be drilled with a differential from the formation into the wellbore. In general, the magnitude of the changes due to the pressure effect were small compared to changes in drilling rate obtainable by changing either bit weight or rotary speed. INTRODUCTION In the course of Humble's drilling research program, the desirability of investigating several factors which lend themselves to laboratory rather than field study became obvious. Principal reasons for this are the expense involved in field studies and the difficulty of exercising the required degree of control. Of primary importance are investigations of the effect of fluid pressure on rock rate, the effect of pressure on rock drillability, and a study of the fundamental mechanics of rock failure and chip generation. Several years ago some work in the laboratory on the effect of mud properties on drilling rate was re- ported to the API', but the completion of this work and the investigation of the other variables affecting drilling rate required equipment somewhat more elaborate than that used on these earlier tests. This equipment has been assembled to form Humble's Drilling Engineering laboratory. To date only the effect of pressure on rock drillability while using water and air has been investigated, and this work is not yet complete. Facilities are available to investigate the effect of fluid properties on rate of penetration, and information is being assembled on a current basis on the mechanics of drilling. The sequence of presentation in this progress report is somewhat different from that in which the data were obtained since the order of ex-

By E. B. Brauer, B. F. Pennington, E. W. Hough, G. L. Stegemeier

Interfacial tension divided by the difference in density between the liquid and the vapor phases was determined experimentally by the pendant drop method on several isotherms in the two phase region below the critical point for the methane-normal decane system. The density difference data of Sage and Lacey was used in the calculation of interfacial tension. Both interfacial tension and and interfacial tension divided by density difference were found to vanish at the critical point. Interfacial tensions of less than one dyne/centimeter were observed as far as 1,000 pounds per square inch below the critical pressure. EXPERIMENTAL PROCEDURE The interfacial tension divided by the density difference for the methane-normal decane system was determined at the 100°, 130°, 160' and 190°F isotherms, from pressures of about 1,000 psi to the critical pressure, which is more than 5,000 psi for these isotherms. Particular emphasis was placed upon the investigation at pressures slightly below the critical pressure where the interfacial tension is less than 0.5 dyne/cm. Volumetric properties in the two-phase region, including the critical pressures and temperatures, were taken from the work of Sage and Lacey.1 The experimental pendant-drop technique used for the determination of interfacial tensions at high pressures incorporated the ideas of Michaels and Hauser,2 Hough, et a1,3 Walker4 and Heuer.5 In addition, the technique for determination of extremely small interfacial tension by Jennings6 was utilized in the region near the critical points. A detailed description of the apparatus is given in a dissertation by one of the authors.7 Cleaning operations on the stainless-steel sample system included successive washings with chromic acid, tap water and, finally, distilled water. Subsequent cleanings were performed with re-distilled normal pentane, which had an extremely low residue upon evaporation. Specific composition requirements necessitated a fairly precise sample introduction — although, fora two-phase, two-component system, the composition of each phase is completely determined if pressure and temperature are controlled. The normal decane was delivered into the evacuated sample system as a liquid from a burette. The methane was then introduced into the system from a calibrated isothermal container, so that pressure differentials could be used to determine the amount introduced. High pressures were obtained by compressing the sample with a mercury injection pump until the critical pressure was reached for the particular isotherm being studied. Experimental data were then obtained for specific pressures by first decreasing the pressure slightly so that two phases would appear, and then photographing a drop at that pressure. Subsequent photographs were made at increments throughout the pressure range. Calculation of interfacial tension divided by density difference was made from measurements

By J. D. Rice, P. L. Wearden, W. L. Hensou

Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Scbiltbuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co. 's Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir perlormance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method. INTRODUCTION The numerical approach to the unsteady-state partial water-drive reservoir performance problem heretofore has been limited in that solutions have been resolved only for certain fixed parameters. Also, prior to the advent of high-speed electronic digital computers in the last few years, calculations were so tedious and time-consuming that they ordinarily were neglected, or some other means of obtaining the solutions were used. The analogue approach had been used for obtaining solutions to the transmission-of-heat problem and, consequently, means were developed for applying the electrical analogue to the unsteady-state reservoir performance problem. Bruce submitted a paper for AIME publication in Sept. 1942, in which he described an electronic device (now called the Bruce Analyzer) for analyzing the water-drive performance of any reservoir, based on either steady or unsteady-state flow characteristics. 1 Sun Oil Co. adopted the analogue approach in 1949 and now has two special-purpose high-speed electronic reservoir analyzers in use.2,3 Two main features of Sun's analyzers are (1) the high repetitive rate of reproducing the entire history of reservoir performance cyclically a number of times per second, and (2) the elimination of the necessity of knowing the properties of the associated aquifer. Since the advent of larger and faster digital computers, the possibility of incorporating this second feature into a numerical approach appeared feasible. Previous work has been done and material published covering the application of numerical methods to the behavior of the pressure with respect to time at any point in an associated aquifer? However, the aquifer parameters must be known from some source. The material presented in Ref. 4 has been used to a great degree in developing the numerical method described herein. DIFFERENTIAL EQUATION AND BOUNDARY CONDITIONS The problem of simulating the performance of a reservoir and the associated aquifer is to determine the characteristics of the aquifer such that the

By R. J. Blackwell

By G. H. F. Gardner

The boundary conditions F = 1.0 and 4 = 1.0 (100 per cent) are dictated by the definition of F in the equation 1/F = aFp. These conditions have physical significance as the "limiting conditions" for the observed behavior in systems of dispersed particles. The other boundary conditions, cited by Gardner in his Eq. 3 as applying to this system, have no significance in the systems we studied. Maxwell's equation (Eq. 2) cited in Gardner's comments was developed for and limited to a regular, rather than random, dispersion of spheres which are sufficiently removed from each other so that they do not interfere with current flow about their neighbors. These restrictions also apply to Rayleigh's analysis. The title of Rayleigh's paper cited by Gardner is "On the Influence of Obstacles Arrayed in Rectangular Order upon the Properties of a Medium". He is not discussing randomly dispersed spheres. It might be inferred from Gardner's comments that Rayleigh specifically considered the differential equation (Gardner's Eq. 3). This is not the case. Mathematically, Gardner's Eq. 3 is exactly true for the system to which it applies, however, as both Rayleigh and Maxwell note that their equation for F in terms of F is not for randomly dispersed spheres. At the time we wrote our paper, we were aware of the work of Wyllie and Gregory as cited by Gardner. We cited their work in Ref. 5 of our paper. Our comment on page 287 of the paper about the validity of an m value of 1.3 for spheres with a porosity of 38 per cent remains as our answer to Gardner's question on this point. Our data, at 38 per cent porosity, show that the condition a = 1 and m = 1.3 holds for spheres near 40 per cent porosity.