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By John J. Croston

THE year 1935 witnessed one of the world's oldest industries-gold mining-attain the stature of a billion dollar business. Preliminary estimates indicate that somewhat over 30,000,000 oz. of gold was pro-duced, the largest output ever recorded and exceeding the previous year by more than 11 per cent. Of this huge total the Witwatersrand field produced about 10,800,000 oz., compared with 10,480,000 oz. in 1934. Russia was apparently the stellar performer, and from incomplete data it appears that between five and five and a half million ounces were produced by the Soviets compared with 4,200,000 last year and 2,814,000 in 1933. The United States nosed Canada out of third place with a production of 3,546,000 oz. against 2,916,000 in 1934, while Canada increased her total from 2,965,000 to 3,291,000 oz. Similarly, gains of lesser magnitude were made in Australia, the Gold Coast and other countries. As a result of great activity in developing outlying areas on the Rand, and the great number of new companies building mills in Canada, Australia, the Gold Coast and the United States, the years 1936 and 1937 should see new high records, as these new producers will more than offset any decline in the older properties. The whole world has become "gold conscious" during the past three years. It has been the subject of innumerable articles by economists and others, but, unfortunately, because of their lack of actual mining knowl-edge, they have treated the production of gold as a static affair, ignoring geological and technical factors. It is hardly necessary to draw attention to the fact that the world's gold-mining industry was slowly but steadily shrinking in importance, owing to the gradual depletion of known deposits that were profitable to work at costs existing prior to 1929. The International Geological Congress at Pretoria and the League of Nations Committee drew atten-tion to the estimates of the mining experts of the various governments predicting a steady falling off in world production. On the Rand there

Jan 1, 1936

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy's Law is valid. 4. The formation is saturated with a single homogeneous fluid.

By H. T. Bowman

For more than 80 years the Bessemer process has depended upon the ability, skill, and judgment of the blower, although as early as the I860's it was recognized that the process would benefit by some type of instrumental contro1.l IIowever, instruments with sufficient recording speeds did not exist, so the end-point determination was always dependent upon the blower's eye. This placed an obstacle in the way of precise experimental work, because of the absence of the necessary records and reference points as reported by Work.2 The use of the photocell provided the instantaneous record of the blow that made this experimental work possible and provided more scientific control for the process as discussed by Graham,3 A brief description of the progress of the blow will illustrate the recording function of the instrument. The silicon in the iron is being oxidized during the first minutes of the blow, as pointed out by Henning4 in a table showing the order of metalloid elimination. The product of this oxidation is a solid that remains in the converter, so there is virtually no flame during this part of the blow. This low flame luminosity is illustrated by the flame recording shown in Fig. I, where the silicon blow is plainly marked. The dull flame of the silicon blow gradually gives way to the brilliant carbon flame as the increasing quantities of carbon monoxide formed inside the converter burn to dioxide upon contact with the atmosphere above the vessel. When the carbon reaches some low value under 0.20 per cent, there is insufficient menoxide formed to maintain the dioxide flame, so its intensity drops. Throughout the flame drop carbon continues to burn, until at some value around 0.05 per cent an arrest occurs in the recorded drop. This point has been designated as the end point. The period of time from this end point until the vessel is turned upon its side and blowing has stopped has been called the afterblow. This afterblow is used as a measure of the degree of metal oxidation, and uniformity demands that it be controlled within narrow limits. Iron and blowing conditions are likely to change several times during a turn, necessitating corresponding changes in end-point control. It is the purpose of this paper to discuss these changes, the factors that make them necessary, and their bearing upon the quality of steel. Carbon-FeO Relationship In the Bessemer process oxidation relationships are precise. Fig. 2 shows a graph of the carbon-FeO relationship. The familiar "bomb-test" method, described by Mccutcheon and Rautio,5 was used for obtaining these and all other dissolved FeO values herein reported, all tests being taken from the converter before deoxidation unless otherwise noted. All tests of 0.10 per. cent carbon and above were obtained from metal blown for duplexing. McGinley and Woodworth6 reported iron oxide values for blown metal, but their tests were obtained by a . different method than were those

Jan 1, 1942

By H. T. Bowman

For more than 80 years the Bessemer process has depended upon the ability, skill, and judgment of the blower, although as early as the I860's it was recognized that the process would benefit by some type of instrumental contro1.l IIowever, instruments with sufficient recording speeds did not exist, so the end-point determination was always dependent upon the blower's eye. This placed an obstacle in the way of precise experimental work, because of the absence of the necessary records and reference points as reported by Work.2 The use of the photocell provided the instantaneous record of the blow that made this experimental work possible and provided more scientific control for the process as discussed by Graham,3 A brief description of the progress of the blow will illustrate the recording function of the instrument. The silicon in the iron is being oxidized during the first minutes of the blow, as pointed out by Henning4 in a table showing the order of metalloid elimination. The product of this oxidation is a solid that remains in the converter, so there is virtually no flame during this part of the blow. This low flame luminosity is illustrated by the flame recording shown in Fig. I, where the silicon blow is plainly marked. The dull flame of the silicon blow gradually gives way to the brilliant carbon flame as the increasing quantities of carbon monoxide formed inside the converter burn to dioxide upon contact with the atmosphere above the vessel. When the carbon reaches some low value under 0.20 per cent, there is insufficient menoxide formed to maintain the dioxide flame, so its intensity drops. Throughout the flame drop carbon continues to burn, until at some value around 0.05 per cent an arrest occurs in the recorded drop. This point has been designated as the end point. The period of time from this end point until the vessel is turned upon its side and blowing has stopped has been called the afterblow. This afterblow is used as a measure of the degree of metal oxidation, and uniformity demands that it be controlled within narrow limits. Iron and blowing conditions are likely to change several times during a turn, necessitating corresponding changes in end-point control. It is the purpose of this paper to discuss these changes, the factors that make them necessary, and their bearing upon the quality of steel. Carbon-FeO Relationship In the Bessemer process oxidation relationships are precise. Fig. 2 shows a graph of the carbon-FeO relationship. The familiar "bomb-test" method, described by Mccutcheon and Rautio,5 was used for obtaining these and all other dissolved FeO values herein reported, all tests being taken from the converter before deoxidation unless otherwise noted. All tests of 0.10 per. cent carbon and above were obtained from metal blown for duplexing. McGinley and Woodworth6 reported iron oxide values for blown metal, but their tests were obtained by a . different method than were those

Jan 1, 1942

By E. H. Citron

CLEANING fine coal in jigs is not new in Europe, where the feldspar jig is being used almost exclusively for this purpose. A feldspar jig operates with an artificial bed made up generally of feldspar or other hard rock material. Dimensions and specific gravity of this material must be of suitable values for good bedding qualities. For good efficiency, the size should range between 1x2 in. and 2x2x½ in. thick. The disadvantage of an artificial bed is that it is not mobile and must be replaced every so often with new material to obtain good cleavage characteristics. A semi-mobile bed has been developed to retain only a part of the feldspar on the sieve screen— the other part is drawn off with the refuse material, from which it is reclaimed and returned to the jig feed. Recirculating this feldspar rock offers definite advantages. However, in time it will lose its original shape because of wear, and new bed material must be added to the jig feed. The latest feldspar jigs arc generally air-pulsated, Baum-type jigs, although more than 70 pct of the feldspar jigs operating in Continental Europe are still of the piston type. These jigs are very popular in Europe, but they do require a great deal of time and attention. New Theory to Eliminate Artificial Bedding: At the preparation plants of Pittsburg & Midway Coal Mining Co. it has always been the contention that a small piston-type jig could be developed to clean fine 1/4x0-in. coal down to 28 to 60 mesh efficiently by obtaining and admitting bedding material from the present plant refuse circuit to the jig feed. This eliminates use of artificial bedding materials. The jig should incorporate these essential adjustable features as follows: Adjustable Sieve Screen A screen that can be raised and lowered to increase or decrease washing compartment depth. The sieve screen also can be set on an incline level, or decline. Adjustable Plunger Eccentric Length of stroke can be adjusted to increase or decrease pulsion and suction. Variable Plunger Speed Variable speed reducer for decreasing and increasing the number of strokes per minute. Water Distribution Adjustable baffle plate separating the plunger and sieve compartment so the water can be distributed uniformly over the entire sieve screen area. Refuse Ejector Special unique rubber-type refuse ejector gate operated by air and electrically controlled (as a conventional jig). Automatic Control Conventional float that measures the specific gravity of the coal-water refuse medium in the jig is of the submerged type. The float is mounted on a vertical stem held in position by two parallel arms. A movable weight regulates the effective specific gravity of the float. The float stem can be raised and lowered, having a graduated scale to indicate the depth of bed for the setting of the float. Hutch Drawoff Hutch material is drawn from the cell compartment to the elevator compartment by gravity. The first one-cell experimental jig incorporating all these features was built in January 1955 by Ore

Jan 1, 1959

By John T. Galey

A combination of two factors in addition to the current Federal drilling and price regulations reduced by 120 from I942 the number of new wells completed in southwestern Pennsylvania during the year. No new prospective area was found comparable to the Armbrust gas pool, Westmoreland Co., which accounted for a seventh of the last year's drilling, and it is considered doubtful whether, even if such a field had been discovered, the drilling contractors, who have been seriously affected by the manpower shortage, could have drilled many more wells than they did during the year. New wells totaling 445 were completed for a combined footage of over 1,250,000 Dry holes numbered 131 and had a footage of nearly 400,000. Old wells drilled deeper total 55, of which 17 were found nonproductive. Shallow Development Oil Oil completions yielded an initial of only slightly over one hundred barrels from 21 wells for about the same per well average as that of a year ago. However, 65 bbl. of this total came from two wells in two new strikes. The footage drilled of nearly 33,000 gives an average of nearly I00 ft. less per well than a year ago. Two old wells drilled deeper had a combined initial of only 4 bbl. The largest oil well of the year, 40 bbl., was found in the Speechley (U. Dev.) sand at a depth of 3492 ft. in German township, Fayette County. The location is several miles east of the nearest oil production hut as the area that could be occupied by a pool is fairly well delimited by drilling, the extent of this production would not appear to be large. The other notable oil production was found in the Dunkard (Penna.) sand, Cumberland township, Greene County, at a depth of 1065 ft. Here the first well had an initial of g bbl. and the second 25 bbl. However, a third proved dry, and as this area is also delimited by drilling, the pool doubtless will be of small area. Gas Gas completions yielded an initial of slightly over one hundred million cubic feet per day and new wells, totaling 303, account for all but four million of this volume. Old wells drilled deeper, numbering 35, found gas. The per well average in new drilling of approximately 320 M cu. ft. is nearly 165 M cu. ft. less than a year ago and the total footage is slightly over 830,000, which is about a quarter of a million feet less than in 1942. Average rock pressure of new completions is approximately 365 lb. per sq. in. The entire volume of new production is from the Upper Devonian or higher stratigraphic horizons. In Allegheny County, the grestest activity was in Forward and Plum townships. Wells there account for more than one half the completions. One large well was drilled in Forward township and an open flow of 3.623 million cubic feet was found in an old Gantz (U. Dev.) sand area. The top of the sand was encountered

Jan 1, 1944

By John T. Galey

A combination of two factors in addition to the current Federal drilling and price regulations reduced by 120 from I942 the number of new wells completed in southwestern Pennsylvania during the year. No new prospective area was found comparable to the Armbrust gas pool, Westmoreland Co., which accounted for a seventh of the last year's drilling, and it is considered doubtful whether, even if such a field had been discovered, the drilling contractors, who have been seriously affected by the manpower shortage, could have drilled many more wells than they did during the year. New wells totaling 445 were completed for a combined footage of over 1,250,000 Dry holes numbered 131 and had a footage of nearly 400,000. Old wells drilled deeper total 55, of which 17 were found nonproductive. Shallow Development Oil Oil completions yielded an initial of only slightly over one hundred barrels from 21 wells for about the same per well average as that of a year ago. However, 65 bbl. of this total came from two wells in two new strikes. The footage drilled of nearly 33,000 gives an average of nearly I00 ft. less per well than a year ago. Two old wells drilled deeper had a combined initial of only 4 bbl. The largest oil well of the year, 40 bbl., was found in the Speechley (U. Dev.) sand at a depth of 3492 ft. in German township, Fayette County. The location is several miles east of the nearest oil production hut as the area that could be occupied by a pool is fairly well delimited by drilling, the extent of this production would not appear to be large. The other notable oil production was found in the Dunkard (Penna.) sand, Cumberland township, Greene County, at a depth of 1065 ft. Here the first well had an initial of g bbl. and the second 25 bbl. However, a third proved dry, and as this area is also delimited by drilling, the pool doubtless will be of small area. Gas Gas completions yielded an initial of slightly over one hundred million cubic feet per day and new wells, totaling 303, account for all but four million of this volume. Old wells drilled deeper, numbering 35, found gas. The per well average in new drilling of approximately 320 M cu. ft. is nearly 165 M cu. ft. less than a year ago and the total footage is slightly over 830,000, which is about a quarter of a million feet less than in 1942. Average rock pressure of new completions is approximately 365 lb. per sq. in. The entire volume of new production is from the Upper Devonian or higher stratigraphic horizons. In Allegheny County, the grestest activity was in Forward and Plum townships. Wells there account for more than one half the completions. One large well was drilled in Forward township and an open flow of 3.623 million cubic feet was found in an old Gantz (U. Dev.) sand area. The top of the sand was encountered

Jan 1, 1944

By P. S. Rudman

Crystal-structure occurrences in binary phase diagrams of fifth- and sixth-period elements, zirconium through palladium and hafniun through platinum, are surveyed with the conclusion that average .group number GN is the dominant correlative. This is interpreted in terms of curves of enthalpy differences between competitiue structures that are continuous func -tions of GN. It is further reasoned that the absolute formation energies may also be continuous functions of GN and if so can be simply obtained from the regatives of the heats of sublimation of the elements. It is shown that from such a heat of formation-GN plot the heats of mixing of alloy systems can be quantitatively predicted. For example, for sixth-period alloys very large exothermic heats of mixing are predicted for systems that span GN = 6 (i.e., Hf-Pt, Ta-Os, ...). Thermodynamic data with which to test these predictions do not appear to be available. If in the latter transition (A subgroup) elements we eliminate from consideration the fourth period where magnetic terms contribute to crystal-structure stability, as shown in Table I, there is a very regular sequence of structures. Using the group number (GN) assignments of Table I, which differ from the usual assignments of 8 to the elements listed as 8 through 10, it is perhaps trivial to say that the phase occurrence is a unique function of GN. However, the interesting aspect of alloys from among these elements is that the alloy structures also appear to correlate with GN. The GN for an alloy is given as GN = SixiGNi, where xi and GNi = atomic fraction and GN of component i, respectively. It is difficult to credit anyone in particular with having discovered this correlation, so many people have implicitly or explicitly employed it in the last 10 years. However, Bloom and Grant' in their correlation of s-phase occurrence with total number of d + s electrons were certainly one of the first to appreciate the correlation and Hume -Rothery2 appears to be responsible for the use of average GN as defined above. Only in the last few years have the phase diagrams of enough alloy systems been determined for this correlation to be surveyed with any degree of completeness. We shall here, in an abbreviated format, summarize the available phase-diagram literature and discuss some consequences of the GN correlation. BINARY DIAGRAM SURVEY In Figs. 1 to 3 the phase occurrences are summarized. In Fig. 4 the occurrence limits for the more common structures are summarized. That the GN of an alloy falls within the occurrence limits of a particular structure is a necessary but not a sufficient condition for the appearance of that structure. The preceding figures certainly illustrate that GN is a dominant correlative for structures of these elements. Many of the diagrams have complications, with ordering and other phase changes occurring in intermediate phases, that cannot be clearly accommodated in such a schematic survey and have hence been left out. Such omissions cannot, however, negate the GN correlations discussed here. Relative atomic size is also an important crystal-structure determinant and since atomic size varies quite regularly with GN for these elements it is possible that the apparent GN correlation is basically a size correlation. In Fig. 5 relative size occurrence limits are given for intermediate phases and extended terminal solutions. The relative volume, ?v/(v) - 2(vA - vB)/(vA + uB), has been taken as the measure

Jan 1, 1968

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By J. W. Peirce

Advances in instrumentation now make it possible to measure accurately flaw of such difficult-to-mea-sure liquids as mining slurries. A mass flowmeter, which introduces no restrictions in the line, will measure the mass flow of slurry equal to the volume flow times the mms/unit volume. In the mass flowmeter system a volume flow measurement is electrically multiplied by a density measurement in order to give mass flow. Fig. 1 shows a typical mass flow measuring system. The volume flow is measured by a magnetic flowmeter and the density is measured by a gamma gauge cell, neither of which have any restrictions in the line. Consequently, there is no clogging and no more loss of head than there would be in a similm length of standard pipe. None of the parts extend into the flowing stream and there are no moving parts in the measuring elements. PRINCIPLE OF OPERATION OF THE VOLUME FLOW TRANSMITTER The magnetic flowmeter, which is used for the volume measurement, operates on the principle of a generator (Fig. 2). This principle states that when a moving conductor cuts lines of force in a magnetic field, a voltage is induced in it. Moreover, if the dimensions of the conductor remain constant, then the induced voltage is directly proportional to the velocity of the conductor. Since the voltage is strictly a function of flow velocity, the transmitter output can in no way be influenced by such factors as temperature, viscosity, turbulence, or conductivity. The linear output is detected by flush mounted electrodes (as shown) and transmitted to a potentiometer flow receiver. Magnetic Meter Construction: The metering tube is constructed of nonmagnetic stainless steel. (See Fig. 3.) To prevent shortcircuiting of the generated voltage, the tubes are lined with a suitable liner, depending upon the corrosive, erosive or other properties of the liquid or slurry to be measured. A uniform magnetic field is produced by two saddle-shaped coils of insulated copper wire. A laminated iron core focuses the magnetic field at a 90' angle to the flowing liquid. The voltage generated by a flow of liquid through the magnetic field is detected by two point electrodes mounted flush with the inner wall of the metering tube, 180' apart. Electrodes are made of Type-316 stainless steel or other material suitable to the application . Volume Flowmeter Operation: The millivolt output of the metering transmitter is transmitted to a potentiometer-type receiver (Fig. 4). The self-balancing, self-standardizing receiver has a drive unit for circuit rebalancing. The measurement change imposes an unbalanced input on the twin windings of the drive unit. The resulting unequal pull on a segmental rotor provides the motion which drives a pen, while simultaneously and steplessly repositioning a rebalancing element. Changes in conductivity have no effect on the accuracy of the measurement or the calibration of the instrument. The minimum conductivity values are determined by the length of the transmission cable and the size of the transmitter. They can be as low as five micro mhos, since there is such a small load on the electrodes. Because the meter electrically averages all of the incremental velocities in an irregular flow profile, it is ideally suited for turbulent flow and suspended solids. Straight runs of pipe are therefore not required. The transmitter can be installed close to

Jan 1, 1962

By J. F. Evers, S. Sadiq, F. W. Preston, G. W. Swift

Proper scaling of unsteady-state flow in laboratory gas reservoir models can be achieved if the permeability/fractional porosity ratio is less than 0.5 md. Porous media meeting this specification can be obtained from mixtures of sand and Portland cement provided (1) the water/cement ratio is in the range of 0.35 to 0.40, (2) the sand/cement ratio is in the range of 1/1 to 2/1, (3) the sand grain size is in the range of 48-100 to 18-28 mesh, (4) the mortar curing time is 7 days or more and (5) the cured mortar is dried under vacuum to reduce the temperature level employed during the drying process. The areal homogeneity of the mortars tested is reasonably good, although significant trends in vertical permeability were noted. The Klinkenberg and non-Darcy coefficients of mortar are such that proper scaling of these effects in the laboratory model could be expected. INTRODUCTION A long term deliverability prediction for a gas well is generally based on data determined from flow tests that are of short duration relative to the producing life of the well. These data, together with an estimate of gas reserves in place, form the basis for establishing the parameters of the mathematical model used to predict performance at future times. Results obtained from a mathematical model represent only an interpretation of the physical process being modeled. Experimental verification of the production process from discovery to abandonment is needed where production occurs under carefully controlled conditions. Ideally, one might consider such an experiment to be conducted in the field. Even if the cost of such an experiment could be justified, the time required would make it impractical to consider. However, if the time scaling problem could be handled properly, an experimental model of the gas reservoir production process could provide the necessary data to study the mechanisms of the production process in a reasonable time period. An experimental model has been designed and constructed using the data of this study as a basis. The model reservoir system consists of one producing well located at the center of a right-circular cylinder of porous material. Ten to 15 observation wells are located at strategic offset positions from the producing well. These wells, and the producing well, are fitted with pressure transducers so that the pressure-time history can be recorded at various radial and azimuthal positions in the drainage area during the entire production life of the system. Time is scaled in the model so that the time required to produce gas from discovery pressure to abandonment pressure is about 2 hours. This compares with a 20-year producing life in the model's field counterpart and gives a time scale factor of approximately 1:100,000. DESIGN CRITERIA To establish design criteria for the experimental model, the reservoir is considered to be a finite right-circular cylinder of radius rr, and height h with a producing well of radius rw located at the center and completed through the producing formation. This reservoir consists of a porous medium which has a uniform permeability k and gas porosity and the gas contained in the reservoir has density p, viscosity µ and molecular weight M. Initially, the pressure at all points within the reservoir is uniform at po. and the reservoir temperature is T. Since the reservoir production process has been demonstrated to occur in two distinct transient modes for either Darcy or non-Darcy flow,l it is

By W. W. Gerberich

SINCE the original formulation of fracture mechanics concepts,&apos;y2 relatively little work has related the fracture mechanics description of metal behavior on a gross, structural component scale to the behavior of its microstructural constituents. The purpose of this note is to suggest the utilization of fracture mechanics to describe material behavior on a microscopic scale. A Fracture Concept for Two-Phase Structures. A critical displacement concept considering the tough unidirectional phase in a relatively brittle matrix is first examined. It is assumed that a flaw exists at position 1 as depicted in Fig. 1. As the crack moves from position 1 to 2 the plastic zone could be of the shape described with the size approximated by the Dugdale3 model: where c is the half-crack length, OO is the applied stress, and oyS is the yield strength. Hahn and Rosen-field4 have presented a simple fracture criterion for homogeneous materials based upon the displacement at the crack tip. They also have shown the equivalence of the critical displacement, v*, to fracture toughness by Kc = (2v*oysE)1/2 [2] The displacement at the crack tip is given by and the displacement at any distance in front of the crack tip may be determined knowing the plastic zone size and utilizing the development of Goodier and Field.5 Recalling Fig. 1, the value of v* for fracture in material M1 may be calculated from Eq. [2] providing the critical stress intensity factor is known. As the material is loaded, when vc > vM1 the crack moves from position 1 to position 2 where it encounters the tough second phase. If vc2 < vm2, then the crack will be arrested providing the width of the M2 phase is sufficiently large. This condition is necessary since the displacement at position 2 has increased due to the longer crack length. Thus, the displacement at the distance X (representing the dimension of the second phase) in front of the crack may be larger than the critical displacement for failure in the brittle material. If v, > vm, then failure will proceed in the brittle material. The value of v, may be calculated as indicated above. This latter consideration is the same as predicting fracture of a brittle second phase at some distance in front of a crack located in a ductile matrix. Experimental Evidence. On a macrostructural scale, tungsten wires in a ductile Be-Cu matrix are seen to fracture well ahead of the main crack front in Fig. 2. Utilizing a Kc value of 14.2 ksi-in.1/2 obtained by Schroder et al.6 for as-received tungsten, the critical displacement 2v*, for fracture is calculated from Eq. [2] to be about 6.5 X 10-5 in. The crack tip displacement, 2vc, is calculated from Eq. [3] to be 0.0028 in. indicating that fracture would occur at a considerable distance in front of the crack tip. From the ratio of v*/vc and the plastic zone estimate of Eq. [I], the distance in front of the crack tip at which a tungsten wire should fracture is calculated to be about 0.195 in. As shown in Fig. 2, a fractured wire occurs at a distance of 0.140 in. (fractured in three places), not at 0.250

Jan 1, 1968

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.&apos; Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train&apos; The &apos;ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961

By K. M. Busen, J. Lindmayer

A heterojunction model is suggested for descrihzng the electronic conditions at oxide -semiconductor interfaces. Detailed study of the silicon oxide-silicon interface shows that the heterojunction model explains many experimental facts; however, it is necessary to assume that a transition layer exists at the interface. It will he demonstrated that ionic contrbution way also he present. Extended low-temperature heating stabilizes the oxide to a charge carrier density in the order of 10&apos; cln-: determined by the heterojuncton model. OXIDIZED semiconductor surfaces are widely used, since they offer technological advantages and "passivate" the surfaces of semiconductor devices. However, it has been recognized that there are always n-type inversion layers formed in the silicon oxide-silicon system, which must be regarded as a definite disadvantage. An added complication is the "instability" of these inversion layers;&apos; the inversion layer appears to vary with the processing and they change at temperatures as low as 100" to 200°C This paper will point out that the inversion layer is a result of the dissimilarity of the contacting materials and therefore must always be present. The dissimilarity is the essence of the heterojunction or electronic model and involves directly the structure of the materials involved. In addition, one finds the contribution from ions; this disturbance, however. can be eliminated for the case of silicon oxide-silicon interface. The strength of the inversion layer or channel will be expressed in terms of the density of elementary charges per square centimeter, N*, maintaining the channel. The next section contains the formulation of the heterojunction model by assuming a contact between two homogeneous materials. This calculation should not imply that silicon oxide is homogeneous; it serves only to point out the general properties of the electronic model. Following the electronic model, the practical case of the silicon oxide-silicon interface will be discussed. I) THE HETEROJUNCTION MODEL Contacting an oxide with a semiconductor, a work-function difference must be accommodated. Fig. 1 represents the oxide and the semiconductor before and after contact. When the contact has been made, one finds that qVi + qV, = A@; i.e., the work-function difference is distributed between the oxide and the semiconductor. Normally, the work-function difference appears on the wide-bandgap material, but in the present case the oxide is thin and far from being a single crystal. Accordingly, a significant fraction of the work-function difference must appear on the semiconductor. The work function of silicon2 is about 4.8 ev, but we shall not assign any particular work function for the oxide as it may vary. However, oxides usually have lower work functions and therefore the potentials must build up in the manner shown in Fig. 1. Such an argument predicts that the inversion layer must be n type, as opposed to the clean surface which is p type. Another important factor to be considered is that the oxide is disorderly and therefore contains many trapping levels. As a result, the charges in the oxide arise primarily from the change in trap occupation, while on the semiconductor side the space charge is composed of mobile free electrons. The consequence of this fact is that a change to another thermal equilibrium will require some time, dictated by the traps in the oxide. The conditions can easily be calculated on the semiconductor side. Assuming an intrinsic semiconductor, Poisson&apos;s equation is

Jan 1, 1965

By J. J. Gilvarry, B. H. Bergstorm

The first part of this paper describes a new approach to the problem of energy relationships in fracture and comminution. The basic theoretical method used (as contrasted to previous empirical or semi-empirical approaches) is an attempt to verify or disprove the hypothesis of von Rittinger, In the second part of the paper, theoretical conclusions for the three headings of single fracture, plural fracture, and comminution are tested. Agreement between theory and experimental results is demonstrated. The classical hypotheses on the energy relationship in brittle fracture are those of von Rittinger-that the energy required is proportional to the new surface formed— and the alternative one of Kick.&apos; Over the years, repeated attempts have been made to discriminate experimentally between the two assumptions, or to replace both of them, as has been done by Bond? However, no semblance of agreement seems to exist among different investigators. This paper is the first in a series essaying a new approach to the entire problem of energy relationships in fracture and comminution. The purpose of this program of research is to verify (or disprove) the hypothesis of von Rittinger. In contrast to previous empirical or semi-empirical approaches to the problem, the basic method adopted is theoretical. The prime aim is to determine the distribution function for fragment size theoretically and to verify the predicted distribution experimentally. This approach should make possible determination of the total surface of the particles by integration over the corresponding distribution function; one may hope that this direct procedure will yield more definitive results than use of gas adsorption or other methods. The surface area so obtained can then be compared with experimental energies, as obtained by Bergstrom, Sollenberger, and Mitchell,4 for example. It is convenient to distinguish between single fratture, plural fracture, and comminution. Single fracture of a brittle solid is defined as fracture by an external stress system which is removed instantly and permanently when fracture is initiated. Plural fracture consists of single fracture of the original specimen, followed by a sequence of only a few secondary fractures; comminution differs in that the sequence of secondary fractures consists of a large number of repetitive steps. For single fracture, Gilvarrys has given a rigorous derivation of the proper distribution function for fragment size, based on a closely defined physical model and deduced strictly by the laws of probability. Gilvarry and Bergstrome have compared the predictions of the theory with experiment, and have found excellent agreement. The prior work of Gilvarry and of Gilvarry and Bergstrom considers only single and plural fracture. The purpose of the present paper is to extend the discussion to the case of comminution. For prefatory purposes, the theory of Gilvarry for single fracture will be outlined. The considerations will then be applied to the cases of plural fracture and comminution. SINGLE FRACTURE The derivation is based on the Poisson law.7 For Points distributed with mean density y over a domain, this law states that the probability p(t)dt of one point lying in the range t to t + dt with none in the interval 0 to Ms p(t)dt = ye-yt dt. For this distribution to be valid, it is necessary and sufficient that the points be distributed at random, individually and collectively in the sense of ~~~.7 The former qualification requires that the position of One Point be independent of another, and the latter implies that the probability of a region containing a

Jan 1, 1961

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors&apos; knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.&apos; Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors&apos; knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.&apos; Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By Gareth Thomas

The analysis of Kikuchi pattersns of exct ovientalions from single cryslals and paired Kikuchi lines from single and overlapping crystals is shown to be useful and quanlitalve and is applied to Phase transfovnzcitions including ordering, spinodals, mavten-silic, and nuclealion and growth pyocesses. 112 pinciple, the analysis of exacl orientations enables the crystal system and the Bravais lattice of a crystal to he determined. The advantages of the davk-field imaging technigure for detecting vevy small precipitates are also described. ALTHOUGH Kikuchi electron-diffraction patterns were first observed nearly 40 years ago,&apos; little systematic application seems to have been made of them, until fairly recently during electron microscopy, when their usefulness in contrast experimen and for determining exact orientations8&apos;9 has been pointed out. With the availability of gonio-metric specimen tilting stages it has now become possible to make much wider use of diffraction patterns, particularly the Kikuchi pattern, which is the main subject of this paper. The treatment presented here is not exhaustive but it is hoped that it will stimulate more use of Kikuchi patterns during electron-microscopy investigations. The Kikuchi pattern is formed as a result of Bragg diffraction of the inelastically scattered electrons produced during the interaction of the beam and thick specimens, The important feature of these patterns is that they give an accurate representation of the symmetry of the crystal being investigated, so that it is possible to identify crystal systems and even the Bravais lattice. This means that new structures, e.g., formed in phase transformations, may be identified during normal electron microscopy, so that Kikuchi-pattern analyses considerably extend the uses of the electron microscope. Recent work has also shown that dark-field images are more informative than bright-field images, particularly, for observing small precipitates. The second part of this paper discusses some applications and advantages of dark-field imaging in studies of two-phase systems. 1) DIFFRACTION PATTERNS 1.1) Spot Patterns. Electron-diffraction spot patterns have their limitations because of the importance of the form factor on the intensities and shape of the reciprocal lattice points. Because of the extension of these points into relrods, reflections are possible over a large angular range (+5 deg) and the patterns from thin regions can be complicated because second-layer relrods intersect the reflecting sphere. Spot patterns can thus give only an approximate idea of the crystallography unless the foil is tilted into exact orientation. In this case the spot pattern is symmetrical, with equal numbers of spots on the positive and negative zone directions about the origin. Such cases are necessary for structural analyses and have been used recently to determine the crystal structure of the ordered Ta64C phase." Exact orientation means that the plane of the reciprocal lattice lies exactly normal to the incident beam as shown in Fig. 1(b). It should be noted that in exact orientations the angle of reflection is less than the exact Bragg angle 9 so that the reciprocal lattice points lie to the outside of the sphere, Fig. 1(b). This deviation is denoted by the parameter s and in the usual convention4 s is negative for exact orientations and, of course, zero at the exact reflecting position shown in Fig. l(a). In order to avoid secondary reflections from thickness relrods it is advantageous to work in thicker regions of foils. Diffraction from thick regions may also produce Kikuchi patterns and as dis-

Jan 1, 1965

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy&apos;s law3. while the rate of flow of heat is given by Fourier&apos;, (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain