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INTRODUCTION AND SCOPE This chapter is intended as a brief review of the mathematics of compound interest and of the meaning of time equivalent money. In order to make valid economic evaluations of various investment alternatives, it is important that they be analyzed on an equivalent basis, taking into account the time value of money. Compound interest has been said to be one of the eighth wonders of the world. Certainly compound interest is a fact of life in today's economy. Whenever we deal with money over time-investments, earnings, savings, loans, etc.-we are immediately confronted with the principles and effects of compound interest. In such an environment it is necessary to be able to determine time value equivalence of various sums of money received or paid at different dates. It follows that all future payments or series of payments that would repay a present sum with interest at a stated rate can be said to be equivalent with each other. Equivalence, then, is a function of the interest rate. MATHEMATICS OF COMPOUND INTEREST FACTORS In order to develop mathematical formulas for various time value equivalence of compound interest we will use symbol designations: P is Present or principal sum of money; usually refers to value at time zero. F is a single sum of money at some designated future date. R is The amount of each payment in a uniform series of equal payments made at the end of each period. n is Number of interest compounding periods (may represent annual, semiannual, quarterly, or even daily periods). i is the period compound interest rate. Figure 20-1 illustrates the increase of princi-

Jan 1, 1980

By Toshihisa Adachi, Shosei Serata, Shunsuke Sakurai

The present state of knowledge of three-dimensional rock properties does not provide an adequate basis for evaluating the safety of under- ground structures in situ. Most of the triaxial studies reported in the past have dealt with crushing strength, but have failed to consider the intergranular behavior and triaxial strain state of rocks. Without this information, the structural competence of rocks cannot be accurately assessed. The absolute three-dimensional testing method (ATT) was conceived for the purpose of analyzing the three-dimensional states of stresses and strains in aggregate rocks under conditions commonly encountered in underground structures. In-situ stress-strain states are not simple, even in the simplest possible form of opening, excavated in a homogeneous and isotropic rock medium. In general, there are four basic stress-strain states which are present in underground openings, regardless of the complexity of their geological conditions. They are the yielded, brittle-fractured, stress-relieved, stress-concentrated states, as illustrated in the schematic diagram, Fig. 1. The ATT machine was designed to create and study all these states in the laboratory. A theory describing the aggregate behavior of rocks under these diversified states is essential to evaluate the safety of underground structures. The Griffith theory is limited to tensile failure of ductile materials and therefore does not apply to behavior of aggregate rocks under compression. The Griffith theory also fails to consider the grain boundary characteristics of aggregates, which is the determining factor of rock behavior. The Mohr-Coulomb theory of failure ignores the importance of the intergranular behavior of rocks. An application of the continuum theory to

Jan 1, 1972

Year of Election 1959 Andrew Fletcher, New York, N Y "For his outstanding leadership in the lead and zinc mining industries, and for his able and devoted services to the Institute as its Treasurer and President, and as a Director for many years " 1917 Herbert Hoover, New York, N Y 1955 George M Humphrey, Cleveland, Ohio 1950 Zay Jeffries, Ptttsfield, Mass 1942 Essington Lewis, Melbourne, Vic, Australia 1959 John M Lovejoy, New York, N Y "For his distinguished service to the Institute, for his outstanding contributions in furthering the professional status of petroleum engineers, for his pioneering in application of engineering to petroleum production, and for his outstanding record of public service on behalf of the petroleum industry " 1957 Donald H McLaughlin, San Francisco, California 1957 C H Mathewson, New Haven, Connecticut 1938 Albert M Portevin, Parts, France 1957 Fred Searls, Jr, New York, N Y

Jan 1, 1960

By E. B. Hunt

Paraffin deposition has been studied in the laboratory under conditions simulating deposition in well tubing. A theoretical analysis has been made of the cooling of the oil and the precipitation of paraffin from the oil as it flows up the well tubing and through surface flowlines. It is proposed that paraffin deposits are initiated by the precipitation of paraffin directly on or adjacent to the pipe wall and grow by diffusion of paraffin from solution to the deposit. This mechanism is consistent with laboratory and field observations, and has proved useful in the design and interpretation of laboratory paraffin-deposition tests. Tests have been made of the effect of plastic pipe coatings and chemical additives on paraffin deposition. INTRODUCTION Paraffin deposits which form in well tubing and surface flowlines interfere with production and must be removed. Over the years much progress has been made in developing and improving methods of removing these deposits after they form. Much less progress has been made in developing methods of preventing or inhibiting the formation of paraffin deposits. This is due, it is believed, to the lack of knowledge of the mechanism of paraffin deposition, the absence of satisfactory laboratory testing methods and the difficulties in evaluating the results of field tests of preventive treatments. The present investigation was undertaken to elucidate the mechanism of paraffin deposition and to develop suitable laboratory tests for studying the inhibition of paraffin deposition in well tubing and surface flowlines. Current theories on the mechanism of paraffin deposition have been evolved from field observations, from laboratory studies of various factors which might be involved in paraffin deposition, and from laboratory paraffin-deposition tests.1-9 Paraffin deposits have been formed in the laboratory by immersing a cold finger into a hot wax-oil solution and by flowing hot wax-oil solutions through cooled pipe or over cooled plates. These laboratory conditions differ in important features from field conditions, and the observed deposition behavior is not entirely field-like." Thus, there is reason to question the field applicability of the results of these tests. The present investigation was undertaken to determine how to perform and interpret laboratory paraffin-deposition tests to obtain information on the inhibition of deposition in the field. The paraffin problem in the broadest sense encompasses the formation of any predominantly organic deposit in well tubing, surface flowlines and other equipment in contact with crude oil or gas. The present investigation was limited to paraffin deposition involving the precipitation of paraffin wax from solution by cooling and its concentration in a deposit on a cooled surface. This probably excludes its applicability to those problems arising from asphaltic-base crudes, but not those arising from paraffin-or mixed-base crudes. This also excludes its applicability to emulsion and congealing oil problems which are often included as part of the paraffin problem. The phenomenon of cooling appears to be the controlling factor in paraffin deposition involving the precipitation of paraffin wax and its concentration in the deposit. Deposits of this type are usually found in the field only where cooling occurs. Early in this laboratory investigation, it was not found possible to form deposits under constant temperature conditions from a wax-oil slurry, either by steady flow through pipe or by gas-lift up a pipe. Thus, the investigation was limited to situations involving cooling. THEORY The relationships involved in establishing the temperature profiles in an oil stream as it flows up well tubing with a linear (geothermal) pipe-wall temperature distribution or through surface flowlines with essentially constant pipe-wall temperature are presented in the Appendix. The relationship between radial distance in the pipe and the rate of cooling of the oil is then combined with a relationship between cloud point and rate of cooling to develop the pattern of formation of a wax cloud in the oil. The following discussion of paraffin deposition under various laboratory and field conditions is based upon this development which is presented in the Appendix. PARAFFIN DEPOSITION IN SURFACE FLOWLINES The average temperature of the oil coming out of a well is somewhat higher than the ground temperature. Thus, the oil continues to cool on its trip through the surface flowline, and wax deposition can occur. The temperature distributions calculated from Eq. A-4 are given in Fig. 1. As can be seen, almost all the cooling occurs in the first 500 ft from the wellhead. In addition, the radial temperature gradient near the wall decreases rapidly with distance and becomes very small after a few hundred feet. Thus, growth of a paraffin deposit would be expected to decrease rapidly with distance from the wellhead and become negligible after a few hundred feet, since growth is dependent on concentration gradient. Wax precipitation and diffusion of wax to the already

By W. D. Lowry

As most of the industrial activity of Oregon is centered in the Portland area, the foundries there consume the bulk of the foundry sand produced in Oregon. Although a number of the larger towns scattered throughout the state have gray-iron foundries, the sand used by most of them is of local origin: The yearly consumption of foundry sand of all types for the past few war years in Oregon is estimated to have been approximately 40,000 tons valued at about $285,000, of which an estimated 18,000 tons was shipped in from the Ottawa, Ill., district for use largely by the steel foundries. Until 1945 much of the silica sand consumed by the steel foundries in the Pacific Northwest, approximately 50,000 tons in 1944, came from Ottawa, Ill. and surrounding regions. Although some silica sand was shipped in from Belgium in the past, none is known to have been imported in recent years. Early in 1945, a very promising high-grade silica sand being produced near Eugene, Oregon, was introduced, and all but two of the Portland steel foundries are using this new sand. Until a few years ago, the search for good local (Oregon) foundry sands was carried on largely by the foundry supply houses. Recently the Oregon Department of Geology and Mineral Industries has investigated a number of deposits and has carried on and fostered research on the most promising deposit near Eugene, about 120 miles south of Portland. High-grade silica foundry sand from this deposit is now being marketed in Oregon, Washington, and British Columbia. The Eugene sand is one of the very few outstanding western steel-foundry sands. Field investigations by the Oregon Department show that there are relatively few deposits of sand in Oregon suitable for foundry use. A knowledge of the geology of the state makes this readily understandable. The only major primary sources of the quartz present in sandstones in Oregon are the intrusive masses of granite, granodiorite, and quartz diorite of late Jurassic or early Cretaceous age found in the Siskiyou Mountains of southwestetn Oregon, a part of the old Klamath Mountain highland, and in the Blue Mountains of northeastern Oregon. Transportation militates against the development of any possible deposits of foundry sand found east of the Cascade Mountains in central and eastern Oregon because few railroads traverse that area. East of the Cascades, which separate western from eastern Oregon, many of the older sediments of Paleozoic and Mesozoic age have either been metamorphosed or contain much volcanic eruptive material, and even if some of the Mesozoic sediments are highly quartzose in places, they are in relatively inaccessible areas. All the Tertiary sediments there are of continental origin and contain much ash and other volcanic debris, for there was great volcanic activity during much of that period. In western Oregon much the same is true of the Paleozoic and Mesozoic rocks

Jan 1, 1947

By W. D. Lowry

As most of the industrial activity of Oregon is centered in the Portland area, the foundries there consume the bulk of the foundry sand produced in Oregon. Although a number of the larger towns scattered throughout the state have gray-iron foundries, the sand used by most of them is of local origin. The yearly consumption of foundry sand of all types for the past few war years in Oregon is estimated to have been approximately 40,000 tons valued at about $285,000, of which an estimated 18,000 tons was shipped in from the Ottawa, Ill., district for use largely by the steel foundries. Until 1945 much of the silica sand consumed by the steel foundries in the Pacific Northwest, approximately 50,000 tons in 1944, came from Ottawa, Ill. and surrounding regions. Although some silica sand was shipped in from Belgium in the past, none is known to have been imported in recent years. Early in 1945, a very promising high-grade silica sand being produced near Eugene, Oregon, was introduced, and all but two of the Portland steel foundries are using this new sand. Until a few years ago, the search for good local (Oregon) foundry sands was carried on largely by the foundry supply houses. Recently the Oregon Department of Geology and Mineral Industries has investigated a number of deposits and has carried on and fostered research on the most bromising deposit near Eugene, about 120 miles south of Portland. High-grade silica foundry sand from this deposit is now being marketed in Oregon, Washington, and British Columbia. The Eugene sand is one of the very few outstanding western steel-foundry sands. Field investigations by the Oregon Department show that there are relatively few deposits of sand in Oregon suitable for foundry use. A knowledge of the geology of the state makes this readily understandable. The only major primary sources of the quartz present in sandstones in Oregon are the intrusive masses of granite, granodiorite, and quartz diorite of late Jurassic or early Cretaceous age found in the Siskiyou Mountains of southwestern Oregon, a part of the old Klamath Mountain highland, and in the Blue Mountains of northeastern Oregon. Transportation militates against the development of any possible deposits of foundry sand found east of the Cascade Mountains in central and eastern Oregon because few railroads traverse that area. East of the Cascades, which separate western from eastern Oregon, many of the older sediments of Paleozoic and Mesozoic age have either been metamorphosed or contain much volcanic eruptive material, and even if some of the Mesozoic sediments are highly quartzose in places, they are in relatively inaccessible areas. All the Tertiary sediments there are of continental origin and contain much ash and other volcanic debris, for there was great volcanic activity during much of that period. In western Oregon much the same is true of the Paleozoic and Mesozoic rocks

Jan 1, 1948

By W. D. Lowry

As most of the industrial activity of Oregon is centered in the Portland area, the foundries there consume the bulk of the foundry sand produced in Oregon. Although a number of the larger towns scattered throughout the state have gray-iron foundries, the sand used by most of them is of local origin. The yearly consumption of foundry sand of all types for the past few war years in Oregon is estimated to have been approximately 40,000 tons valued at about $285,000, of which an estimated 18,000 tons was shipped in from the Ottawa, Ill., district for use largely by the steel foundries. Until 1945 much of the silica sand consumed by the steel foundries in the Pacific Northwest, approximately 50,000 tons in 1944, came from Ottawa, Ill. and surrounding regions. Although some silica sand was shipped in from Belgium in the past, none is known to have been imported in recent years. Early in 1945, a very promising high-grade silica sand being produced near Eugene, Oregon, was introduced, and all but two of the Portland steel foundries are using this new sand. Until a few years ago, the search for good local (Oregon) foundry sands was carried on largely by the foundry supply houses. Recently the Oregon Department of Geology and Mineral Industries has investigated a number of deposits and has carried on and fostered research on the most bromising deposit near Eugene, about 120 miles south of Portland. High-grade silica foundry sand from this deposit is now being marketed in Oregon, Washington, and British Columbia. The Eugene sand is one of the very few outstanding western steel-foundry sands. Field investigations by the Oregon Department show that there are relatively few deposits of sand in Oregon suitable for foundry use. A knowledge of the geology of the state makes this readily understandable. The only major primary sources of the quartz present in sandstones in Oregon are the intrusive masses of granite, granodiorite, and quartz diorite of late Jurassic or early Cretaceous age found in the Siskiyou Mountains of southwestern Oregon, a part of the old Klamath Mountain highland, and in the Blue Mountains of northeastern Oregon. Transportation militates against the development of any possible deposits of foundry sand found east of the Cascade Mountains in central and eastern Oregon because few railroads traverse that area. East of the Cascades, which separate western from eastern Oregon, many of the older sediments of Paleozoic and Mesozoic age have either been metamorphosed or contain much volcanic eruptive material, and even if some of the Mesozoic sediments are highly quartzose in places, they are in relatively inaccessible areas. All the Tertiary sediments there are of continental origin and contain much ash and other volcanic debris, for there was great volcanic activity during much of that period. In western Oregon much the same is true of the Paleozoic and Mesozoic rocks

Jan 1, 1948

By John Birkinbine

This piece of Carpenter crucible steel has exhibited a tensile strength of 116,000 pounds per square inch, an elastic limit of 89,170 pounds, an elongation of 25 per cent., and a reduction in area of 42 per cent. The test-specimen had a length of 2 inches between fillets, and was an inch bar reduced to an area of 0.504 square inch. This unusual tensile strength was determined before the bar had been hardened so as to show the remarkably velvety fracture here exhibited; but a piece of the same, tested after hardening, is reported to have stood a stress of 214,000 pounds per square inch. Another test-piece is said to have shown 136,000 pounds tensile strength, 97,300 pounds elastic limit, 20 per cent. elongation in 2 inches, and 40 per cent. reduction of area. Mr. Carpenter claims that this steel, containing 2.27 per cent. chromium and 1.04 per cent. carbon, can be welded like iron, and has proved most desirable,for the highest class of die-steel.

Jan 1, 1895

The following letter has been received from Prof. Alfred C. Lane, of Tufts College, who is now in charge of the department, of mining in the College of Engineering, American E. F. University, Beaune, France. My DEAR MR. STOUGHTON: I have had a very interesting time here. We were received fast Saturday with great courtesy by the Schneiders at the Creusot plant, and saw many interesting things, from the mammoth guns clown. In one trip I saw a coal mine, an iron mine, an oilshale mine, a gypsum mine, and a most beautiful fluorspar mine. So you see we were not badly located. A mine like Epinac, which has a washery, a briquetting plant, and great central electric plant where coal that might otherwise be waste is converted into electricity and shipped away at 30,000 volts pressure, is of interest mechanically as well as geologically. Many of the French coal seams are very thick here and have especial mining methods. The Department of Mining has been manned by men with whom it was a pleasure and an honor to be associated, as well as with Dean Reber who was in charge of the College of Engineering as a whole. Names like Captain H. C. Ray, former professor at the University of Pittsburgh, on leave in the army, Captain Archbald of the Colliery Engineer at one time, whose work in the Pennsylvania coal mines is well known, Captain Vail of the Engineering and Mining Journal staff and Captain E. C. Dietrich of the Southwest, are familiar to members of the Institute, and Are guarantees of competent instruction.

Jan 7, 1919

NATURE produces iron ore abundantly in many regions of the world, especially in Italy where not only is there a great abundance of it but also there are various kinds. In these our Tuscan parts it is a very familiar thing, since we are situated close to the island of Elba which is so overflowing and rich in this ore that it surpasses every other place where it is found. Thus not only do the regions of Tuscany share its great quantity because of their proximity, but more than two-thirds of Italy as well as Sicily and Corsica are supplied, and perhaps some more distant place. In addition, this ore is of such perfection that it

Jan 1, 1942

W. VAN DER GRACHT, Tulsa, Okla. (written discussion.*).-I fully agree with Mr. Daly's observation that there is such a coincidence between petroleum deposits and geosynclines as to suggest them to be "closely allied phenomena." However, I accept no "identity of cause." To me the explanation is a simple one. Geosynclinal deposition is the first phase in the formation of a mountain, chain, and petroliferous deposits are indeed closely allied to zones of, mountain folding. In fact, petroleum is a typical occurrence in those beds, which represent the flysch facies, to use the Swiss expression. The uplifting of a great mountain chain is a very slow process; it gradually sets ill as a slow geo-anticlinal upheaval within a zone off former geo-

Jan 1, 1918

By F. C. Frischknecht

Most early development and application of electromagnetic prospecting methods took place in Scandinavia, where geological conditions favor their use. In other parts of the world these methods have aroused cycles of interest, but in Scandinavia they have been used continuously and successfully since the 1920's. Electromagnetic methods may be classified into two general groups. One group includes methods in which the source of the electromagnetic field remains stationary while the receivers are moved about to explore the area. The other includes procedures in which the energizing and receiving systems are moved together. Other classifications could be based on the size of the energizing source, the particular components of the electromagnetic field which are measured, or the mode of transporting the equipment. The difference between fixed-source and moving-source methods, however, is of such great fundamental importance that it will be emphasized in this discussion. FIXED-SOURCE METHODS Essentially, a fixed-source method consists of the measurement of electromagnetic fields about the source. The mutual coupling between the source and the earth is constant, but the mutual coupling between the receiver and the earth (unless the earth is homogeneous) and also between the source and the receiver changes at each station. The results are usually normalized by relating the field data to the calculated free space or primary field. Turam and Radio Reference Signal Methods: The turam or two-frame* (see Fig. 1A) is probably * Turam means two-coil. the most common fixed-source method. The energizing source is an insulated cable grounded at both ends or formed into a large rectangular loop. Measurements are taken along a traverse at 5 to 50-meter intervals using two small receiving coils, the lagging coil being placed at the position previously occupied by the leading coil. The complex ratio (i.e., inphase and out-of-phase ratios) of the voltages induced in the two coils is measured. Operating frequency range is about 100 to 800 cps. In a typical turam survey a straight, grounded cable several kilometers long is laid out parallel to the probable strike of the ore deposits or conducting strata being sought. An area extending 1 or 2 km on each side of the cable, and within 1 or 2 km of the ends of the cable, is surveyed. Measurements are made at stations 5 to 25 m apart along traverses perpendicular to the cable. Measurements may be made along lines parallel to the cable to serve as base lines for the traverses or for other special purposes. Commonly the receiving coils are oriented with their planes horizontal so that only the vertical component of the field is measured. If additional information is required, one of the hori- zontal components may also be measured by orienting the coils with their planes vertical. In a modified turam technique developed recently for both ground and airborne measurements (Fig. 1B) the amplitude of the complex voltage induced in a single receiving coil is measured and its phase compared with that of a reference signal transmitted from the energizing system by a radio frequency carrier. Thus the un-normalized field is obtained directly, whereas with the turam method it is obtained by calculation from the ratios. The turam method and its modifications have a greater working depth than the other electromagnetic procedures used in ore prospecting. Under favorable conditions conductors have been located at depths of 200 to 300 m. A modified turam method with one of the electrodes grounded in the upper end of a plunging orebody was used to follow the extension of this body to a depth of 200 m beneath a layer of conducting schists. Straight grounded cables are usually preferred to insulated loops because they are easier to lay out and because they often make the method more sensitive. The greater sensitivity of a grounded cable is a result of ground return currents which may flow in the orebodies in addition to the eddy currents caused by induction from the current in the cable. Anomalies in the vertical field due to eddy currents are characterized by a correspondence between high values for the inphase component and positive out-of-phase components and/or low values for the inphase component and negative out-of-phase components. Also the inphase component may approach zero, but it does not become negative. In very long continuous conductors that are parallel to a grounded cable the effect of ground return currents may far exceed the effect of eddy currents. These ground return currents cause a lack of correspondence between the inphase and out-of-phase components and may cause negative inphase or anti-phase components. It becomes difficult to carry out the measurements and often difficult to interpret the results. Such results immediately suggest the presence of graphitic strata, however, since ore deposits are rarely extensive enough to accumulate sufficient ground return current to cause these results. A cable laid out perpendicular to the strike or an insulated loop is sometimes used in areas where graphitic schists and slates are present. Anomalies are then completely or almost entirely due to eddy currents and are easier to interpret. The measured voltage ratios are normalized by either subtracting or dividing by normal field ratios calculated from free space considerations. The normalized ratios are then plotted as individual profiles. When significant anomalies occur in the ratio measurements, the actual normalized fields are calculated by beginning with a measured or an assumed value for the field at a point near the cable and successively multiplying this value by the normalized ratios. There is a similarity between this process and a numerical integration of the ratio curve. Conversely, in many respects the ratio curve is similar to the first derivative of the field curve.

Jan 1, 1960

By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy's law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy's law' has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy's law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.'s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.' To others,' turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy's law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.' In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy's law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy's law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy's law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy's law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy's law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By J. J. Cosgrove, J. E. Warren

A general model which approximates the effect of cross- flow has been developed to give a practical method for predicting the waterflood behavior of a stratified reservoir. The model is based on a modification of Dietz's theory and allows for variations in both the permeability and hydrocarbon pore volume. In the particular cases considered, it is assumed that the permeability can be characterized by a log-normal distribution and the hydrocarbon pore volume by a normal distribution. A simple graphical method which enables the practicing engineer to predict the behavior of a stratified system is presented The results obtained by the proposed method are compared with those obtained by the Dykstra-Parsons method. As a result of this study the following conclusions have been drawn: (1) The effect of cross-flow in a stratified system can be appreciable, particularly at very favorable or very unfavorable mobility ratios; (2) Under normal conditions, the effect of variations in the hydrocarbon pore volume can be neglected; and (3) The failure to use all of the available permeability data can lead to large errors in the prediction of the behavior of a stratified reservoir. INTRODUCTION Various methodshavebeenproposedto characterize and to predict the waterflood behavior of a stratified reservoir. Most of the methods assume that the reservoir is composed of discrete homogeneous continuous layers. With this model, the degree of stratification can be measured by several parameters based on core-analysis data. Among these are the Lorenz coefficient1 and the variation of a log-normal permeability distribution? The behavior of stratified systems is usually predicted by the Stiles, Dykstra-Parsons method or some modification of these. In both of these methods the reservoir is divided into discrete homogeneous layers with no cross-flow between layers. In the Stiles method the mobility ratio is assumed to be equal to unity while in the Dykstra-Parsons method it is allowed to take on any value. Other predictive methods have been proposed; method allows for cross-flow between the beds and a method by Schmalz and Rahme6 correlate.s the recovery directly with the Lorenz coefficient. In this new approach, which is essentially a continuous analog of Hiatt's method, the effects of both mobility ratio and cross-flow between the beds have been included. It is assumed that the permeability can be represented by a log-normal distribution and the hydrocarbon pore volume or porosity by a normal distribution. These types of distributions have been observed by several authors, 1,2,4 and most field data seem to confirm their observations; e.g., if these distributions are assumed and there is a 1:l correspondence between porosity and permeability samples, the commonly encountered linear relationship between porosity and the log of permeability is obtained. Since, in many field cases the permeability and poro sity data are truncated or cut-off at predetermined upper and/or lower values, the effect of discarding part of the data was investigated with the proposed method. A better technique for truncating the data is suggested. THEORY In the derivation of the method to be described in this paper the following assumptions are made: 1. Capillary forces are negligible per se; their effects are only manifest in the relative permeability curves. 2. The fluids are immiscible, incompressible and homogeneous. 3. The reservoir is horizontal and uniformly thick; it is initially liquid saturated i.e., connate water and oil. 4. The reservoir is composed of discrete layers, each having its own permeability, porosity and connate water saturation; each layer is homogeneous,

Jan 1, 1965

By J. F. Poland

B. C. Burgess-—Prior to hearing this paper presented at the San Francisco meeting, I travelled by car from Yuma, Ariz., across south-central California and up through the San Joaquin Valley. After hearing the paper I returned by the coast route to San Diego then along the Mexican border to Yuma. The striking feature of these trips, related to this paper, was the dry river and creek beds at a time of year not the dry season. Contrasted with this was the wasteful use of water in irrigation canals and laterals. Poland says "at least 90 pct of the ground water pumped is used for irrigation." That being the case, it would appear that first consideration should be given to conservation of this use. Probably a small part of this is actually reaching the plants. Some measure of this loss between pump and crops would be revealing. Methods that might be employed to reduce this loss are pipe lines and spraying of some crops such as the banana planters are using in Central America. Another idea which might be investigated is to line canals and ditches with some water-repelling mineral like pyro-phyllite. Perhaps a comparatively thin sprayed-on

Jan 1, 1951

By J. F. Poland

B. C. Burgess-—Prior to hearing this paper presented at the San Francisco meeting, I travelled by car from Yuma, Ariz., across south-central California and up through the San Joaquin Valley. After hearing the paper I returned by the coast route to San Diego then along the Mexican border to Yuma. The striking feature of these trips, related to this paper, was the dry river and creek beds at a time of year not the dry season. Contrasted with this was the wasteful use of water in irrigation canals and laterals. Poland says "at least 90 pct of the ground water pumped is used for irrigation." That being the case, it would appear that first consideration should be given to conservation of this use. Probably a small part of this is actually reaching the plants. Some measure of this loss between pump and crops would be revealing. Methods that might be employed to reduce this loss are pipe lines and spraying of some crops such as the banana planters are using in Central America. Another idea which might be investigated is to line canals and ditches with some water-repelling mineral like pyro-phyllite. Perhaps a comparatively thin sprayed-on

Jan 1, 1951

MIXED emotions were produced by the announcement that the buildup of weapons will be stretched out till mid-1954 instead of the previous 1953 deadline. Reason: government assistance programs will be tougher to get but there will be easement in materials allocations. Earlier in February, DPA had announced that tightening up on regulations governing rapid tax -amortization would become effective March 1. In the future, DPA will have to certify amortization contracts for all construction and permanent installations costing more than $100,000. This action was necessary according to DPA's James F. King, so that new industrial expansions already approved could be assessed in the light of the changing critical mineral picture. When DMPA inherited the backlog of government assistance, requests from DMA, it moved in fast. The results of DMPA's work is described in the article on p. 351 by James K. Richardson; The speed with which these requests were approved and the lengthening of the military program have made a reappraisal of the critical mineral list necessary. It looks as though the consumer industries will be getting more metal soon and, led by steel, there is an industry push toward the abandonment of CMP. Relaxing of materials controls appears imminent but discontinuing CMP is in the "let's talk this thing over" stage.

Jan 1, 1952

By Charles S. Barrett, Frederick N. Rhines, Robert F. Mehl

The solid solutions which aluminum forms with copper, and with magnesium and silicon, are not extensive, and accordingly could not be expected to form Widmanstatten figures profusely nor with great ease. A study of the Widmanstatten figures in these systems seemed desirable, however, because of the interest which these alloys bear towards age-hardening theories resulting from the necessary relationship between the age-hardening phenomena and the atomic processes leading to the formation of Widmanstatten figures.' Alloys of Aluminum with Copper The most accurate determination of the solid solubi1it.y of copper in aluminum seems to be that by Dix and Richardsoq2 whose results are represented in Fig. 1. According to this work, aluminum dissolves 5.6 weight per cent of copper at 548", and less than one per cent at room temperature. Judging from the constitutional diagram, this solid solu-lion on cooling tends to precipitate the compound CuA12, and this conclusion has been confirmed experimentally by Schmid and Wassermann.

Jan 1, 1932

By Hugh Marriott

MANGANESE and its ores have been recently dealt with in comprehensive papers to the Iron and Steel Institute by Sir Robert Hadfield, and in a series of papers read before the A. I. M. E. at the Cleveland meeting. I have taken the opportunity of adding this mineral, to my records of the "World's Mineral Production and Consumption," as recently pub-lished in the Economist ?. The tables bring out the following significant facts: The world's production has increased by 10 per cent since 1913. India's production has increased by 3 per cent since 1.913, the supply from this source now being 31.1 per cent of the world's output. Russia is now producing at about half its pre-war rate and yields 19 per cent of the world's production. West Africa supplies 12.5 per cent of the world's total output. Brazil's present output is 2.5 times that of the pre-war period, being 11.3 per cent of the world's output.

Jan 9, 1927

By W. H. Wamsley

Used in combination with conveyor belt haulage, bucket wheel excavators offer unusual possibilities for low excavation and haulage costs. Originating in Germany, these machines are now in use or on order for Australia, Northern Rhodesia, the Belgian Congo, Italy, Yugoslavia, France, Belgium, Indonesia, and the Union of South Africa. A diamond mine in South Africa that has been using German bucket wheel excavators since 1928 purchased American cable-way excavators and American scraping equipment after the war. Operating cost for this equipment was double that for the bucket wheel machines operating in the same mines with crawler-mounted stackers. Machines built and operated in the U. S. are, as far as the writer knows, confined to the northern Illinois coal field, where they are used in conjunction with large shovels to strip overburden too high to be reached by the 30 to 40-yd shovels. Their long stacker belts can deposit the spoil far enough behind the coal face to avoid slides, in such a manner as to make reclaiming the land easier. These large, specialized machines are now being made by Bucyrus-Erie Co. but are not adaptable to many open pit mining situations.

Dec 1, 1956