Search Documents

By E. T. Cox

WHILe engaged, in the year 1856, in determining the oil-bearing properties of some bituminous coals from Western Kentucky, by subjecting them to dry distillation in an iron retort, which held about a pint;, and to the neck of which were attached several bottles, for collecting the carbon oils, and washing and measuring the gas, I observed that there was a very great gain in the weight of coke thus made, over that obtained from the same coal when charred in a platinum crucible, as is usual in the laboratory for making the proximate analysis of coal. It was thought at the time that the increase of coke, by the former mode of treating the coal, was due to the pressure which the retarded gas exerted upon the solid carbon, and the possible fixing of a portion of the carbon from the volatile hydrocarbons. For the purpose of obtaining a more definite idea of the effects of pressure on the coking of coals, a series of experiments were made this spring under my direction, by my assistant, Dr. G. M. Levete. The results are highly instructive and full of interest, since they point out some peculiarities in the nature of bituminous coals which

By C. A. Crawford

Nickel and the nickel-copper alloy, the latter generally referred to as monel metal, are available in a variety of wrought and fabricated forms, of which the following are regular commercial products:

By A. Lubinski, J. L. Logan, W. S. Althouse

A4ost gas twells and flowing oil wells are completed and treated through a string of tubing and a packer. Changes in temperature and in pressure inside or outside the tubing will: (I) if free motion of the tubing inside the packer is permitted, increase or decrease the length of the rubing; or (2) if free motion is prevented, induce forces in the tubing and on the packer. If pressure inside the tubing is greater than outside, the tubing may buckle helically even in the presence of a packer-to-tubing tension. The tubing will always buckle, and much more severely, if free motion is permitted. The buckling may be prevented by pulling the tubing in sufficient tension. The prediction of these forces and tubing movement has here to fore been based upon calculations that did not inciude helical buckling. This paper preseitts means with which these length or force changes can be calculated while taking into account the effect of helical buckling. To avoid damaging formations, failure of remedial operations, or damage to the tubing or packer, application is made to practical problems involving calculations of the required length of seals, amount of sluckoff or tension, and prevention of permanent corkscrewing. INTRODUCTION Leakage of a packer may result in costly failures of such operations as squeeze cementing, hydraulic fracturing, etc. To avoid such failures, the authors are often asked questions pertaining to the length of necessary seals, the amount of necessary slackoff, etc. Published work' does not take into account helical buckling of tubing. Investigation of helical buckling was prompted by the fact that allowance must be made for this phenomenon in order to provide relevant answers. In the past, theoretical work on helical buckling was confined to conditions for which such buckling does not The mathematical treatment of behavior in a buckled condition, given in the Appendix, is novel. Assumptions upon which this investigation is based are listed and discussed in a special section. The following are a few of the many kinds of problems which may be solved with this paper. 1. Consider a packer in which tubing may move. Such movement will occur after pressures and temperature are changed. The paper provides means for: (a) calculating the amount of such movement and, therefore. the required length of seals; and (b) calculating the necessary amount of initial slackoff, for which there is no danger of unsealing the packer, if the length of seals is given. Such calculations, as well as those which follow, tully take into account the fact that part of the movement ib due to elastic helical buckling of the lower part of the string. This buckling may occur even in tubing under tension. Insufficient initial slackoff for a given length of seals, or insufficient length of seals for a given slackoff, may result in costly failures. A field case of such a failure will be given further in this paper. 2. In the case in which tubing cannot move in the packer, changes of pressure and temperature result in tubing-to-packer forces and forces in the tubing above the packer, both of which may be calculated. This knowledge is important because, if these forces are too large, the) could damage the packer or the tubing. 3. For wells in which wireline tools are to be run through the tubing, the paper provides means to keep the tubing from buckling, thereby permitting free passage of tools. 4. In deep wells, mainly in the presence of large casing, tubing may become "corkscrewed", i.e., take a permanent helical set. A field case is described further in the text. Using this paper, one may calculate in advance conditions under which permanent corkscrewing would occur, and then take preventive steps. HELICAL BUCKLING Consider a string of tubing, freely suspended in the absence of any fluid inside casing, as shown in Fig. I(a). Now consider an upward force F applied at the lower end of this tubing. This force compresses the string; and if the compression is large enough (which is always the case in actual problems), the lower portion of the string will buckle into a helix, as shown in Fig. 1 (b). The lower end of the tubing is subjected to a compression F. This compression decreases with the distance from the bottom and becomes nil (neither compression nor ten-

By Kenneth F. Whinery, John M. Campbell

Basically, the Buckley-Leverett theory involves two systems which are similar in nature but are differentiated by time. These systems may be described by the fractional flow and frontal advance equations which essentially characterize the mechanics of oil movement while being expelled from the reservoir. The fractional flow equation originally developed by Leverettl may be expressed in the more usable form The development of this equation is based on Darcy's law describing fluid flow through porous media and applies to the flow at only one point (it is a point function). For simplification, the fractional flow equation is written in the above form because the capillary forces always increase the fractional flow of the displacing phase regardless of the direction of flow or the displacing phase. If, for simplicity, the effects due to gravity and capillary pressure differences are neglected, the fraction of the displacing fluid, f, at any point in the flowing stream is related to the properties of the system by 1 Thus, it is seen that in the absence of capillary and gravitational effects, fd for a given sand and fluids varies only with saturation and pressure. The magnitude of the viscosity ratio, —a has an effective range (range of about 30) in the system where gas is displacing oil and a much smaller range for water displacing oil. In order to make the fractional flow equation more versatile, it is necessary to connect the fractional flow at a given point and saturation with time. This problem was approached by Buckley and Leverett" who developed the frontal advance equation, Eq. 3 states that the rate of advance of a plane that has a fixed saturation, Sd, is proportional to the change in composition of the flow stream caused by a small change in the saturation of the displacing fluid. It is, essentially, a transformation of a material balance equation representing the net rate of accumulation of the displacing phase within a homogeneous sand block. This accumulation is proportional to the difference between the rate at which the displacing fluid enters the sand and that at which it leaves. Eq. 3 describes the velocity with which a plane of constant displacing phase saturation advances through a porous system. Buckley and Leverett," Babson,' Kern," Welge, and others have adequately discussed the basic mechanism and application of the fractional flow and frontal advance equations. APPLICATIONS OF THE FRONTAL ADVANCE THEORY TO PETROLEUM RECOVERY Two general applications of the Buckley-Leverett frontal advance theory involve the system in which the oil is being displaced by an expanding gas cap overlying the oil zone and that in which the oil is being displaced by water. Displacement by Gas in the Presence of an Immobile Water Saturation A system in which gas is the displacing phase may be thought of as having two forces effecting the displacement process. These forces are the gravitational force and that force exerted by the displacing gas. The gravitational effects control the displacing efficiency of the gas. The gravitational effect will be less at higher rates of flow, thereby reducing the effectiveness of the displacement of the oil by the gas. The more efficient displacements occur at flow rates which are less than the gravity free fall rate. Capillary forces can be neglected without materially changing the magnitude of the gas saturation. The Mile Six pool is used herein to illustrate the calculating procedures in evaluating gas drive-gravity drainage field perfomlance. These calculations represent the determination of the gas-oil contact when the distribution of the hydrocarbon pore volume is considered. Two methods

By William Metcalf

It is the object of this paper to oppose unnecessary changes, and the introduction of new and confusing terms. From the earliest times of which we have ally record on the subject, iron has been divided into general classes. Whether iron was first known in the form of wrought iron or of steel, is a matter of no importance; but at the time when cast iron first became a prominent article of commerce, wrought iron and steel were old products— steel, at that time, being generally made from wrought iron by the process of cementation. As steel was then properly defined as iron containing more carbon than wrought iron, so cast iron was appropriately defined as iron containing more carbon than steel. Until the year 1776, when Huntsman first began the manufacture of a new kind of iron by melting wrought iron and steel in crucibles, the above definitions were all that could be desired. At first, probably, owing to imperfect appliances, only a highly carburized iron was melted in crucibles, and this led to its being called cast steel. If our ancestors had found a name for this material not involving the use of the word steel, we would have been saved the trouble of the present discussion. As the arts developed, new uses were found for steel, and the products of the crucible were varied, until at the present day it is quite common to find steel containing no more carbon than average wrought iron, and other steel containing nearly or quite as much carbon as some cast iron. All of these various products of the crucible have retained, or received, the name cast steel, usually abbreviated to the simple word steel, without caus-ing any confusion among producers or consumers in regard to terms or their meaning. In 1865, twenty-one years ago, the Bessemer process was introduced ; this was followed in a few years by the Siemens-Martin process, and the products of both were at once, and have ever since been, called steel, from the fact that they were identical in chemical and physical properties with crucible cast steel. At the present time, then, we have three subdivisions of cast steel, viz.: Crucible cast steel, Bessemer cast steel, and Siemens-Martin,

By Rossiter W. Raymond

As I have attempted briefly to show you, gentlemen, the present position of the mining and metallurgical industries of this country offers in several respects most important indications of radical change. This is an epoch for more than one branch of these industries. We are commencing again to export copper; we have shifted the main production of lead from the Mississippi Valley to the far West, besides developing a new production of that metal in Missouri; we have seen the price of quicksilver go up, and the price of iron go down to such an extent as to affect profoundly, on the one hand, the great business of extracting silver by amalgamation, through the Washoe process in this country and the patio process in Mexico, and, on the other hand, the various manufactures employing iron as a raw material; above all, the manufacture of steel. But the epoch which has occurred in the relative value of gold and silver, in consequence of causes which I shall attempt to explain, and among which the extraordinary increase in the silver product of Nevada is not the least; this epoch is, perhaps, the most striking feature in the review of our situation. Since my official duties in connection with the mining industry of the Pacific slope and the Great Interior Basin have led me to pay particular attention to this subject, I have thought it not inappropriate to lay before you a somewhat extended account of its history. It is a topic of peculiar interest, because of the general use of these two metals as standards of value in the exchange of commodities. Neither of them is suitable to be, for the political economist, a real standard of value. That standard is rather to be sought in some more universal product of labor, such as wheat—the relation

By Anton Eilers, R. W. Raymond, O. H. Hann

THIS paper will treat of such works only as beneficiate ores directly in the mining districts. And when it is said that more than twenty

By H. F. Seifert

The classification and preparation of non-ferrous scrap mctals is a subject of interest to every individual and corporation that employs in its processes of manufacture non-ferrous metals and alloys and accurnulates in such manufacture scrap from these materials for disposition in the form of turnings, borings, short ends, punchings, clippings, grindings, washings, etc. All too frequently the disposition of such scrap is left to indivitluals who have no knowledge of the subject either from a metallurgical or a commercial standpoint, or both. Much money is thus lost whicli with a little more intelligent effort might be saved, and in this day of fierce competition and small profits such an opportunity cannot be ignored. The Mineral Resources of the United States for the year 1925, the latest issue available (Part 1, page 221), gives the secondary non-ferrous metals of certain classes recovered in the United States for the year 1924 to 1925 as shown in Table 1. The figures are tabulated simply to give the reader some idea of the scope of the secondary non-ferrous metal industry. Approximately 900,000 tons of an annual value of $244,000,000 were recovered in the year cited. In 1916 (again using thc Mineral Resources of the United States as authority) the tonnage reclaimed was approximately 632,000 tons and the value, because of the high prices for metals prevailing at that time, amounted to $265,000,000. It is not the purpose of this paper to discuss smelting and refining operations or the feasibility of an organization, primarily engaged in some other activity, conducting smelting and refining operations to convert its own non-ferrous scrap metals and alloys. The classification and preparation of these non-ferrous materials is a preliminary step, regardless of what subsequent operations the material may pass through or where these operations may be conducted. For that reason the subject can he readily discussed without any reference to subsequent activities. Space must be provided, with suitable handling facilities, scales and the necessary storage bins where the material may be accumulated. The scope of the activity, the nature of the industry and the tonnage handled will determine, in a large measure, what preparation, if any, it rrlay he desirable to give these scrap materials to put them in the best niarketable condition. By preparation is rneant largely what, for the want of a

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

P,, and v, may now be solved for by trial and error between Eqs. 2 and 3, by assuming time approaching zero and equating PI, to P12. Observe that the pressure under the slug, P12 of Eq. 3, does not remain equal to the P1, at the valve in Eq. 2 as the slug proceeds up the hole. To plot the profile of pressure vs depth, it is necessary to express P12 in terms of P11. To do so, the extent to which the original submergence length S changes with respect to time must be analyzed. At the end of time t after injection, the actual value of L in Fig. 3 is The fall-back v,(t) is now distributed in the gas and exerts pressure on the bottom. This, in addition to the weight of the gas, amounts to the difference in pressures from point to point. With the average pressure profile calculable, a true numerical value for the average pressure in the tubing may be obtained. The value of v, must be obtained experimentally, and since v,, S and D are known, the basic Eq. 1 may be solved for the amount produced. Knowing P, and the actual volume of tubing occupied by gas (vat), it is possible to calculate the volume of gas at standard conditions which is present in the

By L. L. Handy

The development of a theory for miscible liquid displacement requires evaluation of the variables which affect growth of the mixing zone between solvent and displaced oil. Factors which appear to be important are individual fluid viscosities, viscosity ratios, flood rate, fluid densities, flow characteristics of the porous medium and molecular diffusion coefficients of the fluid components. The primary purpose of this paper is to evaluate diffusion effects. Theoretical treatments to date have been limited to floods for which the viscosity ratio is one. Two principal theories have been proposed. Von Rosenberg adapted for porous media a theory derived for capillary tubes by G. Taylor.' ,' In this theory molecular diffusion perpendicular to the direction of flow is a primary factor in sharpening the flood front. Slow floods give sharper fronts for a given distance traveled than fast floods. An alternative theory considers miscible liquid displacement as a statistical problem.3,4,5 Diffusion is not an important factor in this theory, but it leads to the same general type of equation as von Rosenberg's. Both theories predict S-shaped concentration profiles with the same dependence on distance traveled. The statistical or "dispersion" theory predicts rate independence, however. To supplement rate studies a direct measurement of a diffusion effect would be helpful in evaluating which of the two proposed mechanisms best describes miscible liquid displacement for one-to-one viscosity ratio systems. No quantitative theory has been proposed for floods in which a low-viscosity fluid displaces a high-viscosity fluid. It might be anticipated, however, that the extensive fingering observed in floods with adverse viscosity ratios would increase opportunities for an exchange of components between displaced and displacing liquids by a diffusional process. Even if molecular diffusion were not an important mixing mechanism for one-to-one viscosity ratio systems, it could be significant in systems with adverse viscosity ratios. METHOD FOR EVALUATING DIFFUSIONAL MIXING In solvent flooding the displacing liquid can become mixed with the displaced liquid by a number of processes; in general, either mechanical or diffusional in character. To evaluate the contribution of diffusion, a method was sought that would distinguish diffusional mixing from mechanical mixing. Suppose two soluble tracers are added to the displacing liquid and that one tracer has a diffusion coefficient much greater than the other. Then, if diffusion is important during miscible liquid displacement and if diffusional transport is primarily transverse to the direction of flow, substances with high diffusion coefficients will have sharper concentration profiles than those with comparatively low molecular diffusion coefficients. In order to have material balance the profiles for the two tracers must intersect. For one-to-one viscosity ratios the intersection would occur at the 50 per cent concentration point. It is generally assumed that diffusion in the direction of flow is negligible. This assumption appears reasonable because flow velocities are ordinarily orders of magnitude greater than diffusional velocities. If this is not a valid assumption, however, the shapes of the fronts will be further degraded by longitudinal diffusion. The effects of rate and molecular diffusion coefficients are the opposite for longitudinal diffusion to those for lateral diffusion. Higher rates or lower diffusion coefficients would tend to give sharper fronts. The double tracer method offers several unique advantages in evaluating effect of molecular diffusion. First, the method gives a direct measure of the effect of diffusion on mixing zone size. Second, the effect of a difference in diffusion coefficients is determined from a single experiment. Comparison of several experiments at different rates is not required. Third, the method is applicable for any viscosity ratio. Fourth, the method is unaffected by density differences between the two fluids which might result in rate dependent gravity effects. EXPERIMENTAL PROCEDURE Suitable tracers are substances whose diffusion coefficients differ as widely as possible, but whose adsorptions on rock surfaces is negligible. The two tracers selected were methanol and sucrose in water solutions. The approximate diffusion coefficients for methanol and sucrose, as given in the International Critical Tables, are 1.3 X 10-5 and 0.3 X 10-5 m2/sec, respectively. Concentrations in the water solutions were 200 gm/liter of solution for both methanol and sucrose. These high

By John F. Blandy

The map on Plate I illustrates a part of the works of the Red Bank Mining Company, on the Upper Freeport seam of coal, in Armstrong County, Pennsylvania. The contour lines give a careful representation of the conformation of the surface, showing also the line of outcrop of the seam, and the gangways of the mines are shown by the black lines. Upon assuming charge of the works in January last, I found that the first and greatest difficulty lay in the great uncertainty of the

By W. Hurst

The authors of this paper, in substituting values in a material balance equation associated with a gas reserve and a water drive, cannot find sustainment of what the gas in place should be; therefore, their conclusion is that this type of problem dealing with gas reservoirs is insoluble. They have introduced the word, "cybernetics," based on the work of Norbert Wiener, that further extends this line of reasoning, namely, to the effect that the system is a "black box", and that the gas reservoir and aquifer can take on infinite aspects 'based upon their past performance, to quote the authors. The inference is that this black box is an unknown. which permits in computer programming to subscribe as many variables as possible to observe by adjustment of one to another those combinations of conditions that fit field behavior. This may satisfy those in this discipline whose dedication is to programming, but to the others this is a comparison to the rationalization of the combinational results of the throwing of dice—a probability procedure. In reservoir engineering we are more direct. We learn from the examination of individual we'll and field data exactly what is in this black box. I now come to the impasse that has confronted these authors in their machine calculations. In this I have reproduced from their own production data (Tables 1 and 2 of their paper) pressure vs cumulative gas produced. shown as Figs. D-1 through D-5. A perusal of any of these five plots, for the corresponding fields in the Po Valley, shows the straight-line relation of pressure vs gas produced, evidencing pressure depletion. The point I make is that in their fundamental production data, there is no variance from a straight line that can support a water drive.

THE first session of this meeting was held Tuesday evening, in the chamber of the Common Council, the President, Mr. David Thomas, in the chair. Mayor Carroll, of Troy, gave a cordial welcome to the Institute, which was responded to, on behalf of the Institute, by the first Vice-President, Mr. R. W. Raymond. The Council reported the names proposed for membership with recommendation for election. The following named gentlemen were duly elected: Anthony, J., . .Williamstown, Pa. Babcock, George, . . .Troy, N. Y. Blake, Theo. A., . . . . . . Sa n Francisco, Cal. Blossom, T. M., . . . . . . New Pork. Boalt, James A., . . .San Francisco, Cal. Bowman, Amos, . . . . San Francisco, Cal. Chester, Prof. A. H., . .Clinton, N. Y. Dewey, C., . Pittsfield, Mass. Dock, Gilliard, . Shamokin, Pa. Emerson, O. D., . .New York. Endres, John J., . .Pittsburgh, Pa. Firmstone, Frank, . Easton, Pa. Fowle, W. B., . Philadelphia, Pa. Frazier, Prof. B. W., . . .Bethlehem, Pa. Gardner, George A., . New Pork. Goodyear, Watson A., . .6an Francisco, C al. Griswold, Chester, . Troy, N. P. Griswold, J. A.,* . . .Troy, N. Y. Hague, J. D., . . .San Francisco, Cal. Hahn, 0. H., . .Eureka, Nev. Harkness, T. C., . . . . . . Wilkes-Barre, Pa Harris, Samuel, . . .Hudson, N . Y. Henry, &. T., . Oxford, N. J. Holley, A. L., . .Brooklyn, N. Y. Howe, H. W., . . .Troy, N. Y. Hunt, Dr. T. Sterry, . Boston, Mass. Jannet, J., . Troy, N. Y. Knapp, John A., . .New Pork. Laughlin, Henry A., . . .Pittsburgh, Pa.

By G. R. Pickett

Examples are presented which show that the velocity~ amplitude, attenuation and apparent frequency of several acoustic waves can be recorded in the borehole. Examination of such recordings, termed "character" logs, indicates that the wave types observed include a refracted compressional wave and a wave which travels with formation shear velocity. Laboratory data are used to show that compressional and shear wave velocities are dependent on porosity, effective stress and lithology; but that the change in reciprocal velocity per unit change in porosity is larger for shear waves than for compressional waves. We, therefore, conclude that. the accuracy of porosity determinations can sometimes be improved by use of shear wave velocities, provided that the shear wave amplitudes are large enough to delineate the shear arrival from the preceding compressional arrival on the character log. Borehole data are presented which show that the difference between shear wave and compressional wave reciprocal velocities can be used to predict porosities. This is a refinement which may allow the prediction of porosities from single-receiver acoustic logs without introduction of errors from borehole fluid traveltimes. Laboratory and field data are presented to show that the relationship between compressional and shear wave velocities can be used to indicate lithology. An example is presented to show that fractures usually cause a greater reduction in borehole shear wave amplitudes than in compressional wave amplitudes, an effect which may offer a more reliable means of detecting fractures. The complexity of the borehole acoustic wave train can rake presently available cement bond logs highly sensitive to the gate and bias settings used. The character log offers a means to circumvent possible misinterpretations by recording all amplitudes, from which the interpreter can select the appropriate data for evaluating the cement bond. Character logs may also be used as a quality control for open-hole transit-time logs when existence of small compressional wave amplitudes interferes with the proper functioning of bias-controlled timing devices. Evaluation of the potential uses of character log data is not complete; but a character log presented in a form convenient for routine use would be a desirable addition to currently available logs. To summarize, possible applications for such a log in formation evaluation include the following (1) quality control of transit-time logs, (2) refinement of porosity predictions, (3) determination of lithology, (4) improvement of fracture detection and (5) improvement of cement bond evaluation. Suggestions are made regarding the requirements for a suficient but practical character log for routine use. INTRODUCTION Acoustic logs have become a widely used porosity tool in formation evaluation. In addition, there is a growing application of acoustic logs in cement bond evaluation and fracture detection. These applications have mainly involved the use of logs of first-arrival transit times and amplitudes and have not included detailed studies of the complete signal. The purpose of this paper is to show that significant benefits in formation evaluation can be gained by a more complete use of the acoustic wave train generated in the borehole by an acoustic logging tool. We hope that this discussion will also stimulate further development of logs suitable for routine use so that these benefits may be realized. Examples of acoustic wave train logs, termed "character" logs, are presented to show that several identifiable acoustic waves are present in the borehole. The measurable characteristics of these acoustic waves and some of their relations to formation properties of interest are also discussed. The more obvious potential uses of character logs are listed, and some suggestions are made regarding the requirements for a sufficient but practical character log for routine use. CHARACTER LOGS Some 10 years ago, Vogel' and Summers and Broding' noted that the signals received uphole from an acoustic logging tool located in a borehole had a number of interesting characteristics. The logging tool consisted of two or more pressure transducers spaced on an acoustically insulated body (Fig. la). One of the pressure transducers was used as a transmitter to generate pressure waves in the borehole fluid. The other transducer served as a receiver to detect any pressure waves reaching it in the borehole. The receiver then converted these pressure waves to electrical signals which were transmitted to the surface and displayed on an oscilloscope as a record of time vs receiver-signal amplitude. Fig. lb is a schematic representation of a typical record. The interesting characteristics seen in the earlier' and subsequent experiments were (1)

By J. S. Aronofsky

The first step in a quantitative analysis ot the mechanism of oil displacement by water in a fractured reservoir is usually conceded to be the solution of the differential equation describing the saturation distribution of two immiscible fluids flowing in a porous medium, where the capillary pressure is taken into account. In such a system the production mechanism may consist of displacement of oil both by the flow of water due to natural or artificially imposed pressure gradients and by imbibition, which implies a flow of water not due to external pressure gradients. Owing to the presence of the two oil displacement mechanisms, the mathematical model given by the differential equation intended to describe the system may not properly represent the behavior of the physical system. In fact, in the reservoir the rate of water advance may be very slow, and in the case of a fractured reservoir with a great number of large fractures, the pressure difference determining the flow of water through the matrix may be much less than 1 lb/'psi over lengths of a few feet. In such a case, imbi-bition (the exchange between oil in the matrix and water in the fractures resulting from capillary forces) may become, with time. a significant element of the production mechanism. It occurred Lo the authors, however, that without going into a physical analysis of the process of production, it might be possible by means of simple abstract reasoning to throw some light on the variation of recovery with time under conditions occurring in a highly fractured oil reservoir with rising water table. The object of this paper is to present both the reasoning and its application to a reservoir of the highly fractured type. Specifically, the analysis given here was undertaken to try to explain the increase of recovery (as defined later) with time as observed in this reservoir, without having to assume unlikely variations in the reservoir parameters with depth. This attempt has been successful as will become clear upon comparison of the computed recoveries with the actual field data. ABSTRACT MODEL Let us consider a small volume. of porous matrix saturated with oil at time, t = 0. Let the process of oil displacement by water start at time, t = t,,. At some time, t, the process will have terminated. Then a volume of oil equal to or smaller than the original oil contained in the matrix will have been produced. The first basic assumption that describes the model and guides the forthcoming reasoning is that the oil production from the small volume. dv, is a continuous monotonic function of time and that it converges to a finite limit. Such an assumption is not inconsistent with the results of laboratory waterflood tests as well as with results of imbibition tests where this is, in fact, observed. The second basic assumption is that none of the properties which determine the rate of convergence change sufficiently during the process to affect this rate or the limit. Let it be assumed that the form of the function of time relative to production from the matrix volume. dv, is given by where V,(t) is the volume of oil produced up to that time t. R is the limit toward which the recovery converges, A is a constant giving the rate of convergence, and V,(t) is the volume of oil originally in place in the volume, dv. It should be noted that recovery at time I will be understood here to he It follows that r. tends to R as t tends to infinity. CONSTRUCTION OF RESERVOIR FROM ABSTRACT MODEL Let the reservoir consist of a series of identical blocks of porous matrix stacked vertically and separated by fractures. Let each of these blocks satisfy the conditions of our abstract model. These conditions are: (1) that recovery is a continuous mono-tonic function of time converging to finite limit, and (2) none of the properties that determine the rate of convergence change sufficiently to affect the rate or the limit. Let water be rising in fractures so that oil production from any part of the block starts when the water comes in conLact with it. TOTAL RECOVERY FROM THE RESERVOIR COMPARED TO RECOVERY FROM A SINGLE MODEL ELEMENT As stipulated in Eq. 1, in the case of the abstract model,

By C. Gatlin, C. E. Nemir

A common cure of lost circulation is the introduction of granular bridging agents into the mud system. Many materials, such as ground nut shells, are used for this purpose. If the trouble causing void (fracture, fissure, vug, etc.) is not too large, the granular agent forms a "bridge" across or within the opening. Successively smaller particles in the mud stream then accumulate on and/or within this bridge until normal filtration is finally established. The efficiency of many bridging agents has been studied in the laboratory using various slot testers.',' Many investigators have remarked that a granular bridging material should have the proper particle size distribution. With the exception of the broad range specified in the patent of Goins and Nash,3 here is apparently no definition as to what this distribution should be. A bridge may be initiated when several particles of lost circulation material lodge against each other in a fracture or other void. Smaller particles then may bridge the openings between the larger, previously bridged particles. This process continues until the voids become quite small and the problem becomes one of filtration. It would seem logical that an optimum particle size distribution exists, i.e., one containing the proper quantity of properly sized material to fill the successively smaller voids of the bridge. The filtration characteristics of drilling fluids may be subject to a similar analysis. It has been clearly demonstrated by many workers that the filtration behavior of various muds can be altered by particle size control.'.' Slusser, et al, divided filtration into three periods and showed that particle sizes affecting a given period did not necessarily affect other portions of the filtration curve. An analagous problem is the proper sizing of gravel, liner slots and screen sizes in various sand-exclusion problems. Here the situation is reversed in that a proper "void" size, rather than the size of the bridging agent, is sought. The classic work of Coberly 9 forms the quantitative basis for most sand-exclusion processes. It is interesting to note that, in general, Coberly's work has been overlooked by most drilling-mud researchers. Other investigators have made various studies of the effect of particle size distribution .on drilling-mud properties. As a part of their studies, Fancher and Oliphant reported 30-minute filtration loss of a variety of mixtures of particle sizes.'' Gates and Bowie noted an effect of particle size distribution on filtration, as well as on other physical properties.' MAXIMUM DENSITY THEORY A maximum density mixture has been mentioned as the possible solution for both lost circulation and mud filtration problems. Furnas 12 derived mathematically a method for obtaining maximum density of beds of packed solids, having either a given number of component sizes or a continuous gradation of sizes. This work was verified experimentally by Anderegg.13 or mixtures having a continuous grading of sizes, the interval between sizes is taken as successive screen sizes of interval 2 The ratio of the quantity of each size and the next smaller size is given by the equation Fig. I, number of size intervals of ratio 2 taken from Furnas' paper, gives the value of n + 1 for any given values of + and K, where K is the ratio of the diameter of the smallest particles to the diameter of the largest particles. Measurement by weight assumes, of course, constant density for all particle sizes. Choosing the quantity of the smallest particle size as a unit weight, the required weights of the successively larger interials are then r1 r2 r3 . ®1,2,3. Thus, the grading curve of a maximum density mixture represents a geometric pro gression of ratio r.

By Rossiter W. Raymond

I desire to call the attention of the Institute to an interesting experiment, which may turn out to be an indication of a valuable improvement in the manufacture of steel. As the members are aware, the addition of ordinary spiegeleisen, in the open hearth or Bessemer converter, to a bath of decarbonized iron, has a twofold object,—the recarbonization of the bath to a desired degree, and the remedy of the red shortness otherwise found to be inevitable in the final product. This red shortness is ascribed to the presence of oxide of iron in the molten metal; and it is supposed that the manganese of the spiegeleisen, uniting with the oxygen of such oxide, carries it into the slag. At the same time there is a small percentage of the manganese usually left in the cast steel, probably to the improvement of its quality. Whatever be the true explanation the effect of the manganese is acknowledged to be not only beneficial, but necessary. But the use of spiegeleisen containing high percentages of carbon limits the quantity that can be introduced, because the carbon must be limited if soft steel is desired. This inconvenience becomes so serious as to prevent the use of ordinary spiegeleisen in the manufacture of steel containing more than, say two-tenths per cent. of phosphorus; since the quality of the steel can be made tolerable only by reducing its contents of carbon in proportion as the

By N. H. Harrison, J. K. Rodgers, S. Regier

This paper presents comparisons of data obtained from a laboratory reservoir study and from a calculated behavior prediction with the actual production history of a condensate reservoir. A small non-commercial discovery was depleted under closely controlled conditions and the well fluids were sampled at frequent intervals. Data on the reservoir and production variables were accumulated on a fixed schedule. A laboratory reservoir study war made using the initial well fluid samples as charging stock. The production procedures and operating conditions were held constant throughout the study wherever possible and in general paralleled the field work. The well fluid compositions and the cumulative recoveries ar a function of the reservoir pressure were also calculated using conventional flash vaporization procedures and equilibrium constants. Comparisons based on the composition of the well fluid show good agreement, the laboratory study agreeing within experimental accuracy with the field work and the calculated data comparing equally well. The gas-oil ratios are also in good agreement, but with somewhat greater deviations at the higher pressures. In the overall picture, it is believed that a model st,~tiy can predict within experimental accuracy the production history of a condensate reservoir. Better equilibrium constants for the heavier hydrocarbons are needed in order to attain improved composition accuracy by calculation. INTRODUCTION In Aug., 1955, a gas condensate well was completed in San Juan County, Utah, that was initially thought capable of good commercial production. These conclusions were derived principally from core data and electric logs, which indicated good permeability, porosity and gas content. However, after the usual series of potential tests it was found that the reservoir pressure had declined some 22 per cent, and it was obvious that the zone tapped was but a small pocket or trap. It became apparent that, with a controlled depletion of a small reservoir, a unique opportunity was available to compare laboratory and calculated studies with an actual field depletion and to further the present knowledge of condensate reservoirs. FIELD WORK The Coalbed Canyon Well No. 1 was conventionally completed in the Paradox limestone formation to a total depth of 5,912 ft. The producing zone from 5,762 to 5,806 ft was perforated with four jet shots per ft. The wellhead and field equipment were also conventional, the major items consisting of a two-pass indirect fired line heater, a high- and a low-pressure separator with the necessary controls and accessories, gas meters, back-pressure regulators, flare stacks and condensate stock tanks. The initial testing of this well con-sisted of a series of flow potential and pressure build-up tests during which some 30 MMcf of gas was produced. The reservoir pressure declined from an estimated 2,300 to 1,782 psig during this period, from which it was concluded that the reservoir was very small. In order to approach steady-state conditions in the reservoir and so provide optimum conditions for making comparisons, the field depletion was programmed to approach, if possible, constant production conditions. Bi-hourly readings were taken of the tubing pressure, the pressure and temperature of the separators, oil and gas rates, and other pertinent operating data. The gas rate, as indicated by the orifice meter, was held constant by the adjustment of the choke in the line heater. The temperature of the first stage separator was held constant by adjustment of the line heater jacket temperature. Practical considerations of production made the maintenance oi a constant gas rate impossible. The test started with a gas rate of 4 MMcf/D and a separator pressure of 250 psig. This rate was maintained until the choke was fully opened. The gas rate then declined with the falling tubing pressure and production was continued until the rate was about 2