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By G. R. St. Pierre, A. J. Wilhelem

In connection with the reduction of hematite or magnetite to metallic iron, it appeared desirable to study the rate of reduction of each oxide to the next lower oxide under conditions which excluded all other condensed phases. For this purpose, pellets of Fe,O,, Fe,O,, and oFeOo were prepared. A gas train for the preparation of Ar-Hz-H20 mixtures was employed to establish a continuous flow of a controlled atmosphere over a pellet suspended on a balance. In this manner the following individual reduction steps could be studied: For example, pellets of hematite were reduced solely to magnetite by adjusting the gas atmosphere such that it was oxidizing to wustite. In other words, the reaction was complete when the hematite pellet had been totally converted to magnetite. The pellets were prepared from Baker Chemical ferric oxide. The ferric oxide powder was moistened and handrolled. Air sintering at 950°C produced Fe,0, pellets with a density of 3.65 g per cm3. The pellets ranged in size from 0.6 to 1.2 cm diam. The magnetite and

Jan 1, 1962

By E. P. Abrahamson II

The effect of transition elements which form binary solid solution upon the recrystallization temperature of zirconium has been investigated. All additions raised the recrystallization temperature. A correlation is obtained between the logarithm of the rate of change of recrystallization temperature with atomic percent solute and the free atom ground state electron configuration of the solute element. ThE work of Abrahamson, et al., on dilute binary solid-solution alloys indicated a correlation between the free-atom ground state electron configuration of the solute and either the brittle-ductile transition or recrystallization temperature. These studies were carried out on bcc base materials. The implication is that the outer s and d electrons of the solute are the prime determinant of the absolute rate of change of recrystallization or transition temperature. Furthermore, the limit of linearity has been shown to be a function of solute electron configuration for recrystallization in iron and vanadium. To date no Complete systematic recrystallization study of dilute binary zirconium base alloys has been made. It is the purpose of this study to note whether the change in solvent structure from bcc to hcp will influence the correlation. It was also desired to learn more of the role of the electron configuration of the solvent on recrystallization temperature. PROCEDURE All alloys were made using 99.87 pct Zr with 0.01 Cr, 0.04 Fe, 0.006 Hf, 0.003 Mg, 0.003 Mn, 0.003 N, and 0.080 0 (132 BHN). The solute elements were 99.9 pct pure. According to the published binary phase diagrams6 and metallographic examinations at X750, all alloys used were solid solutions. The alloys were arc melted and remelted six times in the form of cubic 200-g buttons under an argon atmosphere. They were then hot pressed at 950°C to 0.450 in., upset pressed to 0.350 in., and annealed at 800°C for 1 hr. The specimens were then Blanchard ground to 0.250 in., removing 0.050 in. from each side. The grain size of the material at this stage was found to be 8000 100 grains per sq mm. The specimens were then cold rolled to 0.130 in. and cold pressed to 0.125 in., yielding 50 1 pct cold work. All alloys were then chemically analyzed for the principal addition. The interstitial contents remained at the values of the starting material when checked on random alloy specimens. The rolled sheet was cut into 6.75 by 0.25-in. lengths and heat treated in a gradient furnace for 1 hr. The gradient was 250o to 900°C over the 6-in. length, recorded continuously by six thermocouples resting on each specimen. Control was 3oC, accomplished at the hot end. The recrystallization temperature was determined metallographically using polarized light. The criterion chosen was the point on the specimen showing the first recrystallized grain at a constant magnification, X200. Specimens were repeated, and the agreement was found to be 3°C. RESULTS Three different pure zirconium specimens were tested, and the recrystallization temperature was

Jan 1, 1962

By Waldemar Lindgren

THE following pages present data accepted by many geochemists and geologists regarding the succession of minerals and the temperatures of formation in ore deposits affiliated with igneous rocks. They also present the individual views of the author on the composition of the solutions that were active and on the mode of deposition. He does not regard these views as speculations or hypotheses but as forming a well motivated and consistent theory. It is not certain, however, that all investigators will subscribe to them.

Jan 1, 1936

By P. B. Baxendell

The appraial of producing properties and profitability ntzalysis of a proposed capital expenditure are based on the same principles. In both problems a projection of future cash income is. cornpared to one or more capital expenditures. Several different methods have been in use either to compute a price to obtain a given earning power on the investment or to compute the earning power which will result from a given capital expenditure. One of these, the "Average Annual Rate of Return" method, computes in a simple manner the ratio of the present value of the future earnings after amortization to the present value of the undepreciated balances of the investment over the life of a project. This method, not well known generally, appears to have some rather unique advantages in reducing the computation work required, eliminating trial-and-error solutions, and providing a more accurate answer when applied to oil industry investments subject to the unit-of-production basis of amortization. Its derivation is given and its versatility demonstrated in the solution of certain everyday investment problems. A number of charts, useful in applying this method to profitability analysis and appraisal work, are provided. The current trend in the market values of producing properties is shown. INTRODUCTION Making sound capital expenditure decisions requires an objective means of measuring the productivity of individual investment proposals. Since the best measure of the economic worth of such proposals is their ability to produce profits, it is common practice to grade proposed capital expenditures according to their annual earning power as a percentage of the outstanding capital. The same principles which govern the determination of the rate of return of proposed capital expenditures also apply generally to the problem of determining the appraisal value or purchase price of income-producing oil and gas properties. Both problems are of prime importance in the producing phase of the oil business, where management is faced daily with decisions to drill or not to drill certain development wells, or with the determination of the appraisal value of producing properties. The common feature in both problems is that a projection of future cash income is compared with a known or estimated capital investment to determine itsiearning power or annual rate of return. In the case of development drilling, the cost of the proposed well can usually be estimated with a fair degree of accuracy and the problem consists of finding the rate of return on the invested capital. In the case of appraising producing properties, on the other hand, the desired rate of return is usually known in advance and the problem consists of determining the purchase price which, for the given income projection, results in the fequired rate of return. Certain accounting procedures common to the oil and gas producing business make these two problems and their solutions somewhat different from corresponding problems in other industries, and, in certain ways, simpler. The main difference is in the amortization policy which, for oil and gas production, is frequently on a unit-of-production basis, compared to the amortization on a time basis used in many other industries. The purpose of this paper is to discuss briefly the various methods currently in use for the measurement of productivity of invested capital in producing properties and, in more detail, the derivation and application of what will be called the "Average Annual Rate of Return Method". This rather interesting and not too well known method has some very definite advantages in the solution of many problems common to the oil industry. For the sake of simplicity, federal income tax considerations have been disregarded in the examples used, since they do not affect the principles involved. The use of the production payment route in the sale or purchase of producing properties, which has been amply covered in many other publications, has also not been included in this analysis. METHODS FOK MEASUKING THE EARNING POWER OF INVESTED CAPITAL, Of the many different methods used to measure the earning power of invested capital, four are applicable to oil or gas production ventures. Depending on whether these four methods utilize one or two interest rates, and whether a fixed amortization pattern is used, they may be classified as follows.

Strain-Hardening Exponent of Cross-Rolled Beryllium Sheet by S. R. Maloff, Vol. 215, No. 5, page 872, was omitted from Table of Contents for the October issue. Stabilization Phenomena in Beta Phase Au-Cd Alloys by Howard Birnbaum, Vol. 215, No. 5, page 786. The figure denoted Fig. 1 should be Fig. 3, Fig. 3 should be Fig. 4 and Fig. 4 should be Fig. 1. The captions are in the proper sequence. Activity of Carbon in Liquid Iron Alloys by Tasuku Fuwa and John Chipman, Vol. 215, No. 4, page 708. First equation, right hand column, page 710 should read

Jan 1, 1960

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

ONE DAY IN the mid-1880s, in a suburb 0f Pittsburgh, Pennsylvania, there dismounted from a train the two foremost leaders of the day in the coal and steel industries-Andrew Carnegie and H. C. Frick. Their attention was drawn to a well-loaded car of coke, which their experienced eyes recognized as a superior product. "I'll bet you that coke is from the H. C. Frick Coke Company," Mr. Frick challenged. "I'll bet it was shipped by my company." In a spirit of fun Mr. Carnegie accepted the wager. Mr. Frick lost the bet: the coke had come from M0rewood, one of three sites being operated under the direction of a young entrepreneur, Erskine Ramsay. If Mr. Frick's confidence was somewhat dented by this occurrence, the responsibility was his own. He himself had opened the way for Erskine Ramsay to become the youngest of mine superintendents; and he had dispersed all dissension regarding his choice with the words : "I'm not interested in his years, I'm interested in his record. He makes more coke in an oven than any other superintendent. And I'll take 'em out 0f the cradle if they can make coke... Suppose he is only twenty years old? ... The d --- kid is a genius, I tell you." Erskine Ramsay was to follow in the tradition of Carnegie and Frick. Not only was he ambitious and a worker his background had prepared him for it. Coal mining was in the Ramsay blood. His father, Robert Ramsay, of whom the son once stated that he had no superior as coal mining and mechanical engineer in this country, once accounted in these words for the phenomenal accomplishments which had attached to the name "It does no harm to belong to a family of mining engineers who are just as good as any in America-if it is myself that says it." Anyone acquainted with Robert Ramsay's character realized that he was not given to overstatement. And the above-mentioned Mr. Carnegie encountered young Ramsay again, a few years later in his career, and wrote of him to young Erskine's father, that he was "going to be a credit `tae us a' " (a quotation from Robert Burns.) Nor have Mr. Ramsay's achievements been identified exclusively with the industrial field in which he early asserted himself. He has been an inventor whose techniques in mining engineering have received international recognition. As an investor of foresight, he has benefitted others immeasurably, as well as himself, being an influential factor in the upbuilding of several communities in his chosen and well-loved adopted home state of Alabama since 1887. He is a philanthropist whose benefactions have run into millions, the chief beneficiaries being educational and charitable institutions. Amidst his accomplishments the lighter side of life has not been neglected and he is known for his hospitality, his

Jan 1, 1953

By Ivan B. Cutler, Milton E. Wadsworth

Coprecipitation of anionic and cationic polyelectrolytes has been applied to floccula-tion of several mineral systems. Results obtained in a study of the flocculation of kaolinite and hematite suspensions of polycationic and polyanionic electrolytes are presented. Greatly increased settling rates were observed following precipitation of positive and negative polyelectrolytes on the surface of finely divided minerals in aqueous suspension. The ratios of polycationic to polyanionic electrolytes required to produce maximum sedimentation have been shown to correspond closely with the equivalence points obtained by light scattering studies of systems containing the positive and negative polyelectrolytes by themselves. DISPERSION of colloids has been of interest to surface chemists for many years. Flocculation studies have been employed to evaluate the limits of colloid stability. In water suspensions, colloids become unstable and flocculate when the 5 potential, the potential of the kinetic solvation sheath, falls to a value at which van der Waals forces may act to draw the particles together. This may happen through an adjustment of the pH of the suspension or by addition of a salt. Optimum conditions for rapid formation of large flocs are found in the region of minimum < potential. In addition to these well known considerations, colloids in water suspensions are known to be flocculated by certain large organic macromolecules. These polyelectrolytes in some cases minimize the 5 potential and in other instances increase the attractive forces by supplying sites for hydrogen bonding.&apos; Use of organic polyelectrolytes in flocculation of mineral colloids has increased rapidly in recent years. These materials are now recognized as indispensable aids to fluid-solid separations in many extractive metallurgical operations. They have been found to increase both the settling rate in thickeners and the filtration rate of filters. In the elucidation of the characteristics of these organic reagents as floc-culants in this laboratory, it was discovered that interaction of certain polyelectrolytes had a surprisingly good effect on flocculation of mineral colloids. Experimental Procedure: The anionic flocculants used in this study were Lytron 886 and 887, produced by Monsanto Chemical Co. Both reagents are copolymers of vinyl acetate and maleic anhydride. Lime is added to Lytron 886, whereas Lytron 887 is all organic. These reagents possess two carboxyl groups for each acetate group and are therefore anionic in character. The cationic reagents used were the Peter Cooper Co. 1-X and 2-X glues. The structures are not definitely known, but the re- agents are amines and are cationic in character. The glues were prepared in the chrome-alum form. Both types of reagents may be classified as polyelectrolytes in that they are high molecular weight polymers and ionize in water. All data presented are in terms of sedimentation rate, measured in 250-ml glass-stoppered graduated cylinders. With suitable precautions such measurements are fairly reproducible and provide a sensitive means for selecting important parameters such as PH, reagent concentration, and floc size and density. Agitation was standardized with five complete end over end cycles of the suspensions in the stoppered graduated cylinders.

Jan 1, 1957

By G. Thodos, W. F. Stevens

The point-source function introduced by Horner&apos; us a solution to the general unsteady-state equation for the flow of fluids through porous media has been utilized to calculate pressure profiles for adjacent wells as a function of time. By trial and error, the time at which the pressure waves meet to cause interference can then be calculated. For this calculation, the time of interference is arbitrarily defined as that time when both pressure waves exhibit a pressure decrease of 25 psi ar the same point within the formation. To illustrate the method, an example involving two adjacent wells producing at different rates has been worked out and is presented in detail. INTRODUCTION The initiation of production of a new well is usually accompanied by pressure drawdown measurements in order to establish the extent and characteristics of the formation. The interpretation of such pressure drawdown data is based on mathematical developments involving a single well in an infinite reservoir. If more than one well is present in a reservoir, the possibility of interaction between wells exists. Therefore, care must be taken in interpreting the pressure drawdown data. It becomes important to be able to determine when this interaction, or interference, becomes significant. This paper presents a method for the prediction of the approximate time of interference between two such adjacent wells. The basic differential equation describing the pressure distribution existing during unsteady-state flow of a slightly compressible fluid has been solved by Hor-ner.&apos; for a constant production rate from a circular homogeneous reservoir of infinite extent. The solution utilizes the point-source function to define the pressure at various points within the formation as a function of time. The resulting expression is: q = production rate, STB/D ,;= formation volume factor, dimension-less µ = fluid viscosity, cp k = formation permeability. md H = formation thickness, ft C - fluid compressibility, psi&apos; F = formation porosity, dimensionless R = distance from centerline of well, ft T = production time, hours Ei(—u) = Ei-function of U Eq. 1 may be used to calculate the pressure profiles generated during production from a single well in an infinite reservoir.

By C. H. Mathewson

CONSIDERABLE progress has been made during the last few years in analyzing the action of plastic deformation in metallic crystals. This is due largely to the development of X-ray spectrographic methods for studying changes in the orientation of single crystals, or of conglomerates, as they occur during the process of plastic deformation, but partly to the widespread knowledge of suitable technique for preparing large (single or variously combined) crystals for direct crystallographic observation under stress or in various conditions of strain. These two methods of studying changes in the crystalline structure of metals may of course be used in conjunction with features of mutual support, but unfortunately the advantage of direct crystallographic observation is lost when we proceed to the study of severely cold-worked structures, owing to the occurrence of real or apparent crystalline discontinuities which become more and more complicated as the amount of plastic action increases. Furthermore, the X-ray methods do not appear to be adequate, at least in their present stage of development, to fix definitely the character of structural alteration in the parent crystal lattice by plastic deformation. The principal question at issue concerns the nature of the crystalline particles that remain after plastic deformation. These are generally known in our American metallurgical literature as crystalline fragments,&apos; and they seem, indeed, to diffract as individuals causing the Hull pattern of a severely cold-worked metal to resemble the pattern of a fine powder,2 with certain features of preferred orientation among the particles deter- mined by the manner and intensity of cold working. We must freely concede that there are conceptions of lattice alteration, apart from that of simple fragmentation, which would account for an increasing number of lattice positions according to X-ray spectrographic observation as the degree of deformation increased.

Jan 1, 1927

By . M. Muskat

A THEORETICAL consideration of the mechanics of various water-flooding systems with the viewpoint of comparing their relative merits involves the study of two fundamental properties of such systems. On the one hand, it is important to determine the efficiency of the flood as measured by the percentage of the total area that is swept out by the encroaching water before water actually reaches the output wells. This is really a measure of the regional tendency of the water to "bypass" the oil. On the other hand, the various systems must be compared from the viewpoint of their resistances which determine the rate of fluid production obtainable for given pressures maintained at the water input wells. The first of these questions has been studied and very definite answers have been obtained by means of simple electrolytic models.1 These models showed that, in an ideal system, the percentages of the areas flooded out before water reaches the output wells are about 57 per cent for the direct line-drive flood (the input and output wells being equally spaced and placed in alternate parallel lines), 74 per cent for the regular five-spot network, and 79 per cent for the seven-spot network. With respect to the efficiency of the usual flooding arrangements, they are, therefore, given quite accurately by the above numbers. With regard to the resistances of the flooding networks, electrical conduction models have also been used successfully2 and are well adapted to the problem of determining experimentally the pressure distribution and streamlines, or over-all resistances of specific flooding networks. However, such models do not permit readily a study of the effect of changing dimensions or configuration within a network, since a new model must be made up for each set of dimensions considered.

Jan 1, 1933

By W. C. Phalen

The production of salt in the United States divides itself at the outset into two distinct classes…

Jan 1, 1915

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By James M. Link

Slurry transport of industrial minerals has proven to be practical, economical, and efficient. Industrial minerals currently being pumped for long distances include cement, clay, phosphate, sand, and various waste product from industrial mineral processing operations. This paper will touch upon the basic theory of hydraulic transport of solids and then consider the economic and engineering considerations upon which construction and operation of such a line would be based. Where possible, actual cost data will be presented.

Jan 1, 1974

By J. M. Weehuizen

Complete details are given of the drilling method by which two shafts were sunk at the new Beatm&apos;x mine of Staatsmijnen in the Netherlands. The nature of the rock strata in the Dutch mining district determined choice of the drilling rather than the freezing method. Data for each step and details of the equipment used are given in the illustrations. Staatsmijnen was founded in 1902 with government financial backing, but it is run as a private enterprise, on a commercial basis, with the normal fiscal obligations. The company now has four mines in operation with annual outputs amounting to 7 1/2 million tons of coal. In 1952 it was determined that a new mine—the Beatrix—would be opened. Details of the shaft-sinking operation are described in this paper. SHAFT LOCATION The coal-bearing carboniferous rock in the Dutch mining district is overlain almost completely by soft water-bearing strata, which at the site of the new shafts are about 1600 ft thick. The sinking of the new shafts through this soft water-bearing overburden (Fig. 1) is a costly and time-consuming affair. From the two availaible sinking methods: 1) Poetsch&apos;s well known freezing method or 2) the drilling method of Honigmann-de Vooys, the latter was preferred, not only because of its relative cheapness, under the prevailing conditions, but primarily because by using the drilling process, a special type of shaft lining of steel, concrete, and bitumen could be used. The new shafts, located 330 ft apart, have an inner diameter of 18 ft, 4 1/2 in. The boreholes, which have a diameter of 25 ft and which were drilled through nearly 1600 ft of overburden and some 100 ft of carboniferous, each contain more than 29,000 cu yd—by far the largest in the world. DRILLING METHOD The drilling method is based on the use of mud-flush—a thin mixture of clay and water—to keep the borehole filled during the entire drilling period and during insertion of the lining (Fig. 2). The pressure of the mudflush against the borehole wall is greater than that of the water in the surrounding

Jan 1, 1961

Jan 1, 1970

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush&apos;s work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7&apos; ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01&apos; calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i&apos;rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.&apos; Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers&apos; knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

Jan 1, 1963