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By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By H. J. Beach

This paper describes the properties and uses of cementitious mixtures containing 10 to 20 per cent bentonite and 2 per cent or more sodium chloride. Salt additions improve bentonite cement by increasing early strength and stabilizing viscosity without changing thickening time. The volume yield of cement is increased 20 per cent or more without lowered early strength. The unique properties of salt in this type of system make savings of more than 10 per cent possible where light-weight, low-strength cementitious material is adequate to fill behind pipe. The density range of these mixtures is 12 to 13 1b/gal and the filtration rates are medium-low, aiding the placement of long columns in primary cementing. Where available, sea water is an ideal salt source in preparing these slurries. INTRODUCTION Accelerators increase the rate of cement hydration. In speeding reaction with water, they can affect cement performance by reducing thickening time and increasing early strength after set. Accelerators that cause both effects can be considered "total", and those which produce only one effect can be called "partial". Materials that act conversely to accelerators are retarders. and they also can be total or partial. Partial retarders. make high-temperature cementing possible by prolonging thickening time while impairing early strength only slightly. Most known accelerators are total. A useful partial accelerator would increase strength without altering thickening time. This report concerns material combinations in which a normally total accelerator exerts unique partial properties. Utilizing these limited effects improves bentonite cement. SEPARATE EFFECTS OF SODIUM CHLORIDE AND BENTONITE ON CEMENT Sodium chloride and calcium chloride are commonly used in cement, and at low concentrations their effects are similar. Ludwig1 studied sodium chloride in API Class A and Class E cements.' Figs. 1 and 2 sum- marize his data taken at 140°F on slurry pumpability and early strength. Normal water-to-cement ratios are 0.46 and 0.40, respectively, for Class A and Class E cements. At saturation the salt content is 12 to 14 per cent of the weight of cement solids. The illustrations, therefore, cover the range of salt solubility in the mixing water. The data show that sodium chloride is a total accelerator of the Class E cement studied over the range of solubility. It is total in Class A cement to 6 per cent. Above this concentration salt becomes a retarder— partial from 6 to 10 per cent and total above. These results are general for different brands of Class A cement, although the shift from acceleration to retardation may occur at different salt concentrations for different temperatures. The results are specific for the Class E brand studied. In discussing his data, the investigator emphasized that different Class E cements might respond erratically to salt, depending on the brand chosen. Morgan and Dumbauld3 escribe the properties of bentonite cement in a paper that is a standard reference in using these systems. Bentonite functions in cement as an enabling agent; each bentonite addition equal to 1 per cent of the weight of dry cement makes possible the further addition of 4.5 per cent water.' Thus, 10 per cent bentonite in Class A cement, normally slurried neat with 46 per cent water, enables the slurry to contain another 45 per cent before settling. Water is one of the lightest and cheapest cement extenders; it reduces density and cost. Bentonite cements produce uniform slurries having low susceptibility to solids separation. After set, they offer low resistance to perforation.

By A. G. Metcalfe

Observations at temperature are used to investigate the phase changes in alloys containing more than 50 pct Co and above 1000°C. The nonsuppressible transformations in cobalt above 1120°C and in the intermetallic compound Co2Cr3 are studied. The liquidus and solidus surfaces are determined. Insufficient data is obtained to complete the constitution diagram. A REVIEW of some of the earlier work on cobalt' and on the binary systems with chromium2-4 and with molybdenum,5 showed that one likely source of differences might be attributed to the presence of phases at high temperatures which could not be retained by quenching. Consequently, the decision was made that only methods of examination at temperature should be used in this work. The correctness of this decision was confirmed during the course of the work by the investigation of the martensitic nature of the transformation in cobalt- and by the decomposition of the high temperature form of the phase Co2Cr3 on quenching.' The use of high temperature methods, including dilatometry and thermal etching led to the postula-tion of the existence of a high temperature form of cobalt with a probable hexagonal close-packed structure, transforming from cubic cobalt over a range of temperature from 1119° to 1145°C.8 One of the important pieces of evidence for this transformation was that it was observed in alloys with chromium and molybdenum which were nonmagnetic at this temperature so that confusion with magnetostriction effects was impossible. These results were not reported in this earlier paper, so that the data given here supply further evidence for the existence of a second allotropic transformation in cobalt. High temperature observations are necessarily much slower in producing results than the examination of quenched specimens at room temperature by conventional means such as X-ray diffraction or microexamination. The investigation has only covered a limited part of the field, as a result, extending from the liquidus down to about 1050°C and from the cobalt corner up to 50 pct alloying elements. The differences between the various reported diagrams for the constitution of the Co-Mo and Co-Cr systems have already been mentioned. The best available diagram in the first system is due to Sykes and Graff' which is shown in Fig. 1. Fig. 2 shows the latest Co-Cr diagram due to Elsea, Westerman, and Manning.' A comparison reveals that these are incompatible because of the disagreement with regard to the number of allotropes of cobalt. Elsea, Westerman and Manning took their liquidus and solidus curves from Wever and Haschimoto.2 The temperature horizontal in the two-phase field beneath the eutectic was placed 35" to 39°C higher than in earlier work2,4 with a new interpretation of the nature of this transformation. This interpretation also required a peritectic horizontal at about 1470°C, which has been confirmed here for an alloy with 53 pct Cr. No investigation had been made of the ternary system until after this work had been terminated, when a section at 1200°C was published." In this work a ternary compound was found by the X-ray diffraction examination of quenched alloys. This compound contained less than 50 pct Co, and was thus outside the field investigated here. However, some reactions were found dilatometrically which could not be fitted on the diagram and are now believed

Jan 1, 1954

By T. R. Ingraham

When aluminum sulfate was decomposed in an evacuated apparatus and the sample cooled, Q alumina was found. The thermodynamics of the decomposition reaction were resolved by measurements of the total pressure of SO3, SO2, and O2 generated over the sample at various temperatures. The results were correlated with other published data to calculate the rmges of thermodynamic stability of the various compounds involved. The thermal decomposition of aluminum sulfate was studied by Wijhler, Pluddeman, and Wöhler1 and by Warner and Ingraham.2 The results of both studies were critically reviewed by Kellogg,3 who observed that "each set of data shows considerable scatter and strong curvature on a plot of log pso3 vs 1/T".3 He agreed with Warner and Ingraham2 that both the discrepancy in the two sets of results and their curvature may arise from the indefinite properties of the particular form of A12O3 which is formed during the decomposition. While studying the thermal stability of other sulfate systems, we had noted the presence of nonequilibrium oxide properties in both the cobalt4 and manganese5 systems, but neither had shown any appreciable curvature on a logPSO, vs 1/T relationship, and the data from both systems agreed reasonably well with prior work. It therefore seemed reasonable to reexamine the technique which had been used in our earlier work on aluminum sulfate.2 The principal difference was that a tightly compacted pellet had been used for the earlier aluminum sulfate work, whereas a loose powder, contained in a platinum boat, was used for our work on other sulfate systems. In addition, a better technique had been developed for dehydrating the samples. From work done on the nickel system,6 we had become aware of the highly protective nature of some sulfate layers on their oxjdes, and hence of the necessity of providing a large surface area of P3e sample when equilibrium was to be attained in a reasonable time. That observation suggested that perhaps a steady state, rather than equilibrium, had been reached in the earlier work on aluminum sulfate. This paper reports a repetition of the experimental work with large, finely divided samples of anhydrous aluminum sulfate. APPARATUS AND PROCEDURE The apparatus used in the experimental work was described in earlier papers.2,7 The source material was Anachemia reagent-grade Al2(sO4)3 - 18H2O which was first partly dehydrated by heating at 400°C for 48 hr and then completely dehydrated by repeated baking of an aluminum sulfate-oleum slush to dryness at 450°C. ? Alas was prepared by decomposing some of the sulfate in a muffle furnace at 800° C overnight. Approximately equal amounts of the 7) alumina and aluminum sulfate were used in the experiments. The finely divided samples were handled under dry box conditions, and in addition some of the aluminum sulfate was decomposed in the apparatus while it was under vacuum, to ensure its complete dehydration prior to sealing the apparatus. The samples were heated to a series of constant temperatures on both increasing- and decreasing-tem-perature programs. Two to three days were required to obtain steady readings of the total decomposition pressure on an increasing-temperature program, and 5 to 6 days on a decreasing-temperature program. Three samples were examined on both programs. Within experimental error, the results for each sample and each program could not be distinguished.

Jan 1, 1969

By G. H. Tausch, T. A. Huber

Very encouraging progress has been made ill the develop-ment of the permanent-type well completion which decreases considerable the cost of completions and workovers and aid-in the acquisition of reliable reservoir information at low cost. Completion and remedial operations are performed with tool,; which pass through the well tubing. Perforating and plug-hack operations can be done with the tubing in place and do not require pipe-handling equipment. Because of the many advantages afforded by this method, development work is going forward in anticipation of ultimately being able 10 use it to perform all usual well completion and workover operations. Effort is also being directed to the development of a more permanent type of lift equipment suitable for use with the permanent-type well completion. INTRODUCTION The permanent-type well completion in one in which the tubing and well-head are set in place only once in the life of the well and the completion or remedial work is performed through the tubing with a tubing-type perforator. a retrievable tubing extension. and other wire-line tools. This new type completion has made possible the saving of one to two days' rig time in the completion of each of several hundred wells During the last two years, and use of equipment developed for this type of completion has resulted in a 75 per cent reduction in cost. of certain types of workovers. In addition. the more reliable indication of the commercial value of a reservoir and the more accurate general reservoir information made Possible promise to be of even greater value in oil recovery than the reduction of costs for completions and workovers Recently. several well.. were worked over by using the retrievable tubing extension suspended on a swab line to plug back with cement and then perforating a higher producing interval with the tubing-type perforator, thus opening the way for complete through-the-tubing workovers which may be performed without pipe-handling equipment or mud. Those items attendant to the use of pipe-handling equipment and mud. such as hoard matting rig substructure. and pits. were also eliminated. There are indications that the elimination of drilling mud during completion and workover operations will frequently give increased well productivity, as plugging of the perforation. will not occur. It ii now possible to perforate selectively small sections of the producing interval and to test a well through these sections prior to perforating more interval. The perforating of additional interval will not entail the costly operations of killing the well and pulling tubing, nor will the old or the new perforations be plugged. The productivity of .mall sections of a reservoir and the actual gas-oil or oil-water contacts may now be determined economically under flowing condition.. Selective completions can be made in this manner to delay gas and water problems and bring about maximum oil recovery. At the present time, gas lift appears to offer the greatest potentialities for artificial lift in the permanent-type well com"letion since it can provide full-open tubing to accommodate the through-the-tubing tools and it may be ultimately developed into a fairly permanent type of lift. With precent-day pas-lift equipment. valve or mandrel failure necessitates occacio11al removal of the tubing. thereby reducing to some extent the permanence of the completion. New gas-lift valves are now

Jan 1, 1953

By P. E. Baker

The commercial neutron-gamma log measures the intensity of gamma-rays produced by the interaction of neutrons with nuclei in the formation and in the bore hole. This measurement gives information concerning the distribution of neutrons around the neutron source, and in particular gives information on porosity or fluid content. Another type of information is contained in the frequency or energy spectrum of the neutron capture gamma-rays. The capture gamma-rays of each element, in fact of each isotope, have only those energies characteristic of that isotope.'" The neutron capture gamma-ray spectrum, if obtainable, would permit the identification of the elements producing the spectrum. Such information would have considerable value in oilfield exploration work if it could be applied practically in well logging. Experiments have been carried out at the La Habra Laboratory of California Research Cop. to determine the feasibility of a method of well logging in which neutron capture gamma-ray spectra are measured down hole. In these experiments, spectra were obtained for artificial formations under simulated borehole conditions, using actual borehole geometry. This paper will describe the experimental apparatus and methods and will present the spectrum curves for several formations. THEORY Basic Formulas The neutron capture cross section of an element is a measure of its tendency to capture neutrons. The macroscopic cross section, or cross section per cubic centimeter, of a material composed of several elements is the sum of the cross sections of the nuclei making up 1 cc of the material. This is expressed in the equation SB = Sn1s2, ..........(1) where SB is the macroscopic cross section, s, is the cross section of a nucleus of type i, and ni is the number of nuclei of type i/cu cm. If N is the number of neutrons absorbed per second by the composite material, then the number captured by element j is Ni = N nisi/SB = N nisi/Si ni si ......(2) When the nucleus captures a neutron, a new nucleus is formed, which is usually in an excited state and falls to its ground or unexcited state by emitting one or more gamma-ray quanta.* The emission spectrum has been measured for many elements (see Table 1). The intensity of gamma-rays produced by an element is proportional to the number of neutrons captured per unit time by the element, which in turn depends on the capture cross section of that element and the capture cross sections of the other elements present which are competing with the first element for thermal neutrons. In a small sample of material the number of neutrons, N, captured per second is N = ?SB, ..........(3) where $ is the thermal neutron flux and SB is the macro-scopic cross section defined above. The number of neutrons captured by element j is N1 = ?ni si = N ni si/SB . ......(4) The number of gamma-ray quanta of energy, E, pro-duced per unit time by element, j, is I(E)=Nni si/SB P(E) .......(5) where P(E) is the emission probability of element, j, for this gamma-ray energy. Borehole Effects The capture gamma-ray spectra of many elements have been measured accurately in academic and government laboratories. These measurements are made on small samples, and from these measurements the emission spectra of the elements are obtained.

Jan 1, 1958

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

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

By Thomas S. West

A gravel pack completion is described which, in addition to sand screening, permits the exclusion of water and gas from the oil production. A gravel pack composed of alternate layers of different particle sizes is employed which has horizontal but not overall vertical permeability to drilling mud. A packer is run on the tubing and set in the screen member, around which the gravel layers are placed. The hydrostatic pressure of a mud column prevents the entry of fluid above (or below) the level of the packer. The producing level may be changed by raising or lowering the tubing. Vertical coning is controlled by replacing the mud column with oil and continually injecting oil into the sand section above (or below) the packer. Three well histories with this completion are described in detail. Statistics on the first 100 completions of this general type are given. INTRODUCTION Gravel pack type completions have heretofore been almost exclusively for the purpose of preventing sand production. This paper describes and presents well data on a gravel pack procedure which is primarily a selective completion method. Although complete sand screening is achieved, the exclusion of gas and water is the primary objective. The application of this procedure is therefore not limited to unconsolidated sands. Application to hard sand or limestone reservoirs is equally feasible. GRAVEL PACK PROCEDURE Figs. 1 and 2 illustrate the gravel pack procedure employed. The gravel is placed by means of the frangible disc type dump bailer shown by Fig. 1.' This bailer has its lower end closed by a plate glass or steel rimmed cement disc. This disc breaks when the bailer passes over the liner allowing the gravel to be deposited around the liner. The liner employed is usually 2 3/8 in. to 2 7/8 in. OD and 1.995 in. or 2.07 in. ID (ID of 2-in. tubing or 2-in. line pipe). Two tvDes,. of slotted sections have been employed. One type employs horizontal hacksaw cut or milled slots of about 1/32 in. width opposite the producing section. The other type employs the same type,. of horizontal slot. but slots are placed in groups of six at intervals of about 8 in. A cage composed of half round vertical bars, spaced apart, is then welded to the pipe over the slotted sections. This liner has the bottom end closed, usually by bull plugging. The upper end is closed, while placing the gravel, by a cap which is held in place by means of a shear pin. This cap has a mandrel attached to it which extends downward inside of the liner to within a few inches of its lower end. The top of the liner cap is formed to fit a releasing type wire line core barrel overshot. The liner is lowered to bottom on the wire line by means of this overshot and released. The length of the liner is usually suffi- cient to extend to about 20 ft above the highest level to which gravel is to be placed, the upper end of the liner always being in the casing. The dimensions of the liner and bailer are such with respect to the casing size that the bailer will always pass over the liner. After releasing the liner the bailer is run to bottom. Passage of the empty

Jan 1, 1951

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By J. R. Kyte, C. C. Mattax

Previous workers have developed differential equations to describe oil displacement by water imbibition, but have not explicitly defined the relationship between recovery behavior for a single reservoir matrix block and its size. In the present work, imbibition theory is extended to show that the time required to recover a given fraction of the oil from a matrix block is proportional to the square of the distance between fractures. Using this relationship, recovery behavior for a large reservoir matrix block is predicted from an imbibition test on a small reservoir core sample. The prediction is then extended to analyze recovery behavior for fractured- matrix, water- drive reservoirs in which imbibition is the dominant oil-producing mechanism. Experimental data are presented to support the basic imbibition theory relating matrix block size, fluid viscosity level and permeability to recovery behavior. INTRODUCTION Imbibition has long been recognized as an important factor in recovering oil from water-wet, fractured-matrix reservoirs subjected to water flood or water drive. l-3 Recently, two approaches have been published which might be used to predict imbibition oil-recovery behavior for reservoir-sized matrix blocks. Graham and Richardson4 used a synthetic model to scale a single element of a fractured-matrix reservoir. lair,' on the other hand, used numerical techniques to solve the differential equations describing imbibition in linear and radial systems. This latter method requires auxiliary experimental data in the form of capillary pressure and relative permeability functions. These two approaches, i.e., synthetic models and numerical techniques, have been used to study a variety of reservoir fluid-flow problems. One pur- pose of this work is to present, with experimental verification, a third method for predicting imbibition oil recovery for large reservoir matrix blocks. This method uses scaled imbibition tests on small reservoir core samples to predict field performance. The imbibition tests are easier to perform than the capillary pressure and relative permeability tests required to apply the numerical method. Furthermore, when suitably preserved reservoir-rock samples are used, the properties of the laboratory system are the same as those of the field. This offers an important advantage over the use of synthetic models because there is usually some question as to how accurately reservoir-rock properties can be duplicated in such models. Based on the recovery behavior for a unit matrix block, an analysis is presented to predict oil recovery for a fractured, water-drive reservoir made up of many such unit blocks. In the analysis, it is assumed that the flow resistance and the volume of the reservoir fracture system are negligible compared with that of the porous matrix. These assumptions are generally consistent with observed characteristics of many fractured-matrix reservoirs, and have been employed in previous studies.2,3,6-8 further assumed that the effect of gravity on flow in the matrix blocks is negligible. On first thought, the latter assumption might appear to seriously limit application of the method. However, in a fractured reservoir, the effect of gravity on flow in a matrix block will be restricted by the height of the block. Furthermore, matrix permeabilities are often very low (10 md or less) in such reservoirs. This means that capillary or imbibition forces will be large, thus tending to minimize the relative importance of gravity. For these reasons, imbibition should be the dominant oil-recovery mechanism in many fractured-matrix, water-drive reservoirs. The predictive method presented in this report is applicable to such reservoirs. SCALING IMBIBITION THEORY The "scaling laws" applicable to the operation.

By Charles H. Jacoby

In 1774 a Swedish chemist, C. W. Schule, first recognized manganese as an element. That same year Schule's associate, J. G. Gahn, isolated the element manganese for the first time. In 1856 the Bessemer process of steelmaking gave birth to the economic importance of manganese. Later, in 1882, Robert Hadfield discovered high manganese steels. Although the primary use of manganese is in the ferroalloy industry, two additional important uses for manganese are making chemicals and dry cell batteries. Manganese is also vital to plant and animal life. Various chemical compounds of manganese are used in fertilizers, feeds, glass manufacture, paints, varnishes, and for numerous medicinal and chemical purposes. For the study of industrial minerals and rocks, only the chemical and battery grade material is of- concern, but for the sake of comparison, metallurgical aspects are included in this presentation. Although currently the world's largest consumer of manganese, the United States is producing only minor amounts of ore at the present time. This is due primarily to the fact that although huge deposits of manganese occur within our borders, all are of such low grade as to be economically unfeasible to mine. For many years various government agencies and segments of private industry have devoted sizable sums of money and time in an attempt to upgrade ores from the various deposits, and also in an attempt to recover manganese from blast furnace slags. In view of current world prices, and the quantity of high grade material available, there is little likelihood that any of these approaches will be found to be economically feasible in the near future. Geology and Mineralogy Mineralogy There are over one hundred minerals that contain manganese. These minerals vary from those with compositions that are predominantly manganese to those having only minor percentages. [Chemical Mineral Composition % Mn Hausmannite Mn304 72 Polianite MnO2, 63.1 Pyrolusite MnO24 60-63 Cryptomelane KR8O16R (R=Mn) Variable PsilomelaneBa Mn Mn8O16 (OH).45-60 CoronaditePb R8O16R (R=Mn) Variable Hollandite Ba R8O16R (R=Mn) Variable Manganite Mn2O3•H20 62 Braunite 3 Mn2O3•MnSiO3 62 Tephroite 2 MnO•SiO2 54.3 Rhodochrosite MnCO3 47 Rhodonite MnSiO3 42 Spessartite 3 MnO•AI2O3•3SIO2 33.3 WadHydrous Mn OxidesVariable Franklinite(Fe Mn Zn)O(Fe Mn)sO3 Variable Asbolan Cobaltiferous wad Variable AlabanditeMnS63.14] Geology From a geological standpoint most manganese deposits are complex. In general, it can be said that all primary deposits of manganese are carbonates or silicates. The most productive and profitable have been those of sedimentary origin and residual concentrations. Examples of these residual types of deposits are associated with the metamorphosed lodes of Madhya, Pradesh, India, and the lateritic deposits of Orissa and Bihar, India; nodules in the residual clays of the Philippine Islands, US southern Appalachians and Arkansas, Ghana, and Brazil. Sedimentary manganese deposits are best exemplified by the Nikopol district of Russia and the Tchiatouri area of Georgia, USSR. Hydrothermal replacements are characterized by the rhodochrosite deposits of Butte and Phillipsburg, MT. In general, the hydrothermal type deposit has not resulted in any large tonnages being produced, but may have given

Jan 1, 1983

By Thomas S. West

A gravel pack completion is described which, in addition to sand screening, permits the exclusion of water and gas from the oil production. A gravel pack composed of alternate layers of different particle sizes is employed which has horizontal but not overall vertical permeability to drilling mud. A packer is run on the tubing and set in the screen member, around which the gravel layers are placed. The hydrostatic pressure of a mud column prevents the entry of fluid above (or below) the level of the packer. The producing level may be changed by raising or lowering the tubing. Vertical coning is controlled by replacing the mud column with oil and continually injecting oil into the sand section above (or below) the packer. Three well histories with this completion are described in detail. Statistics on the first 100 completions of this general type are given. INTRODUCTION Gravel pack type completions have heretofore been almost exclusively for the purpose of preventing sand production. This paper describes and presents well data on a gravel pack procedure which is primarily a selective completion method. Although complete sand screening is achieved, the exclusion of gas and water is the primary objective. The application of this procedure is therefore not limited to unconsolidated sands. Application to hard sand or limestone reservoirs is equally feasible. GRAVEL PACK PROCEDURE Figs. 1 and 2 illustrate the gravel pack procedure employed. The gravel is placed by means of the frangible disc type dump bailer shown by Fig. 1.' This bailer has its lower end closed by a plate glass or steel rimmed cement disc. This disc breaks when the bailer passes over the liner allowing the gravel to be deposited around the liner. The liner employed is usually 2 3/8 in. to 2 7/8 in. OD and 1.995 in. or 2.07 in. ID (ID of 2-in. tubing or 2-in. line pipe). Two tvDes,. of slotted sections have been employed. One type employs horizontal hacksaw cut or milled slots of about 1/32 in. width opposite the producing section. The other type employs the same type,. of horizontal slot. but slots are placed in groups of six at intervals of about 8 in. A cage composed of half round vertical bars, spaced apart, is then welded to the pipe over the slotted sections. This liner has the bottom end closed, usually by bull plugging. The upper end is closed, while placing the gravel, by a cap which is held in place by means of a shear pin. This cap has a mandrel attached to it which extends downward inside of the liner to within a few inches of its lower end. The top of the liner cap is formed to fit a releasing type wire line core barrel overshot. The liner is lowered to bottom on the wire line by means of this overshot and released. The length of the liner is usually suffi- cient to extend to about 20 ft above the highest level to which gravel is to be placed, the upper end of the liner always being in the casing. The dimensions of the liner and bailer are such with respect to the casing size that the bailer will always pass over the liner. After releasing the liner the bailer is run to bottom. Passage of the empty

Jan 1, 1951

By Noel Jarrett, Allen S. Russell, Bernard M. Starner, Stanley C. Jacobs

A process has been developed to refine high-grade commercial aluminum to 99.99 pct purity. This enzploys precipitating titanium, vanadium, and zirconiu~ as borides. The upgraded liquid is partially crystallized under conditions that prevent massive freezing. The resulting crystals are compacted and washed free of adhernig impure liquid aluminum by melting the top crystals while draining off the liquid. Finally, the bottorn portion of the crystal bed is melted and removed as the pure product. Leakage from the crystallizat~on vessel is prevented by a layer of alumina granules that are not wetted by the aluminum. ALUMINUM of 99.99 pct purity is desired in a variety of applications. These include electrolytic capacitors, catalyst carriers, decorative trim for automobiles, aluminum powder, and high-strength alloys. This market was for many years filled by refining commercial-purity aluminum in a three-liquid-layer electrolytic cell of the type originally proposed by Hoopes. To meet the expanding need for lower-cost high-purity aluminum, a refining process based on chemical precipitation and fractional crystallization was developed. The availability of this super-purity metal was announced in November 1961, and three patents1-3 relating to the process were issued in 1965. An alternate process, comprising continuous fractional crystallization of a portion of a liquid-aluminum feed stream under conditions of strong agitation at the surface of the growing crystals, was published by Dewey4 in 1965. Earlier proposals by Larsen 5 and by Regner6 also emphasized the advantage of rapid agitation of the melt in the region of the crystallization zone. johnson 7 more recently proposed extracting purified aluminum from an alloy by mixing crystals of pure aluminum into the molten alloy, allowing them to grow, and removing the pure aluminum as by casting. Aamot's 8 recent patent describes a freeze refining process that involves controlled partial freezing against cooled moving retort walls. The Alcoa process to produce high-purity aluminum is schematically described in Fig. 1. Relatively pure aluminum is treated with boron in a furnace (a) to precipitate high melting point impurities, the supernatant liquid is transferred to a crystallization vessel (b), the liquid is partially crystallized with mechanized "tamping" (c), the remaining impure liquid is tapped out and the crystal bed partially and directionally re-melted to wash the underlying crystals (d), and the balance of the crystals is melted and withdrawn as high-purity aluminum (e). PRINCIPLES OF FRACTIONAL CRYSTALLIZATION Commonly encountered impurity elements form two types of systems with aluminum. Titanium, vanadium, and some other transition elements in periodic groups IV, V, and VI are the high melting point impurities. Initial solidification of aluminum containing small percentages of these elements will produce solid markedly enriched in them at temperatures slightly above the freezing point of high-purity aluminum. Most other elements, such as silicon and iron, produce eutectic type reactions with aluminum. In this case the first solid formed on initial solidification at temperatures slightly below the freezing point for high-purity aluminum is markedly depleted while the remaining liquid is enriched in these elements. The equilibrium change in composition during solidification of aluminum contaminated with silicon, iron, or titanium is illustrated in Fig. 2. Here, for clarity, the temperature scale is expanded beyond the

Jan 1, 1968

By Tell Ertl

The term oil shale is defined. Foreign oil-shale developments are outlined briefly. The richest and most extensive oil-shale deposits in the United States lie in western Colorado. The Bureau of Mines is opening two adjacent areas for underground mining. in western Colorado. From the first area the oil shale is mined selectively as required by the retorting plant. The second area is being developed as a unit of a full scale oil-shale mine to ascertain the most practical methods of mining oil shale and to determine costs. In both of these mining areas, research will be carried on to develop new and improved practices for mining oil shale. Introduction Oil shale is a sedimentary rock containing a solid mineraloid of indefinite composition known as kerogen. On heating oil shale, the kerogen undergoes thermal decomposition and some of the vapor products of the decomposition can be condensed as shale oil. Oil from shale can be a major source of liquid fuels since extensive deposits of oil shale are known to exist throughout the world. The United States considers the establishment of an oil-shale industry only when doubt exists of the adequacy of the domestic supply of crude petroleum. On the other hand, oil shale is not strange to foreign oil men. The industry is an old one in other parts of the world. The French industry has been in existence since 1838, the Scottish since 1859, the Australian since 1860, the Estonian and Swedish The since World War 1, and the Manchurian industry since 1929. The most highly exploited oil-shale deposits are the Carboniferous shales of Scotland. About 20 seams ranging from 4 to I2 ft in thickness are worked. The yield during recent years in scotland has been 18 to 25 gal of shale oil per ton, from 3&"30'000 tons per year' The French and Swedish oil-shale deposits are of lower grade than the Scottish. The Estonian oil-shale deposits are 7 ft thick, and the oil yield averages 50 gal per ton. Over 1,000,-ooo tons are mined each year, half of which is used directly as fuel to substitute for coal and the other half is used for the production of oil. Immense deposits of oil shale that will yield 10 to 15 gal per ton exist in Germany. Because of the impending loss of the Rumanian and Polish oil fields and the bombing of synthetic liquid fuel plants, the Nazis in 1943 started a large-scale oil-shale program in Germany. By V-E Day, it is said, oil-shale production had reached the rate of 2500 tons per day and rapid expansion of the industry was imminent. Australian oil shale, known as torbanite, occurs in beds 2 to 6 ft thick. It is of a very high grade and on retorting yields 80 to 160 gal per ton. The oil-shale industry of Manchuria was the largest in the world during the past decade. The well-known Fushun coal deposit in Manchuria has an overburden of 500 million tons of oil shale about 450 ft thick that will yield 10 to 15 gal of shale oil per ton. The oil shale is

Jan 1, 1949

By P. Hazebroek, M. Prats, E. E. Allen

Well locations in water floods frequently do not coincide with the ideal well locations associated with the flood pattern which is used. A question of importance is. "How much oil is lost because of this?". This is the problem treated in this paper. It is assumed that each pattern in a five-spot flood has the proper number of production and injection wells but that the wells may be off-pattern. The distance by which a well is off-patern is given in terms of the pattern spacing, defined as the length of one side of a five-spot. The influence of off-pattern wells on the performance of a five-spot flood has been investigated mathematically for unit mobility ratio. All production and injection rates are assumed to remain equal. The loss in recovery resulting from pattern irregularitie: has been calculated at a cumulative water injection corresponding to a 98 per cent water-cut in a regular five-spot. Displacing a single production or injection well by about one-third the pattern distance reduces the total field recovery by 4.4/N per cent of the recovery obtainable with regular spacing, where N is the number of five-spots in the flood (assumed large). When off-pattern wells are separated by at least one regular five-spot and are displaced by less than one-third the pattern distance, the total loss in recovery in a large-scale flood is, at most, 1 per cent of the recovery obtainable from that field with a regular five-spot pattern. However, much higher losses may occur if the off-pattern wells are not separated by a regular five-spot, if the rates are imbalanced, or if the mobility of the injected water is higher than that of the crude. Although the loss in oil recovery due to pattern irregularity often may be low, the off-pattern case will always require injection of more water to reach the same final water-cut. The volume of water injected per unit volume of oil displaced has been calculated for each five-spot adjacent to a five-spot containing a single 08-pattern well. The cumulative water injection at the time of 98 per cent water-cut may be increased by as much as 37 per cent when a production well is displaced one-third the pattern distance toward an injection well. The existence of differences between actual subsurface locations and the idealized well patterns used in secondary recovery operations is well recognized. However, the methods commonly used for predicting waterflood behavior ignore such differences, even when subsurface locations are known. The reason for this is simple. The idealized well patterns are highly symmetrical and, as such, the production history of the pattern (and even of the field) can be determined from that of a few production wells—usually from only one. Consideration of the many irregular well spacings found in a specific field would entail a large amount of work, and then the results would be applicable only to that specific field. In an attempt to provide an answer to the more general problem, this paper considers a water flood having an idealized well pattern, except for one well which is not at its regular location. When several off-pattern wells are present, their contributions are assumed to be additive unless the off-pattern wells are close to each other. Only four positions of the off-center well (at x, y. of Fig. 1) are considered in this paper. These are shown

By R. E. Carter, C. Wagner, F. D. Richardson

By means of inert markers of radio-platinum, it has been shown that cobalt metal oxidizes by out-ward diffusion of cobalt atoms through the oxide. Oxidation rates have been measured at various temperatures and oxygen pressures and have been found to agree with the rates calculated from the Wagner equation and the authors' values for the diffusion coefficient of cobalt in the oxide. The distribution of radio-cobalt in growing oxide loyers has been accurately measured and found to be different from that predicted from the Wagner oxidation theory. Attempts have been made to measure the change of lattice parameter of the oxide with composition. SEVERAL investigators have shown that cobalt metal oxidizes according to the parabolic law,1-3 but no detailed study has been made of the oxidation mechanism. Cobaltous oxide has a metal-deficient lattice, but the defect concentration which is dependent on the oxygen pressure is only approximately known.' From the similarities in the structures of "CoO" and "FeO" and the rate laws governing the oxidation of cobalt and iron, Gulbransen- as suggested that cobalt, like iron," oxidizes by diffusion of cobaltous ions through the oxide layer. To substantiate this hypothesis, he has attempted to measure the oxidation rate of cobalt as a function of the oxygen pressure but has been able to report only that the rate depends on a "small" power of the pressure. On the other hand, Preece," Valensi,' and Arkharov' all have suggested from indirect evidence that oxygen diffuses through the COO to the metal-oxide interface. The present authors, in a previous paper,' have shown that the rate of diffusion of cobalt in cobaltous oxide is dependent on the oxygen pressure. In that investigation, they also found that cobaltous oxide disks made by complete oxidation of cobalt metal were porous at their centers (Fig. 5L, ref. 4). Both these facts strongly suggest that oxidation of the metal proceeds via outward diffusion of cations. In order to establish the mechanism unequivocally, oxidation experiments were made with inert radioactive platinum markers, and the dependence of oxidation rate on oxygen pressure was measured. In addition, an attempt was made to determine the form of the cation vacancy gradient, which the marker experiment showed must exist across a growing oxide layer. This was done by depositing radioactive Co on the surface of a cobalt disk and then measuring the tracer distribution across the oxide layer produced by partial oxidation of the metal. Finally, an X-ray examination was made in an attempt to find the expected change of lattice parameter of COO with oxygen pressure. Experimental The apparatus and materials used were substantially the same as those previously described by the authors.4 Marker Studies: The use of inert markers to follow oxidation reactions was first attempted by Pfeil" in 1929, and radioactive markers have recently been used by Davies et al.' In the investigation reported here, the markers were applied as an (NH4)2PtCI6 slurry in several thin streaks across both faces of four disks of cobalt metal 1 mm thick and 14 mm in diameter. The disks were then oxidized almost to completion at 1200°C in pure oxygen. After oxidation, they were mounted and sectioned and auto-radiographs were taken to locate the markers. Oxidation Rate: The oxidation rate of cobalt was measured at 1148°C at oxygen pressures ranging from 0.0055 to 1.0 atm and at 1000°, 1148", and 1350°C under 1 atm of oxygen. The rate was deter-

Jan 1, 1956

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By B. Wilhelmi, W. H. Somerton

Simultaneous measurement of pore and elastic properties of socks under a wide range of triaxial stress conditions may be made with equipment and methods developed in this paper. Tests were run on three outcrop sandstones at several confining pressures and axial stresses up to approximately 80 percent of failure stress. The greater reduction in porosities and permeabilities occurred in the hydrostatic loading portion of the stress cycle, but substantial reductions in both properties did occur upon application of deviator (triaxial) stress. Triaxial elastic moduli were calculated from strain gauge measurements. Both Young's moduli and shear moduli were found to increase with increasing confining pressure. Poisson's ratios increased with axial stress but showed no consistent change with confining pressure. Only very general relations were observed between pore and elastic properties. The lesser decrease in porosity and permeability at higher stress values is related to increase in rigidity of rocks at higher stresses. INTRODUCTION Many investigators have studied the effects of hydrostatic stress on the properties and behavior of rocks. A few have studied the effects of triaxial stress fields on individual physical properties of rocks. To our knowledge no one has measured simultaneously pore and elastic properties of rocks under a wide range of triaxial stress conditions. This is the purpose of this work. Rocks exist in the subsurface under what Jaegerl refers to as "polyaxial" stress conditions (all principal stresses unequal). When two of the three principal stresses are equal, this is referred to as triaxial loading. The triaxial method of loading is most commonly used in modern testing work because experimental difficulties in measuring physical properties of rocks are greatly reduced over polyaxial testing. Although triaxial loading may not reproduce subsurface conditions precisely, subsurface stress conditions are never known precisely anyway. Triaxial testing would seem to be more realistic than testing under hydrostatic loading (all principal stresses equal) for application of results to subsurface problems. The objectives of this work were threefold: (1) to develop methods of measuring simultaneously pore and elastic properties of rocks under triaxial stress conditions, (2) to determine whether changes in these properties are of sufficient magnitude to be considered in subsurface calculations and (3) to attempt to relate changes in pore properties and elastic properties since they will have been measured at the same time under identical loading conditions. REVIEW OF EARLIER WORK PORE PROPERTIES Several investigators have studied the effects of stress on the physical properties of rocks. Fatt and Davis2 showed the reduction of permeability of rock with hydrostatic loading. McLatchie et al.3 and Knutson and Bohor4 related permeability reduction to compessibility of reservoir rock, again under hydrostatic loading. Wble,5 and later Redmond,6 evaluated the effects of applied radial pressure on conductivity, porosity and permeability of sandstones. In this latter work, no axial stress was applied. Dobrynin7 reviewed much of the previous work done . on the effects of overburden pressure on physical properties of rocks. He concluded that changes in physical properties are controlled to a large extent by pore compressibility of the rock. Several sets of curves developed from empirical relations are presented. These curves permit estimation of change of properties with net overburden pressure, knowing the pore compressibility and porosity of the rock. Net overburden pressure is defined as (Pe - 0.85 Pi ) where Pe is the

By Oscar Johnson

The industry has been canvassed for information on methods of handling grinding steel at milling plants, an important subject overlooked in most descriptive articles on milling plant arrangements. The data collected are offered in this paper as a guide to designers and planners who have loading and storage problems to solve. WITH capacities of milling plants expanding from a few hundred tons per day to many thousand, replenishment of grinding media is an important phase of mill operation. Information on this aspect of milling procedure, solicited from several mining companies, is summarized here. At International Nickel's Copper Cliff concentrator the normally strenuous job of changing rods is considerably simplified by the use of the Garrow rod charging machine, Fig. 1. The overhead crane, Fig. 2, brings a bundle of rods, weighing four to a ton, to the loading platform of the machine, positioned in front of the mill. The rods roll one by one down the slight incline of the platform onto a conveyor which sends them into the mill. A modified version of the Garrow machine, Fig. 3, is used at the Federal mill of St. Joseph Lead Co. An overhead crane places the portable steel structure in position in front of the discharge end of any one of the five 9x12-ft rod mills. It then raises a bundle of about twenty 3-in. rods to the discharge platform of the charging machine. The rods are 11 ft 7 in. long and weigh about 278 lb. By tripping a lever the operator allows one rod at a time to roll onto the inclined rollers. A slight push by the operator sends the rod smoothly into the mill. The Union Miniére du Haut Katanga rod charging machine, Fig. 4, is mounted on a pair of wheels at the forward end with swiveling castors at the back for steering it to position for use or storage. Wheels are equipped with locking brakes to maintain the machine in position while it delivers rods to the mill. The device is made in two parts. The first consists of the base, which carries the supporting wheels, grooved rollers, and drive. The other part serves as the rod deck, which can carry up to six 3-in. x 12-ft rods. A short boom built integral with the base reaches through the mill trunnion and delivers the rods into the mill barrel. Three grooved guide rollers ,are provided to receive the rods from the sloping charging deck. One rod at a time is fed to the rollers and thus delivered into the mill. Two of the rollers are driven by 11/2-hp motor through a V-belt drive. The third roller is driven off the first by a single V belt in a groove below the rod groove and on the same center line. Rods are delivered to the charger by an overhead crane in bundles of three to six as needed. The power is supplied by cables plugged into power outlets, suitably located near the rod mill discharge end. The Oliver Iron Mining Co. uses a rod charger, Fig. 5, suspended from a monorail by cables. It is constructed .of structural steel and has two decks, each capable of carrying five rods of 4-in. maximum diameter. The rods ride in grooved free-turning rollers. Legs extending down from the mill end of the mechanism act as supports when the unit is ex-

Jan 1, 1955

By M. H. Gaskell, D. M. Kehn, G. T. Pyndus

A correlation of the bubble point pressure for black oil systems is developed using the standard physical-chemical equations of soiutions. The correlation is based on 158 experimentally measured bubble point pressures of 137 independent systems and is expressed in terins of the usually measured field pnrameters— flash separation gm-oil ratio, rank oil gravity, total gas gravity, and reservoir temperature. The data were obtained on systems produced in Canada, Western and Mid-Continent01 United States, and South America. The average error (algebraic) in the representation is 3.8 per cent, and the maximum error encountered is 14.7 per cent. INTRODUCTION In the absence of experimentally measured properties of reservoir fluids, it is often necessary for the field engineer to make estimates regarding the fluid properties based on the usually measured producing parameters. To aid in these estimations, various correlations have appeared in the literature in recent years. Among the pertinent properties of interest is the bubble point pressure. A correlation for this parameter has been reported by Standing'. However, this correlation was based essentially on California produced crudes and this limitation was pointed out with its presentation. The correlation presented in this paper utilized data on crude oil systems from Canada, Wes- tern and Mid-Continental United States, and South America. CORRELATION DEVELOPMENT The basic assumption used in this development is the same as employed by Standing', There is a wide variety of ways to combine these parameters; however, in this instance the combination was made on the basis of Henry's law2. Accordingly, the relationship proposed is Although Eq. 2 defines an individual system, it is of limited value since H' is a function of gas-phase composition and the system temperature. It was observed that for the systems where the bubble point was measured at several temperatures that the ratio of the bubble point pressures and the ratio of the corresponding absolute temperatures (R) were practically identical. Thus, for correlation purposes the bubble point pressure may be taken as a direct function of the absolute temperature. This relation is valid only for those systems that are not near the critical point. Accordingly, this correlation will be inadequate for systems in the region of the critical point. The solubility of the various hydrocarbons found in the gas phase increases with the molecular weight. Thus, the saturation pressure should be inversely related to the gas gravity. Applying these principles to Eq. 2 and rearranging terms gives: The variables 02 the left side of Eq. 3 were designated as the "hubble point pressure factor". The number of mols of tank oil per barrel is a function of the "mclecular weight" of the tank oil. Although the tank oil is a complex mixture, it was assumed for the purposes of this correlation that a unique molecular weight could be assigned to a given oil. This was designated as the "effective molecular weight", and was related to the oil gravity, This empirical relationship was developed simultaneously with the correlation by assuming values of M,. and working to obtain a smooth curve for both the correlation and the effective molecular weight. The relationship between the oil gravity and the effective molecular weight used in this correlation is shown in Fig. 1. The effective molecular weight is somewhat higher than the molecular weight of the C fraction. The difference between these values is largest for the low-gravity systems. It is noted that this effective molecular