Search Documents

By M. D. Cooper

UNDERGRADUATES in mining engineering may be prepared for work by giving them sound instruction in the courses generally considered essential to the profession. The industry is not deeply concerned about the details of those courses. The average man in the coal industry does not wish to insist upon a rigid program. Therefore, he differs little from those in the teaching profession who evidently are not unanimous in their opinions, or all college catalogs would be alike. For the good of the profession, it is just as well that there should be differences in regard to details. It appears that students graduating in mining engineering from the accredited institutions receive similar instruction. It is taken for granted that the graduate will have a good understanding of English, mathematics, mechanics, electricity, chemistry, physics, geology, and surveying, in addition to his major courses in mining. Somewhat belatedly, industry hopes he will have had at least an introduction to the subject of labor relations, the importance of which is only too clear at present. The coal industry expects, of course, that students in mining engineering will be taught the strictly mining subjects by men who have had practical experience in the mines and who keep themselves well informed in regard to current methods. While the undergraduate is subject to the control of members of the teaching profession, industry expects him to be trained in certain ways that are not a part of his textbooks, but can be made an inseparable part of his development by the skillful supervision of his teachers. Of the desired characteristics, dependability is of the utmost importance. Probably most employers would overlook certain short-comings if the young graduate demonstrated that he was thoroughly dependable. If he always appeared at the right place at the right time with the proper equipment, he would soon be well established as a welcome member of his organization. The graduate who gets a reputation for being undependable will have little opportunity for advancement. Closely allied to dependability is loyalty. Athletic teams and social groups in college tend to develop loyalty which may well be carried over into industry. This does not mean that the graduate has to be satisfied with customary practices. The average manager is glad to see the graduate make constructive criticism as long as he demonstrates his loyalty at the same time. It is important that his loyalty keeps him alert arid ready to take helpful action for the benefit of his organization, and especially to stand with it during times of stress. With or without an introduction to labor relations in college, the graduate is expected to develop ability in this most important field. Beginning with himself, he will find it essential to deal agreeably with his immediate associates. Getting along in friendly fashion with his own small group will be a great help as his responsibilities increase and he is required to deal with larger numbers of persons. On a higher scale, his interest in his community may grow at the same time by voluntary work in any one of a great number of useful activities. Industry expects the graduate engineer to be a mature man at the time he gets his first job. Supposing that he has better than average intelligence, industry expects him to continue to grow intellectually and to fit himself for responsible jobs when they are offered to him. For this reason, employers are apt to look over his college record to see what he did that would indicate his fitness for leadership. There is interest in knowing what he did beyond the requirements. As evidence of his mental growth, it is expected that the graduate will do independent thinking; that he will not take too much for granted. When he reads a report, he should develop the ability to see whether the subject is new or whether it is just a description of an old method that has been superseded by something better. For the same reason, the graduate should be able to accept conditions that have been arrived at by sound experience rather than cling to something else that seems better in theory. In this connection, it may be remarked that the ability to operate successfully a personal budget will be noteworthy, as it may be assumed that a man who knows how to conduct his own affairs will be prepared to assume the larger responsibilities of industry. Membership in AIME will indicate to the employer that the graduate is interested in the mining industry as a whole. Therefore, it is good evidence of something more than a local outlook. Quite apart from college training and mental ability, the newly employed graduate will be expected to be willing to do hard manual labor for a time. This will give him an understanding of the actual conditions of work done by those he supervises later. He will gain their confidence and be able to see that the work is carried on in a safe and efficient manner. Part of this experience may be acquired in his summer vacations during his undergraduate career. Such work would make a favorable impression on a prospective employer, especially if the graduate showed a willingness to continue it until he was prepared for something better. To summarize, the man in authority in the coal industry will not quarrel with the professor of mining engineering over details of curriculum. He will be pleased if the school sends him graduates who possess a good foundation in the courses studied, and who may be depended upon to do their work faithfully and intelligently. Such men will be ready when the time comes to assume their places as leaders of an essential industry.

Jan 1, 1951

By Randolph C. Specht

A two year study was made of the waste disposal of the pebble rock phosphate industry. Solid slimes are impounded in large settling areas and the process water is re-used. Clear effluent was not found to be toxic to fish or animal life in field tests or in controlled experiments. Survey: The pebble rock phosphate mining and washing operations in Florida (fig. 1) are along the river basins of the Alafia to the west and the Peace to the east. The elevation of the area varies between 40 and 170 ft above sea level. Effluents from the operations find their way into one of the two river systems (fig. 2), the Peace River which flows into Charlotte Harbor and the Alafia into Tampa Bay, both along the Gulf of Mexico. There are no major industries along these rivers below the phosphate operations. On the Peace River, the town of Arcadia, approximately 50 miles below the phosphate operations, obtains its water from the river. No other communities along the rivers use them as a source of water supply. Small communities, farms, and ranches are located along the rivers and both rivers drain vast swamp areas. Complaints had been received at the office of the Chief Sanitary Engineer, of the Florida State Board of Health,' that both rivers were turbid at various times and that fishing in the Alafia River was "not as good as it used to be." Tests made by another agency on the dissolved oxygen content of the Alafia River revealed that the oxygen content, at times, was comparatively low.= However, it was not shown that the phosphate wastes had any effect upon the oxygen content of the stream. The river waters are normally brown in color due to drainage from vast swamp areas and are very shallow, from 2 to 6 ft in depth. Turbid waters have been noted in streams coming from the present phosphate operations and also from streams along which there are no operations at the present time. It was learned from "old timers" that, when many more companies than at present were operating along both the Alafia and Peace Rivers forty or fifty years ago, no attention was paid to prohibiting the disposal of slimes along the river basins. During dry periods now in some of the river swamps where drainage ditches have been dug, it is indicated clearly that phosphate slimes were disposed of directly into the river swamps for many years past. Places have been observed where there were alternating strata of phosphate mud, leaf mold, and quartz sand. The former practice of indiscriminate disposal of wastes accounts for some turbidity, particularly after heavy rains and washouts and during clearing of land and digging of drainage ditches. During a six months' period in which a large tract of land was being cleared and drainage ditches dug, a small stream (Six Mile Creek), which previously had been clear, showed a turbidity of 600 ppm and remained turbid until the clearing was completed; after which the stream again flowed clear. An interview with the operator of the municipal water plant, which is about 50 miles below the phosphate operations on the Peace River and which used this river as a source of supply, revealed that there had been no taste in the water for the past ten years, other than that occasionally encountered from increased growth of algae. The operations of each of the cooperating com-

Jan 1, 1951

By George C. Howard, P. P. Scott

During the drilling of wells, fractures which are created or widened by drilling fluid pressure are suspected of being a frequent cause of lost circulation. A study of the variables which are believed by the authors to he related to fracturing led to the premise that the presence of an effective lost circulation material in a drilling mud stream would serve to plug small fractures at the moment they are encountered or created and thereby a a possible cause of lost Circula. tion by preventing fluid pressure from widening and extending the fractures. A large number of lost circulation materials were classified and tested in simulated fractures and in shallow wells. Granular type materials with a gradation of particle sizes were found to be the most effective for plugging. Within the limits of pumpahility, the concentration in mud of each lost circulation material tested was found to be a controlling factor in determining the maximum size fracture which could be sealed. A new type centrifugal sorter was given preliminary tests and found to be capable of concentrating cuttings for rejection and reclaiming lost circulation materials. INTRODUCTION The control and prevention of lost circulation of drilling fluids is a problem frequently encountered during the drilling of oil and gas wells. Lost circulation or lost returns may be defined as the loss to formation voids of the drilling fluids or cement slurries used in the process of rotary drilling and well completion. The loss may vary from n gradual lowering of mud level in the pits to a complete loss of returns. Not to be confused with lost circulation is the continuous reduction in mud volume caused by the loss of the fluid phase of muds as filtrate and the solid phase as filter cake during the continuous filt~ation process which occurs on permeable formation surfaces. The loss of drilling fluids and their costly constituents is only one of the detrimental effects experienced when circulation is lost. The loss of drilling time, plugging of potentially productive formations, stuck drill pipe, blow-outs, excessive inflow of water, and excessive caving of formatioils are other effects which contribute to make the control and prevention

Jan 1, 1951

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 E. S. Mardock, Robert E. Bush

The object of this paper is to report recent developments in the quantitative interpretation of radioactivity logs. The use of reference lines is described in the application of the new zero radioactivity reference line for the determination of neutron derived porosities is discussed. Illustrated examples are shown of logs from the reef limestone of the North Snyder Field and from the Lansing-Kansas City limestone of central Kansas. A method of using an interrelation factor calculated from the neutron and gamma ray curves, called the neutron Productivity number, for the estimation of productivity from sandstone formations is discussed. When used in a relative manner the neutron productivity number has aided in Predicting whether a given zone will produce gas or liquid or whether it is too shaly to produce. Examples of logs from wells in the Freites District, Venezuela, and in East Texas are shown to illustrate the application of the neutron productivitv number. INTRODUCTION The petroleum industry was introduced to some of the preliminary results of investigations into the quantitative interpretation of radioactivity logs in October, 1949." It was stated at that time that the methods presented were entirely relative because they involved the use of reference points obtained from the radioactivity log, i.e., shale reference lines, dense zone reference lines, or a combination of both shale and dense zone reference lines. These relative methods offered many advantages to the industry in interpreting radioactivity logs in terms of porosity with particular application to limestone and dolomite reservoirs. However, these relative methods did not offer the wide range of applicability desired because the esta1)lishment of reliable reference points from shale in some areas were difficult. It was recognized that a more reliable mean; of establishing reference lines was vitally needed. Such a method is now available through the introduction of an instrumeutal zero device. It is the purpose of this paper to discuss the application of this new zero reference to the quantitative interpretation of radioactivity logs. Previously all applications of quantitative interpretations of radioactivity logs have been made in limestone reservoirs with little or no emphasis placed on sandstone reservoirs. A brief resumé of investigations into the quantitative interpretation of radioactivity logs in sandstone reservoirs is presented here. This discussion deals primarily with the interrelation of the gamma ray and neutron curves and the response of the latter to the density of the fluids filling the pore space in relatively homogeneous sandstones of uniform porosity. The authors believe that the methods presented herein are only applicable locally to specific fields and reservoirs, and that they probably do not offer a wide range of applicability. However, tile authors believe that the wider use of the new instrumental zero references in sand areas will reveal more information about the specific response of the gamma ray and neutron curves to changes in lithology and saturation. Two applications of quantitative interpretation using the new instrumental zero references are presented. Examples are given which show the comparison of logs and porosity in the limestones and dolomites of West Texas and Kansas. Logs of wells in 'Venezuela and East Texas are compared with the drill stem test data, production data, etc.. to illurtrate the interrelation of the gamma ray and neutron curve: and the rise of methods involving these interrelations to determine certain saturation variables. THE QUANTITATIVE APPLICATION OF RADIOACTIVITY LOGS TO LIMESTONE AND DOLOMITE RESERVOIRS Tile theoretical basis for the gamma ray and neutron curves has been discussed elsewhere.9 he method of recording the logs and apparatus involved has also been thoroughly covered and will not be discussed here.'."".'" It has been shown that the neutron curve responds exponentially to liquid filled porosity over the 1 1/2 to 35 per cent

Jan 1, 1951

By T. E. Ockershauser

The Southwest Antioch Oil Field located in T2&3N - R2&3W, Garvin County, Okla., was discovered in February, 1946, by The Globe Oil & Refining Co. and The Vickers Petroleum Co. at their Melinda Gibson No. 1. Oil production was encountered at a depth of 6,525 ft in 14 ft of lower Pennsyl-vanian sandstone. The producing sand, locally called the ."Gibson" or "Third Deese," is a sand bar deposit strung along the west flank of the Pauls Valley uplift in a northwest-southeast direction. The oil reservoir is defined to the east by the edge of sand deposition along the uplift and to the west by the gradation of sand into shale. Within the Antioch Unit, the sand dips from 150 to 400 ft per mile southwesterly and has a pay thickness varying from 10 to 55 ft and averaging 28 ft. Several areas of Gibson production have been developed, including the Katie pool on the south, the Elmore Area of the Southwest Antioch Gibson Sand pool. the Southwest Antioch Gibson Sand pool proper, the Southwest Maysville pool and the New Hope pool on the north. Production extends over a belt 22 miles long by about two miles wide and is continuous except into the Katie and New Hope pools. It appears that drilling will soon prove these intervening areas productive. To March 1, 1950, approximately 18,000 acres have been developed with 450 Gibson wells. It is likely this count will ultimately reach 32.000 acres with 800 wells. RESERVOIR The natural production of oil from the Gibson reservoir is primarily due to solution gas expansion though gravity also plays a part. There is no indication of water drive or evidence that an initial gas cap existed. Gibson oil has a stock tank gravity of 43" API and was saturated at the original reservoir pressure of 2.925 psi. It contained 1,3440 cu ft of gas per bbl in solution and had a high shrinkage of 70 per cent. Connate water amounts to 15 per cent. Reservoir temperature is 130°F. Porosity averages 15.5 per cent and permeability ranges from less than one md to over 1.000. Based on meacurement of 400 core plugs from 15 wells, 78 per cent of the permeabilities fell within the 10 to 1,000 md bracket and averaged l67. Primary oil recovery is estimated at 140 bbl per acre-ft or 22 million bbl for the present 137-tract unit. Due to unitization

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By O. L. Culberson, J. J. McKetta

Experimental and smoothed data are presented for the solubility of methane in water for temperatures of 77, 100, 160. 220. 280, and 340°F at prejsures to 10.000 psia. The minimum solubility phenomenon exists within this temperature range to pressures of 10.000 psia. INTRODUCTION The study of hydrocarhon-water systems has been extended to the determination of the solubility of methane in water at pressures to 10.000 psia. The experimental apparatus, and the technique. are the same as that previously reported.' - In the determination of the solubility of methane in water, only two phases were present at temperatures between 100 and 340°F. these being the vapor phase and the water-rich. liquid phase. The determinations involved the agitation of methane and water in an equilibrium cell. withdrawal of a sample from the liquid phase, and the analysis of the sample. The experimental value; determined in this manner are pre9ented in Table I and in Fig. 1. Since experimental and analytical techniques have improved since the initial experiments with this equipment, it was decided to repeat the 77°F isotherm determinations.' Fig. I shows that the individual results for this isotherm are much

Jan 1, 1951

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

By D. W. Akins

The case history of a combination gas and water flood instituted early in the life of a field is described. It was recognized from the beginning that recovery would be low, under normal production methods, from the several separate, thin beds of porous limestone which had such poor native permeability that the wells would not produce without acidizing. It is thought that the combination flood gives excellent recovery efficiencies for this type of reservoir. The chief function of the gas flood now is to maintain bottom hole pressure in that part of the reservoir which will not be affected by the water injection program until later. Present estimates are that ultimate recovery will be approximately double the recovery expected under the original solution gas drive mechanism. Wide (80-acre) spacing has enhanced the economics of the over-all field program by the elimination of more than $5,000,000 worth of unnecessary wells. INTRODUCTION The Haynesville Pettit Field was discovered in November, 1941, with the completion of T. L. James Co.'s Callie Akin No. 1, located in the W 1/2 of the NE 1/4 Section 27-23N-8W, Claiborne Parish, La., at an approximate depth of 5,300 ft. The center of the field is about two miles north and a mile west of the town of Haynesville, La. A total of 189 producing wells have been drilled on 14,500 acres. An additional nine dry holes were drilled. The Louisiana-Arkansas state line divides the field so that 34 wells are in Arkansas and 155 are in Louisiana. Governmental sections are divided equally to contain eight production units making 80-acre spacing where the sections are regular. Along the state line in Louisiana there is an irregular tier of sections, each of which contains approximately 456 acres. When divided equally into eight production units the spacing is 57 acres per well for these three and a fraction productive sections. All Haynesville Pettit wells are identified by their section number followed by their position in the section as determined by numbering the production units counterclockwise beginning in the upper right corner of the section. All of the producing wells in the field except two are unit-ized and operated by the Haynesville Operators Committee. These two wells are located in the extreme northern part of the field in Arkansas. Efforts to bring them into the Unit are being continued. The Pettit operators organized the Haynesville Operators Committee and the field became a unit operation May 1: 1944. GEOLOGY The Pettit is Lower Cretaceous in age and is defined as the uppermost porosity in the Sligo formation. The unitized area known as the Haynesville Pettit Field is composed of two separate zones of porosity approximately 40 ft apart and without connection between the two, except in wells. These zones are known as the Upper Pettit and the Lower Pettit. The Upper Pettit is separated into two sections throughout most of its area by a relatively thin but quite impervious shale streak. These are called the "A" and "B" sections of the Upper Pettit. All of these lenticular zones are composed of coquina limestone and a small percentage of normal oolites. The large

Jan 1, 1951

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By M. B. Riordan

A surface indicating pressure, temperature and flow instrument that ernploys variable frequency sensing elements has proved useful in evaluating flow characteristics of wells. Relative productivity of individual oil and gas sands in a given well can be analyzed at several back pressures. The variable frequency sensing elements are an improvement in sensitivity and accuracy and make possible observation of temperature and pressure variations that have not been possible heretofore. The surface indicating featuere results in a more direct approach to solving problems and eliniinate; many assumptions. All three subsurface factors are evaluated, and correlation between them results in a direct means of analyzing reservoir. and well conditions. Surveys have been used to evaluate well performance. locate gas entry In high ratio wells and to investigate gas injection and water flooding conditions. INTRODUCTION In a flowing well that is open to a multiple number of producing sands with varying characteristics. it is valuable to know which sands are producing fluid at a given back pressure and in what relative quantity. Core studies could qualify an interval as productive, and reserves would be computed on this basis. Unless the well is produced so that the interval does contribute. irreparable damage to the interval can occur. It is generally accepted that the optimum condition of pro-

Jan 1, 1951

By James R. I. Henagan, William O. Crego

The Mamou Field, located in Evangeline Parish, La., is an elongated anticlinal structure on the downthrown side of a major east-west fault with oil and gas production from the upper part of the Wilcox formation. Two main producing horizons occur at an approximate depth of 11,500 ft and have been designated the Morein sand and the Deshotels sand. The upper sand (Morein) had an original bottom-hole pressure of 6,788 psig, which is some 1,500 psi above the normal pressure for that depth. Oil production with high gas/oil ratios and fluid analyses giving high shrinkage factors prompted a study of the reservoir in its early stages. The results indicated a closed reservoir producing under solution gas drive with low expected ultimate oil recovery. The early study of the Wilcox formation and its contained hydrocarbons resulted in the presentation of the data to the Department of Conservation of the State of Louisiana. with suggestions for field rules and a request for permission to inject extraneous water into the Morein sand. The water injection plans eventually led to complete unitization of working and royalty interests, to the construction of a gasoline plant, and to a central tank battery installation for the field. Deshotels sand wells were reworked to the Morein sand, and the water injection system was installed and ready for continuous operation in the early part of 1949. The injection of water was started in time to arrest the bottom-hole pressure decline at or near the bubble-point pressure. This injection was calculated to increase the ultimate recovery and to conserve natural resources. Pressure maintenance, the extraction of LPG products, and the sale of residue gas (early 1950) represent an attempt to produce an oil field with utmost efficiency. INTRODUCTION The two principal Wilcox oil horizons in the Mamou Field are the Morein sand and the Deshotels sand, occurring at 11,500 ft and 11,700 ft subsea, respectively. Minor oil production has been encountered in Morein stringer sands. (Fig. 1.) This paper deals only with the Morein sand, which is blanket over the Mamou Field. It is, however, segmented by the northwest-southeast "E" fault as shown in Fig. 2. The west segment is the area involved in the water injection pressure maintenance program. To date the east segment has operated largely under the influence of a strong water drive. The paper presents (1) a brief history of field development, (2) a resumé of reservoir conditions which led to the decision to inject extraneous salt water into the principal producing horizon, and (3) a summary of reservoir analysis and performance. FIELD DEVELOPMENT The Mamou Field is located in Evangeline Parish, La. The discovery well (J. B. Morein No. 1, now Unit No. 5) was completed in December, 1945, after penetrating 200 ft into the Wilcox formation. Initial production from the Morein

Jan 1, 1951

By E. S. Messer

A knowledge of the magnitude of the irreducible inter.;titial water in a porous medium is so important to petroleum engineering that its determination has become routine in core analyses. The method of determination, being a production problem, should encompass the basic requirements of simplicity in technique and calculations, with reproducible results obtainable in a short interval of time. The results of the evaluation tests outlined in this report indicate that the evaporation method for determining the irreducible water is a technique which meets the requirements. The procedure consists, as the name implies. of permitting the saturant in the pore spaces to evaporate until only an irreducible volume remains. The determination of this volume can be made either graphically or by a mathematical comparison of fluid flows; the time required for each determination being dependent on the fluid used. When fluids other than those having reservoir characteristics were used, a volume factor had to be calculated which was based on the relative volume of various liquids adsorbed on grain surfaces and retained in pores. This factor made possible the calculation of an irreducible water volume when more volatile fluids such as toluene and benzene were used as the saturants. Also presented is the theoretical discussion necessary for the calculation of the capillary pressure as determined from the evaporation curve. A comparison is made between the calculated values and those obtained by experimental means. INTRODUCTION In all geological formations there exists, in the pore spaces of the rock structure, water that is held in a state of equilibrium between capillary and hydrostatic forces. "Interstitial water" is the term given to this water and is defined as that water coexisting in the pore space with the oil prior to exploitation. The term ''connate water" has often been used synonymously with this term; however, this can be true only by a specific definition since, geologically, it means the water in place at the time the rock structure was formed. The quantity of the interstitial water is a variable factor in any formation, since it depends on the hydrostatic forces present in any multiple-phase system. These forces may become unbalanced by the introduction of an extraneous force such as the raising or lowering of the "water table" or the migration of oil into a water-filled formation. Any unbalanced force results in a change in the interstitial water. There exists, however, an irreducible interstitial water. for a particular sand, that is the fraction of the pore space occupied by water when the capillary pressure at the particular point in question is at an equilibrium with the hydrostatic head of the oil sand in the reservoir. For this discussion the term "irreducible water saturation" will be used in place of "irreducible interstitial water saturation" for the sake of brevity; however, they are understood to be identical. A great amount of work has been devoted to the theory and methods for studying the irreducible water saturation and its related capillary pressure. As a result of the publications of Leverett;' Hassler, Brunner and Deahl;2 Calhoun and Lewis;3 and others, the role of capillary pressure studies is being accepted by the industry as a tool for studying suhsurface phenomena. Many techniques have been developed and published for determining the capillary pressure and irreducible water. In general, these techniques may be grouped into three classifications. One of the first was the capillary pressure method described by Leverett1 and expanded by Bruce and Welge.4 The experimental results were compared with water saturation of cores obtained using oil-base mud. Thornton and Marshall compared the irreducible water saturation of core samples determined by the capillary pressure method and by salinity and reported good agreement between the two methods. The second classification for determining the irreducible water and capillary pressure may be referred to as the "centrifugal force method." The general technique is similar to the capillary pressure method except that the force driving the reservoir fluid from the sample is of a centrifugal nature. A complete description of this method was presented by J. J. . McCullough and F. W. Albaugh.6 A process, the reverse of the capillary pressure method, was presented by W. R. Purcell.7 Mercury under pressure is driven into the pores of the rock and the saturation of the core determined at each applied pressure. The resulting capillary pressure curve is used to evaluate the irreducible water saturation. The techniques mentioned are singular in their approach to the irreducible water saturation. In all cases. an external force was applied to the core. The forces employed in the evaporation method are the vapor pressure of the liquid causing evaporation, the kinetic diffusion forces. adsorptive forces and. to a lesser degree, the viscous forces resisting flow to the surface. The basic definition of irreducible water is that water held in a state of equilibrium between capillary and hydrostatic forces This water has been described by previous investigators as being held in the microcapillaries too small to support fluid flow. Actually, this fluid volume is made up of the water in the microcapillaries and as a film adhering to the surface of the crystals. All capillaries. therefore, possess some liquid as a film, the thickness of the film being dependent on the properties of the fluid and solid. A discussion of experiments with references pertaining to the measurement of this immobile layer next to the solid surface can be found in the text by J. J. Bikerman.8 Eversole and Lahr calculated the thickness of this layer to be in the order of 10 ' to 10' cm for aqueous solutions and glass. Between two quartz surfaces they found the thickness to be 2 x 10 cm. The work of Volkova, on the capillary movement of water and toluene in quartz grains, indicated the thickness of the Immobile layers to be near 10' cm. Since any measurement is an average value, it is easy to understand that an absolute value would depend on the roughness of the surfaces involved and the complexity of the system. A calculated effective pore radius of 2 x 10 cm is obtained at the, irreducible saturation of a porous media in a water-air system when a capillary pressure of 100 psi is applied. Since the separation of the sand grains is of the same approximate magnitude as the immobile layer.

Jan 1, 1951

By A. D. K. Laird, John A. Putnam

This paper describes the application of x-ray theory to design procedures in connection with fluid saturation determinations during fluid flow experiments with porous media. A reliable and rapid method for calibrating the x-ray apparatuy is described. Extension of the method to fluid saturation determinations in three-fluid systems is described. INTRODUCTION In rerearch on oil production problems a method is required which will give quickly the quantity of each component of a fluid flow system present at any cross-section of a porous medium. The sample of porous medium under investigation is usually referred to as a core. The ratio of the volume of one component to the total fluid volume is defined as the saturation of the porous medium by that component. This ratio is generally given as per cent saturation. Some means of measuring saturation which have received consideration include: electrical conductivity of the fluids;1,2 emissions from radioactive tracers dissolved in the fluids; the radioactivity of silver caused by reflection of neutrons from hydrogen atoms in the fluids;' the attenuation of a microwave beam. the diminution and phase shift of ultrasonic wave trains.4,5 and the reduction in intensity of x-ray beams in passing through the fluids. X-rays have already been used with some success. Since every material has a different power to absorb x-rays, the reduction in intensity of an x-ray beam as it passes through a core depends on the fluids present. The strength of the emergent beam can be found by converting its energy into a measurable form such as heat or ionic current. or by its effect on a photographic plate or fluorescent screen. The beam strengths could be interpreted as quantities of known fluids in the core if, previously, these beam strengths had been identified with a known combination of the same fluids. With some fluid cornbinations it might be desirable to dissolve powerful x-ray absorbing materials in one or more of the fluids, to increase the differences in the beam strengths for various fluid saturations. Boyer, Morgan and Muskat6 have described a method of measuring two component fluid saturation. One component was air or water; the other. minerat seal oil in which was dissolved 25 per cent by weight of iodobenzene to increase its absorbing power. The x-ray source was a tungsten target tube operated at 43 kv potential. The beam emerging from the core was measured as ionic current flowing across an air-filled ionization chamber by means of an amplifying circuit and galvanometer. Another portion of the beam from the x-ray tube was passed through a metal plate and measured in another ionization chamber. This portion, called the monitor beam, was used as an indication of the performance of the x-ray tube. The galvanometer readings were calibrated against air-oil core saturations, gravimetrically determined. The method was apparently established by experimental means. In the present investigation the available theory of x-radia-tion was surveyed with a view to extending the usefulness of the method and to developing design procedures for its application to measurement of fluid saturation in porous media. Application of the theory permits prediction of relative meter readings to be expected for any combination of porous matrix, various saturating fluids and auxiliary filtering media. It is thus possible to calibrate the equipment in terms of fluid saturation by an indirect but rapid technique. The results of calculations based on x-ray theory indicate. and results of the saturation calibration technique confirm. that a valid measurement of the saturation of the core can be made for any two components and in some cases for three components. THEORY The strength of an x-ray beam, after it has passed through a distance. 1, of matter of density, p, and mass absorption coefficient, µ at a given wavelength, A, may be expressed by the absorption formula I = I0 e ...........(1) where I, represents the intensity of the incident x-ray beam and I is the intensity of the emergent beam. The expression e is called the transmission factor of the material. The variation of I,, with wavelength depends upon the materials through which the x-ray beam has previously passed and upon the spectral distribution of energy at the source of the x-radiation. A group of curves. called spectra. which show the variation of intensity with wavelength and x-ray tube voltage are given in Fig. 1. These curves represent the general radiation from a tungsten target tube. When the tube voltage is greater than 69.3 kv, the characteristic radiation of the tungsten is emitted and is superposed on the general radiation. At a given voltage the minimum wavelength A,,,,, at which energy can be emitted by an x-ray tube is given by the formula 12,340 xml. = ——..........(2) volts where A,.,,.. is in Angstrom units. The wavelength at which the spectra have maximum intensity a1so decreases with increasing x-ray tube voltaue. The area under each curve represents to an arbitrarv scale the total energy emerging from the x-ray tube for that voltage. The variation of µ with wavelength has been determined for many substances and may be found in such references as those by Compton and Allison7 and by Hodgman.8 The phenomenon of absorption is composed chiefly of the capture of photons by the atoms of the absorbing material with associated displacement of electrons, and of the scattering, or the deflection, of the photons by the atoms. Curves of these mass absorption coefficients show jump discontinuities. or absorption edges. at wavelengths which are short enough for the photons,

Jan 1, 1951

By R. A. Morse, P. M. Bridges, L. E. Wilsey, Howard N. Hall, P. L. Terwilliger

Theoretical and experimental investigations of a constant pressure gravity drainage system are reported. Experimental data are presented to show that recovery to gas breakthrough by gravity drainage is inversely proportional to rate. The gravity drainage reference rate, which is numerically equal to the so-called "maximum theoretical rate of gravity drainage" is shown to have no particular significance from a recovery standpoint. Before this rate can be used as a basis of comparison for recoveries, it is necessary that the relative permeability and capillary pressure characteristics and displacing fluid viscosities be identical for the systems compared. A method is presented by which accurate prediction of the performance of a gravity drainage system can be made. Close agreement between experimental and calculated drainage performance shows that steady state relative permeability and static capillary pressure data can be used to describe fluid displacement behavior. The very wide range of liquid recoveries before gas breakthrough which result from production rate variation alone demonstrates the importance of this factor in planning depletion of a gravity drainage reservoir. Calculated results are presented which show that little additional recovery can be expected from a high pressure gravity drainage system between the times of gas breakthrough and attainment of such high gas/liquid ratios as to make further pressure maintenance impractical. INTRODUCTION It bas been recognized for some time that gravity forces play an important part in the recovery of oil from some types of reservoirs. Field experience has shown that under certain conditions, gravity drainage can result in very high oil recov- eries. Qualitative reasoning has led most engineers to the general conclusions that: (1) Where gravity drainage is important, the reservoir pressure should be maintained by gas injection at the crest of the structure to prevent shrinkage of the oil in place and to keep a low viscosity so the oil can drain at the fastest possible rate. (2) Recovery by gravity drainage is rate sensitive. A survey of the literature indicates that while considerable work has been done on the effects of gravity in oil production problems, no satisfactory method of calculating the performance of gravity drainage reservoirs has been reported.1,2,3,4,5 In the absence of any proven method of calculating reservoir performance, the level at which pressure should be maintained and the rate of production for most efficient operation has been open to debate. The limits and general character of the recovery us rate relationships are apparent from the following: As rates of production approach zero, oil will drain by virtue of its own weight fast enough that the saturation distribution is always approximately the same as the original static capillary distribution. That is, at the gas-oil contact the liquid saturation goes from 100 per cent to a value of perhaps 10 to 30 per cent in a very short distance, so that as production continues. a relatively sharp gas-oil contact moves down-structure, leaving a very low residual oil saturation in the originally oil saturated zone. At very high rates of production, the oil that drains by virtue of its own weight is negligible and recovery will approach that of a horizontal gas drive, leaving a much higher residual oil saturation. At intermediate rates of production. recovery should be between these extreme*. Despite the lack of quantitative methods, tentative agreement had been reached on the question of optimum producing rate. It has been generally concluded that rather sharp decrease in recovery would occur at rates of production above the "maximum rate of gravity drainage" and hence this rate should not be exceeded. The "maximum rate of gravity drainage" is defined as the rate of production from a 100 per cent

Jan 1, 1951

By O. L. Culberson, J. J. McKetta

INTRODUCTION The equilibrium constants for methane and for water, and for ethane and water have been calculated from experimental data for the two binary systems.2,3,11,12 These constants are for the two-phase systems for the temperature range of 100" to 340°F and the pressure range of 200 to 10,000 psia. The constants for ethane are greater than those for methane. Equilibrium constants for a natural gas from a natural gas-water system6 are about the same as those for methane. Equilibrium constants for water in all three systems are very nearly the same over the greater part of the range of temperatures and pressures studied. In ideal solutions, the vapor-liquid equilibrium constants for a component should be the same in all such solutions at a given temperature and pressure.5 Few solutions are ideal, and consequently the use of generalized constants often leads to error in situations where they do not actually apply. In decidedly non-ideal systems, it is desirable to have equilibrium constant data for the specific system. Vaporization equilibrium constants may be calculated either by thermodynamic methods or from experimental vapor-liquid equilibrium data. In the thermodynamic calculation. the equilibrium constant K may be shown to be" K = fP,/fl'..........(1) where fPi is the fugacity of the pure component i at the given temperature and at the vapor pressure of the pure component, and fp is the fugacity of pure i in the gaseous state at the temperature and total pressure of the system. At best the thermodynamic calculation results in a K applicable to ideal solutions. Equilibrium constants calculated from Equation (1) have been found to have only limited agreement with experimental values, even though the solutions for which they were calculated approached ideality."'" If the more volatile component is at a temperature above its critical, the accuracy of the equilibrium constant for the component is made more doubtful by the use of the vapor pressure term under such conditions. In order to make the thermodynamic calculation on a component above its critical temperature, one must resort to one of the empirical methods of extrapolation of the vapor pressure to conditions above its critical point.13 Application of the thermodynamic equilibrium constant then to the methane-water or the ethane-water systems would be risky since the systems are non-ideal, and the methane and ethane are above their critical in most petroleum operations. ETHANE-WATER SYSTEM In the temperature range of from 100° to 340°F and for pressures up to 10,000 psia, the vapor-liquid equilibrium data 'References given at end of paper. Manuscript received in the office of the Petroleum Branch March 16, 1951.

Jan 1, 1951

By Irwin Politziner F. M. Townsend, L. S. Reid

Recently published data indicate that the water vapor content of a gas, as determined by dew point measurement, is inaccurate when the gas has been dehydrated with diethylene glycol. Water vapor contents and dew point measurements of gases dehydrated with triethylene glycol have been obtained in this investigation in order to determine the magnitude of a similar error, if one exists. Experimental data show a very low concentration of triethylene glycol vapor in gases dehydrated at atmospheric ternperatures and pressures ranging from 500 to 2,500 psia and that the accuracy of dew point measurements is not impaired by the presence of triethylene glycol vapor. INTRODUCTION Nearly all natural gas transported by pipe line to northern and eastern markets must be dehydrated to a low residual moisture content in order to assure maximum transmission efficiency and continuous delivery under peak load conditions. Without dehydration, water vapor often condenses in pipe lines in quantities sufficient to restrict the flow3 and. under low atmospheric temperature conditions, gas hydrates may form and plug gathering. transmission and distribution facilities. Gas may be dehydrated to pipe line specifications by a number of methods. The most widely used methods are (1) adsorption of water vapor on a solid dessicant such as activated bauxite, alumina or silica gel,' (2) by absorption of water vapor by either diethylene or triethylene glycol-water solutions of high glycol concentration,11,13 and (3) by simultaneous expansion-refrigeration of very high pressure gas in which gas hydrates are purposely formed and then quickly decomposed.'"" Of these three fundamental methods, the adsorption and absorption processes provide the bulk of the dehydrated gas moving to market at the present time. The expansion-refrigeration process. a relatively new development, is gaining in favor because of its simplicity but is sharply limited in its application by available differentials between source and gathering system pressures. Where gas sale or purchase contracts contain a maximum water vapor content specification, the water vapor content is usually determined by measuring the dew point of the gas at system pressure. Knowing he dew point temperature and the system pressure, the water vapor content of the gas is determined from a graphical correlation of saturation, or dew point, temperature us the water vapor content of the gas which is customarily expressed as pounds of water vapor per million cubic feet of gas measured at 14.7 psia and 60°F. Dew points are usually measured with the U. S. Bureau of Mines Dew Point Tester. shown in Fig. 1, which is well suited for use at temperatures lower than 120°F and at pressurei; ranging from atmospheric to 3,000 psi. A number of correlations of dew point temperatures vs water vapor content are available,3,5,15 the most recent of which is that by McCarthy et al.4 Where natural gas is dehydrated by absorhing contact with concentrated diethylene glycol-water solutions. considerable difficulty is experienced in observing water dew points due to condensation of liquid hydrocarbon and glycol films on the mirrored surface of the dew point tester. Riesenfeld and Frazierl2 report that the dew point method for determining the water vapor content of a dietllylene glycol-treated natural gas is in error due to the glycol content of the condensate formed on the tester mirror, and that the water vapor content of the gas tested is actually lower than that indicated by the standard' dew point-water vapor content correlation. Extensive experience in testing gases dehydrated by concentrated triethylene glycol-water solutions lias not revesled difficulties of the nature cited above for diethylene glycol. Water dew points are clear and sharp and condensation of

Jan 1, 1951