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By A. B. Stevens, C. J. Coberly

The absolute porosity of a rock or sand may be defined as the volume of the interparticle space expressed as a percentage of the total rock volume. The effective porosity as contrasted with the absolute porosity is the volume of the interparticle spaces which intercommunicate with passages of sufficient size to permit the entrance or recovery of gas or oil, also expressed as a percentage of the total rock volume. A knowledge of effective porosity is of prime importance in estimating the ultimate recovery to be expected from oil and gas-bearing formations. The determination of the effective porosity of a rock includes the measurement of two values: (I) the volume of the rock as a whole, and (2) the volume of the grains and sealed pore space. This paper deals with a new apparatus which has been called a "hydrogen porosimeter" for determining the volume of the grains and the sealed pore space. This volume is determined by means of the pressure relations established in the instrument by the introduction of a known quantity of hydrogen. The Hydrogen Porosimeter The apparatus used in this work consists of an upper chamber for measuring the gas, a lower chamber for holding the sample to be tested, a gage for measuring the pressures, a tank of hydrogen, and the necessary connections. (Figs. 1 and 2.) Of the several gases that might be used for this work, hydrogen has been chosen for three reasons: (1) it deviates less from the gas laws than most gases; (2) it readily penetrates the sample; (3) it is absorbed less than most gases by the solids and liquids with which it may come in contact. Method of Operation After placing the sample to be tested in the lower chamber, the apparatus is thoroughly flushed with hydrogen to remove all air from the system, which is then brought to atmospheric pressure Po. The valve connecting the two chambers is next closed and the pressure in the upper chamber is brought up to a pressure PI by admitting gas from the tank.

Jan 1, 1933

By J. D. Exner

With the introduction of rotary drilling in the Gulf Coast area, some thirty-two years ago, and its subsequent spread to other producing localities in the United States, there has been a constant change in the design of equipment. Only the general features remain, namely the rotating drill stem and the circulating mud. Only recently have the properties of mud and their behavior received attention from petroleum engineers, but circulating problems in present deep drilling demand further study and understanding. It is the purpose of this investigation to determine the relative changes in the apparent viscosity of muds with changes in temperature and to discover other physical effects due to heat. Very little information has been published regarding the effects of temperature on the viscosity of drilling muds. Maustl states: "The viscosity of most muds is decreased on heating, but the interesting thing is that the degree of flocculation is also increased on heating. There will be a greater tendency to seal off formations at high temperatures than at low temperatures." With regard to the effect of temperature on viscosity and yield point, Herrick2 states: "The variation of yield point and viscosity of mud with temperature.....is not very clearly brought out by the data available. Both appear to decrease slightly with increasing temperature up to 200' F." The experimental results presented in this paper further emphasize this point. Two types of viscosimeters are available for measuring the apparent viscosities of drilling muds: the efflux tube type as used by Herrick3 and Marsh, and the torsional type such as the McMichael or the Stormer viscosimeters. Because of its extensive use in measuring the apparent

Jan 1, 1933

By H. C. Fowler

No exact demarcation can be made between producfion engineering and engineering research projects which interest production engineers because the results of today's engineering research make possible many of the applied production engineering methods of tomorrow. A corollary of the development of fundamental research is that so-called practical research becomes necessary. Assuming engineering research to include all subjects related to oil and gas production on which knowledge is being increased through experimentation and through analyses of data obtained from both the laboratory and the field, a review of the work of 1932 shows that the fundamental concepts of at least three major problems have become better understood—bottom-hole pressures, solubility of gas in oil, and fluid movement—and that the established data on the relationships of oil and gas have been applied to obtain more efficient and more economic production of both. Engineers no longer are concerned primarily with the initial development of devices for obtaining the pressures at the bottom of wells. Advancement in the technique of obtaining reliable pressure readings in wells has been rapid. One of the first public suggestions regarding apparatus for obtaining precise information at the bottom of oil wells was made before the Petroleum Division of the A.I.M.E. in 1928. Even during the early development stages in East Texas, reservoir pressures were estimated from well-head observations. Soon, however, a number of proved devices and methods were available, and today bottom-hole pressures in many fields are being recorded and studied as an essential part of the production programs. The research now turns to interpretations of data, obtained with these devices, in terms of reservoir energy and to the development of methods whereby the oil and gas will be withdrawn in accordance with rational and equitable programs based on oil-gas-energy relationships. The term ((bottom-hole pressures" should not be interpreted as indicating the full scope of all research on this problem. By using pressure (and temperature) data obtained in related vertical-flow studies,

Jan 1, 1933

By Stanley Gill

The apparatus is composed of sections of small diameter, seamless steel tubing welded into a continuous flexible tube. At the bottom end a 1/4-in. pipe nipple with a 10 to 15-lb. weight is attached, together with a registering thermometer and a pair of ball check valves. The entire length of tubing is coiled in a single layer upon a drum 4 ft. in diameter which can be attached to the platform of a truck and provided with devices for winding and unwinding the tubing. Connections are made with the upper end of the tubing through a stuffing box, thence to a gas manifold to which a pressure gage is connected. Hydrogen gas is carried in standard 2-ft. cylinders and readings are taken by admitting gas into the tubing from one (or both) of the hydrogen cylinders until the pressure has been built up above that to be measured. At this time the gas supply is cut off. Excess gas escapes through the open end of the tubing and when equilibrium is reached, the pressure is read at the surface gage. Corrections are made for the weight of the column of gas. The advantages claimed for the apparatus include accuracy and the ability to measure the pressures at any number of points without removing the gage. Among the disadvantages of the apparatus are the somewhat bulky size of the equipment and its relatively high initial cost.

Jan 1, 1933

By K. B. Nowels

The attainment of efficient flooding to a large extent depends upon a knowledge of fluid movement through porous media and the pressures used in controlling this movement. Little has been understood con-cerning the fundamental principles involved in the forced drive of water-flooding and an attempt will be made to present some data which may be of interest. Considerable data and technical information pertaining to natural and artificial water-flooding have been presented in the past by Torrey, Umpleby, Fettke, Panyity and others. Their papers have thoroughly covered the description of past and present-day methods of oil recovery by flooding in the Bradford field, especially an article by Torreyl in the Petroleum Engineering Handbook. A bibliography of papers devoted to watcr-flooding, published in Mr. Torrey's article, is appended to this paper. No attempt has been made, therefore, to describe the installations and procedure necessary in flooding, thus permitting the writer to deal exclusively with the mechanics of water movement in flooding operations and its relationship to well spacing. Artificial water-flooding will probably always be the most successful in oil fields described by Herold as being under "capillary control"" and will probably be useless in fields naturally under hydraulic or volumetric control. The natural water drive in an oil field under either of these two controls may give efficient recoveries, as a result of the regulated encroachment of edge water. Such a "natural flood" resulting from the influence of edge water must not be confused with the term as used in this paper, however. Any reference to "natural flood" will here refer to the old method of flooding formerly used in the Bradford field. This was discovered largely by accident and utilized the hydrostatic pressure created by a column of water standing in a watered-out oil well in forcing the oil to an adjacent producing well. The same principles are involved in either natural or artificial flooding, and the latter method simply

Jan 1, 1933

By E. A. Stephenson

In spite of tremendous handicaps notable advances in production engineering have been achieved during 1932. The technique of deep well drilling has continued to progress, notably in California and at Big Lake, Texas. In the latter field a method has been devised by which two grades of oil in contact with each other are produced without intermingling. In rig design many improvements have been made whose objective is to facilitate deep drilling with reduced power losses and increased life of the equipment. Flush joint casing and drill pipe have been improved further, careful tests indicating that the drilling time can be reduced by from 5 to 20 per cent where flush-joint pipe is used. Slow-speed pumping has come into wider use, with further increases in over-all efficiencies. A number of improved well pumps also have been developed and are being tested. One of the most important of these is a positive displacement pump of the rotary type, directly connected to an electric motor placed in the bottom of the hole, and adaptable to various sizes of tubing and casing. In some localities the trend is towards the replacement of electric motors and large-cylinder engines by multiple-cylinder gas engines. Experiments have been conducted and critical analyses made of flow conditions in wells equipped with various styles of tubing which give promise that tubing may be designed to fit individual well conditions. In those wells producing at less than maximum capacity, the gas-oil ratio has been shown to depend on the rate rather than on the method of production, or the design of equipment. Important factors in the design of screened pipe have been carefully analyzed and made the basis of a method for determining the required mesh. Remarkable progress has been made in the use of subsurface pressure data. In East Texas particularly, use of such data is providing a means for the control and equalization of water encroachment and is also pointing the way to a sound means of allocating to individual tracts an

Jan 1, 1933

By R. M. Barnes, A. H. Bell

The ideas set forth in this paper are proposed for consideration and discussion as the result of recent study of various plans for control and proration of gas and oil production from Kettleman North Dome oil field. They would be applicable to any oil field during its flush production stage. The problems of development and proration are so Fig. 1.—Ideal Cross-section, Kettleman North Dome Oil Field. intimately connected in Kettleman Hills and in many other flush fields that they have both been covered in this paper. Many are of the opinion that Kettleman North Dome oil field should be considered as containing only one zone to its present total penetrated thickness of nearly 1500 ft., and that the hydrocarbon content of this zone gradually changes from dark and relatively low-gravity oil with relatively low gas-oil ratios on the flanks and plunges to mostly light-colored and high-gravity oil with high gas-oil ratios in the higher structural positions, somewhat according to the idealized section shown in Fig. 1. At least the lower 400 ft. contains dark oil in the higher structural positions.

Jan 1, 1933

By C. V. Milikan

Allocation of allowed production in a prorated field by the use of bottom-hole pressures is a method which is sound in theory. Thus far it has had limited application because the experience in correlating bottom-hole pressures with the depletion of wells or fields is not sufficient to interpret all the pressure changes. With additional data and more general knowledge of bottom-hole pressures their use in proration will probably become common. Bottom-hole pressure is the pressure at or near the bottom of a well. It is usually determined at the face of the producing horizon. Bottom-hole pressure measured while the well is producing, may be called the bottom-hole producing pressure or bottom-hole flowing pressure. If the well has been shut in or shut down long enough for the pressure in the producing horizon within the drainage area of the well to equalize, it may be called the reservoir pressure. The allowable production from a prorated field may be allocated to the individual wells or leases by three methods: 1. Bottom-hole producing or flowing pressures. (a) The potential capacity of a well to produce. (b) A uniform differential pressure while producing at the allowed rate. 2. Reservoir pressures. 3. A combination of bottom-hole producing pressures and reservoir pressures. In most prorated fields the allowed production is allocated to the individual wells or leases in proportion to their individual potentials. This method is based on the theory that there is a direct relationship between the permeability and the porosity of the reservoir. More directly stated it means that there is a direct relationship between the amount of oil in the reservoir and the rate at which it will move through the reservoir. While in general this relationship is true, it may vary considerably in different wells. Furthermore, in many wells the capacity of the reservoir to deliver oil to the well is greater than the capacity of the flow string to deliver oil to the surface. It is especially true where the potential is determined by flowing through tubing or by pumping.

Jan 1, 1933

By Clifford S. Wilson

ScReened pipe is designed with the view of restraining the fine, free-running sands of the production zone from entering oil wells. Its successful use is dependent on a number of factors. The nature and effects of some of these factors can be determined through experiment and observation, but some of the elements that have a distinct bearing on the use of screened pipe can be evaluated only by estimate. The important subsurface conditions which affect the use of screened pipe are: 1. Depth of production zone. 2. Extent of production zone. 3. Reservoir pressure. 4. Character and relative quantity of oil and gas. 5. Character of sediments: a. Cossolidation of beds. b. Variation in beds. c. Grain-size gradation of sands. d. Free-running characteristics of sand from different levels. Aside from the use of mechanical equipment and tools, the measures to be taken in the installation of screened pipe involve: 1. Size of liner. 2. Length of liner. 3. Design and mesh of screen. 4. Portion of liner to be screened. 5. Manner of setting liner. 6. Preparation of or washing of the well before or during the setting of the screen. 7. Manner of bringing in the well. 8. Manner of flowing the well. Values applicable to the actual subsurface conditions that exist at any well can only be approximated. The accuracy of the estimate will be measured by the amount and quality of the evidence at hand and the personal factor of ability to interpret the evidence fairly, whether

Jan 1, 1933

By F. G. Tickell, R. C. McCurdy, O. E. Mechem

The behavior of fluids in the voids of a rock is fundamental to the study of many of the problems of oil-field development and production. For it is by virtue of these openings between grains that oil and gas are able to move through the rock, to be contained by the rock, and to pass from the rock into the well. The capacity to contain fluids is measured by the porosity of the rock, and the ease of fluid movement is governed by the permeability. When the engineer wishes to estimate the amounts of oil and gas in an underground reservoir he is often concerned with the porosities of the rocks and, when dealing with problems relating to rate of production, he is more likely to be interested in the permeabilities of the rocks. Rocks are permeable because they are porous, but they may be porous without being permeable. Clays are very porous, and yet they are impermeable from a practical standpoint. Attempts have been made1 to correlate permeability with porosity for certain rock members but, where a definite relationship between these two properties is found to hold, it is purely fortuitous and local. Porosity and permeability do not necessarily bear any quantitative relationship to one another. The porosity of a substance is the percentage of void volume to bulk volume. The petroleum engineer is usually interested only in the inter-granular voids that are accessible to fluids. In measuring porosity he does not wish to include scaled openings. The measurement he desires is one of "available porosity," otherwise called "apparent porosity." The porosity of a natural aggregate of solid grains, such as a sandstone or clay, is governed by: (1) Grain-size distribution, (2) angularity of grain, (3) colloidal content, (4) degree of compaction. It is not difficult, for unconsolidated rocks, to measure the effect of any one of these when it alone is varied, and then to predict what the effects on porosity will be for such single variables. It is very difficult, however, if not

Jan 1, 1933

By D. J. Hawthorn

The widespread interest shown during the past year in the study of subsurface pressures warrants brief reference to its early development. Though it is impossible to set an exact date when constructive thinking on the subject first began, nevertheless, evidence is available that thought was given to the problem as far back as 16 or 1.7 years ago. There is record in one of the foreign journals of actual subsurface tests made by crude methods in one of the Rumanian fields in 1918 and 1919.' These tests were performed in conjunction with studies made on wells produced by bailing and, incidentally, the final outcome of the work led to the development of the so-called "duplex bailer" which is reputed to have trebled volumetric bailing efficiency. From this time on to 1927 a few scattered bottom-hole pressure determinations were made with makeshift instruments of one form or another, but probably not until 1927 was any great amount of concerted effort directed to the subject. At this fall meeting of the Petroleum Division four years ago was presented one of the first papers2 to appear in this country written for the express intent of advocating the value and importance of subsurface pressure determinations. It is thought to have been the first to present direct data on subsurface pressures obtained through the use of a specially designed recording instrument. As might be expected, the instrument had its limitations, but reasonably accurate results were obtained and, to say the least, it constituted a progressive step in the right direction. During the period from 1927 to 1931, many noteworthy improvements were made in the design and perfection of subsurface pressure instruments suitable to meet all conditions. Because of the magnitude of this task much credit is due the men who pioneered this work. They should feel a keen sense of satisfaction in the thought that their efforts have paved the way for the continuation of this most valuable study. At the present time more than a dozen companies are operating subsurface pressure instruments in the Mid-Continent field. Engineers in

Jan 1, 1933

By R. Silent, N. A. Rousselot

The first producing wells completed in the Kettleman Hills arca were noteworthy for their high gas-oil ratios. As a result they became the object of criticism, and controversies arose based on their alleged lack of gas conservation. Ultimately protracted hearings ensued in the District Court of the area, and diverse rulings and subsequent modifications have been handed down affecting the permissible gas-oil ratios. When the Kettleman North Dome Association was formed in April, 1931, and the control of the major portion of the North Dome area vested therein, it was decided to produce only those wells which had a relatively low gas-oil ratio. Among the wells having the highest gas-oil ratio were the Milham Elliott No. 1 (the discovery well) and the Continental Elliott 12-8. drilled as an offset to it. Under the numbering system adopted by the Kettleman North Dome Association, these wells are now known as 88-2P and 1-12P, respectively. Milham Elliott No. 1 was originally drilled to 7236 ft., then redrilled to 7108 ft. The upper portion of the Temblor Horizon produces with a very large gas-oil ratio; production which actually consists of light crude oil with an accompanying large.volume of gas. Little was known as to the location of the Temblor formation at that time but it is now generally accepted that its top was encountered at 6180 ft., giving 928 ft. of penetration. Initial production was estimated at 4000 bbl. of oil and 80 to 90 million cubic feet of gas per day, giving a gas-oil ratio in excess of 20,000 cu. ft. of gas per bbl. of oil. This ultimately increased to a ratio of about 48,000 at the time the well was killed when it was producing about 1100 bbl. of oil and 52 million cubic feet of gas, with a flow pressure of 1200 pounds. The Continental Elliott 12-8 was drilled to a depth of 6876 ft. with the top of the Temblor at 6100, giving a penetration of 776 ft. The estimated initial production of this well was 7000 bbl. of oil and 130

Jan 1, 1933

By M. Muskat, R. D. Wyckoff, H. G. Botset

The flow of liquids through porous media is known to follow Darcy's law which states that the velocity of flow is proportional to the pressure gradient. This law is but a statement of the facts obtained from experimental studies and is, therefore, uncontroversial. It should be men-tioned, however, that it applies only when the flow is viscous in nature and that at excessive velocities which tend to produce turbulence, the velocity is proportional to some power of the pressure gradient, the exponent ranging from 1 to 0.5 as the degree of turbulence increases. However., experiments with media having permeabilities corresponding to those of actual producing horizons show conclusively that the actual flow of liquids in a producing horizon must be viscous except perhaps in the immediate vicinity of a well producing at a high rate. Therefore, one is justified in assuming Darcy's law to hold for cases of practical interest, as will be implicitly assumed in this discussion Given this basic law of flow it is possible, theoretically to obtain solutions to any problem of viscous flow of dead liquids1 by the usual methods of potential theory. However, problems of practical interest often present such complex geometrical configurations of sources and sinks (driving sources and output wells) as to make the analytical solutions extremely difficult or even impossible. It is useful, therefore, to note that Darcy's law is precisely equivalent to the law of electrical conduction, so that the pressure distribution in steady state porous flow of liquids is exactly the same as the potential distribution in an electrical conducting medium.2 This analogy permits the use of electrical models wherein the potential distributions may be measured with far greater facility and accuracy than is possible in actual fluid-sand models. Such electrical models were used in determining the pressure distribution about complex arrays of wells, an example of which will be shown later in the discussion of the 5-spot flood. One phase of the porous flow problems which is of considerable practical interest involves the tracing of an advancing fluid front. Thus,

Jan 1, 1933

By E. H. Griswold

PETROLEUM production engineering is essentially the application of the laws of 'physics and mechanics to the production of oil. A true production engineer is one who can apply the principles of mechanics, hydraulics, thermodynamics, and other physical arts so as to facilitate' the efficient and economical recovery of oil. To this end he must have wide knowledge of practical field operations and a working knowledge of geology, with a thorough understanding of the underground state of the fluids which he seeks to control. Generally speaking, there have been two schools of production engineering, the California development and the Mid-Continent development. In California the preliminary production engineering was done by representatives of the U. S. Bureau of Mines and the State Mining Bureau, and was essentially subsurface work in regard to casing patterns, water shut-offs, and completion procedure, inasmuch as these were problems of the utmost immediate importance to the California industry. The oil companies were impressed with the value of such work and placed engineers, or more strictly speaking, engineering geologists on their field staffs. These men, realizing the need of further technical study in the mechanical phases of producing operations, added mechanical and mining engineers, and out of the blend developed what is now known as a production engineer.

Jan 1, 1932

By G. G. Brown

Enthalpy-entropy diagrams are presented for natural gases of 0.6, 0.7, 0.8, 0.9, and 1.0 gravity over the pressure range of 5 to 10,000 Ib. per sq. in. and temperature range of 32º to 700°F. The charts indicate directly the work requirement and temperature rise for adiabatic compression or temperature change for free emansion of natural eases. Computation and Uses of Charts The Mollier diagram (Fig. 4), in which the enthalpy (heat content) is plotted against the entropy with lines of constant temperature, pressure,, and in some cases volume, has been found most convenient when dealing with the compression, expansion, and flow of fluids. In dealing with the flow of fluids, the sum of the increase in the enthalpy, AH, plus the increase in kinetic energy, AM —, plus the increase in potential energy, ?MZ, representing the total increase in energy of the fluid in flow, is equal to the sum of the heat q, and work added, —w, to the fluid while flowing between the entrance and exit of the flow system. AH + AM— + ?MZ = q-w [1] In cases where there is no significant change in potential energy or in kinetic energy (velocity), it follows that the increase in enthalpy is equal to the total energy supplied to the fluid. Under such conditions' the changes in the property of the fluid as it flows through a throttling valve, choke, or any other similar arrangement, may be read directly from the enthalpy-entropy diagram by following a horizolltal line between the known pressures' When compressing Or expanding a gas by means of a Or or engine in which no heat is added to or subtracted from the gas, but only work done, the changes in the properties of the gas may be determined along a vertical line of constant entropy between the entering and exit pressures. The power required for the compression of the gas may be readily determined by converting the increase in enthalpy into the desired units. The enthalpy-entropy diagram for natural gases is to the gas engineer what the steam diagram is to the steam-power engineer. For this reason it would be extremely convenient if a reasonably satisfactory enthalpy-entropy diagram could be prepared as a function of the gravity of the gas. A careful study of the known properties of natural gas indicate that this is possible. The effect of temperature upon the enthalpy at constant pressure is expressed as the "heat capacity" or "specific heat" of the gas. The best available data for natural and petroleum refinery gases indicates the relationship shown in Fig. I. From this it is clear that the specific heat of natural gases is a function only of the gas gravity and the temperature at atmospheric pressure. The effect of pressure on the enthalpy of natural gases is dependent upon the pressure-volume-temperature relationships,

Jan 1, 1945

By Jan Law

Problems of oil recovery are attacked from the approaches dictated by the two strikingly dissimilar complexes that comprise an oil reservoir—the fluid complex and the interstitial complex. Knowledge of the fluid complex, due to labors in the fields of fluid mechanics and physical chemistry, has far outdistanced knowledge of the interstitial characteristics of the sand complex. This paper is concerned with the latter and applies the technique of statistics to petrographic facts—namely, porosity and permeability—dealing with what might be called petrometry. Statisticians have long worked within the problem of reconstruction of a universe oi variables by means of samples that comprise a small percentage of the universe from which the samples were drawn. Core-analysis data comply with the requisite of random sampling as stipulated by theoretical statistics. A basic concept of statistics employs t.he following substitution: 1. The results of sampling are arranged as a frequency distribution. 2. The observed frequency distribution is compared with a mathematically precise distribution. 3. If a sufficiently good agreement is found between the two, the precise distribution is substituted in all subsequent operations involving characteristics of the sampled material. This mathematically precise distribution is also known as the normal curve, curve of error, the probability, the Gaussian, and the bell-shaped curve and is describable with but two figures. Further, these two figures, the arithmetic average and the standard deviation, are subject to mathematical manipulation. This paper demonstrates that, in some cases in the Dominguez field of Southern California, if sufficient core-analysis samples are taken over not too great a thickness of sediments, the resultant permeability and porosity assemblages give satisfactory agreement with ilormal curves. It is shown that the indications are strong that oil wells wherein a satisfactory agreement is found are predictable as to productivity. Since the predictions are made by employing the laws of chance that are operative within sedimentation, it follows that the mechanism by which the predictions were made is a basic concept of reservoir mechanics. Therefore, tentative examples are given of the application of normal curves to the solution of problems of primary and secondary recovery. Nature of Permeability Frequency Distributions Core-analysis data are made available as a tabulated depth vs. permeability profile. The nature of the distribution of permeability values within a given strati-graphic interval may be approximated from an array constructed with samples plotted in the order of their appearance with depth (accession number) against their permeability value in millidarcys. A wide variation in the nature of the distribution of K (permeability) values for

Jan 1, 1944

By Jan Law

Problems of oil recovery are attacked from the approaches dictated by the two strikingly dissimilar complexes that comprise an oil reservoir—the fluid complex and the interstitial complex. Knowledge of the fluid complex, due to labors in the fields of fluid mechanics and physical chemistry, has far outdistanced knowledge of the interstitial characteristics of the sand complex. This paper is concerned with the latter and applies the technique of statistics to petrographic facts—namely, porosity and permeability—dealing with what might be called petrometry. Statisticians have long worked within the problem of reconstruction of a universe oi variables by means of samples that comprise a small percentage of the universe from which the samples were drawn. Core-analysis data comply with the requisite of random sampling as stipulated by theoretical statistics. A basic concept of statistics employs t.he following substitution: 1. The results of sampling are arranged as a frequency distribution. 2. The observed frequency distribution is compared with a mathematically precise distribution. 3. If a sufficiently good agreement is found between the two, the precise distribution is substituted in all subsequent operations involving characteristics of the sampled material. This mathematically precise distribution is also known as the normal curve, curve of error, the probability, the Gaussian, and the bell-shaped curve and is describable with but two figures. Further, these two figures, the arithmetic average and the standard deviation, are subject to mathematical manipulation. This paper demonstrates that, in some cases in the Dominguez field of Southern California, if sufficient core-analysis samples are taken over not too great a thickness of sediments, the resultant permeability and porosity assemblages give satisfactory agreement with ilormal curves. It is shown that the indications are strong that oil wells wherein a satisfactory agreement is found are predictable as to productivity. Since the predictions are made by employing the laws of chance that are operative within sedimentation, it follows that the mechanism by which the predictions were made is a basic concept of reservoir mechanics. Therefore, tentative examples are given of the application of normal curves to the solution of problems of primary and secondary recovery. Nature of Permeability Frequency Distributions Core-analysis data are made available as a tabulated depth vs. permeability profile. The nature of the distribution of permeability values within a given strati-graphic interval may be approximated from an array constructed with samples plotted in the order of their appearance with depth (accession number) against their permeability value in millidarcys. A wide variation in the nature of the distribution of K (permeability) values for

Jan 1, 1944

By W. A. Bruce

Studies of reservoir behavior of 12 Smackover limestone oil and condensate pools are presented. Buckner, Midway, McKamie, Magnolia, Mt. Holly, Schuler (Reynolds) and Village are treated in considerable detail and subjected to analysis with an electrical device for analyzing reservoir behavior. Results and comparisons of these analyses are presented. In addition to these reservoir-behavior studies, an attempt is made to assemble trans-missibility and storage data on the Smackover limestone formation from cores and logs taken in dry holes and producers. This together with the behavior of individual reservoirs leads to a better understanding of the formation as a porous aquifer. The ultimate purpose of this type of study is to improve predictions concerning the future behavior of these pools in such a system. Predictions are presented for several pools. Introduction In 1937 the Phillips Petroleum Co. drilled its J. D. Reynolds No. I to the Smackover limestone formation at Snow Hill, Arkansas. This well found oil in the porous, permeable, upper part of the Smackover, thereafter referred to as the Reynolds lime. Since then, six oil pools and six condensate pools have been discovered in the Reynolds lime, and more than 75 dry holes have explored parts of this formation. By the first of 1943, 44 million barrels of oil and 83 billion cubic feet of gas had been withdrawn from the various reservoirs. The original reserves estimated by the Arkansas Oil and Gas Commission were 342 million barrels of oil and rzoo billion cubic feet of gas. So far all of the production has been from anticlinal structures, most of which are asymmetric and have their axes roughly perpendicular to the dip of the formation top. This is indicated in Fig. I, which shows the pools, dry holes drilled, and contours on top of the Smackover.' These pools are of particular interest for reservoir-behavior studies because the production and drilling has been controlled, and in most cases the records of reservoir data are complete. In addition to the excellent production and pressure information available, more than one half of the wells drilled were cored and all of them were electrically logged. All of the pools show evidence of water drive. While this paper is in a sense a collection of reservoir-behavior studies for several different pools, there has been an attempt to go one step further and to show the importance of the iormation as a porous continuum or a single aquifer in which the withdrawals of fluids from any pool has an important effect on the behavior of all of the pools. An effort will be made to show that the water drives of these pools are dependent upon a much larger area of the Smackover limestone than that occupied by the petroleum accumulations.

Jan 1, 1944

By W. A. Bruce

Studies of reservoir behavior of 12 Smackover limestone oil and condensate pools are presented. Buckner, Midway, McKamie, Magnolia, Mt. Holly, Schuler (Reynolds) and Village are treated in considerable detail and subjected to analysis with an electrical device for analyzing reservoir behavior. Results and comparisons of these analyses are presented. In addition to these reservoir-behavior studies, an attempt is made to assemble trans-missibility and storage data on the Smackover limestone formation from cores and logs taken in dry holes and producers. This together with the behavior of individual reservoirs leads to a better understanding of the formation as a porous aquifer. The ultimate purpose of this type of study is to improve predictions concerning the future behavior of these pools in such a system. Predictions are presented for several pools. Introduction In 1937 the Phillips Petroleum Co. drilled its J. D. Reynolds No. I to the Smackover limestone formation at Snow Hill, Arkansas. This well found oil in the porous, permeable, upper part of the Smackover, thereafter referred to as the Reynolds lime. Since then, six oil pools and six condensate pools have been discovered in the Reynolds lime, and more than 75 dry holes have explored parts of this formation. By the first of 1943, 44 million barrels of oil and 83 billion cubic feet of gas had been withdrawn from the various reservoirs. The original reserves estimated by the Arkansas Oil and Gas Commission were 342 million barrels of oil and rzoo billion cubic feet of gas. So far all of the production has been from anticlinal structures, most of which are asymmetric and have their axes roughly perpendicular to the dip of the formation top. This is indicated in Fig. I, which shows the pools, dry holes drilled, and contours on top of the Smackover.' These pools are of particular interest for reservoir-behavior studies because the production and drilling has been controlled, and in most cases the records of reservoir data are complete. In addition to the excellent production and pressure information available, more than one half of the wells drilled were cored and all of them were electrically logged. All of the pools show evidence of water drive. While this paper is in a sense a collection of reservoir-behavior studies for several different pools, there has been an attempt to go one step further and to show the importance of the iormation as a porous continuum or a single aquifer in which the withdrawals of fluids from any pool has an important effect on the behavior of all of the pools. An effort will be made to show that the water drives of these pools are dependent upon a much larger area of the Smackover limestone than that occupied by the petroleum accumulations.

Jan 1, 1944

By Rex W. Woods, Morris Muskat

A leastmsquare analysis procedure has been developed and applied for the study of the deviations in estimations of oil in place as given by the material-balance equations. The data used were those obtained from field observations on the Jones sand in the Schuler pool, Arkansas, and the Monroe dolomite in the Reed City pool, Michigan. Possible effects of water intrusion were taken into account by expressing the cumulative water influx in terms of various functions previously proposed in the literature. Formulas were developed and values calculated for the minimum deviations and minimal percentage deviations in the calculated volumes of oil in place from the average values, as could be obtained by suitable choice of the water encroachment and initial gas-cap volume parameters. The results show that the fluctuations in these calculated volumes are very insensitive to the values chosen for the rate of water intrusion and initial gas-cap volume, and hence cannot be safely used in discriminating between spurious values for these parameters and such as actually pertain to the producing reservoirs. Moreover, the exact form of the water-intrusion function seems to have but little effect on the fluctuations in the computed oil in place. Accordingly, it is concluded that the material-balance method does not of itself provide a satisfactory criterion for determining the basic physical unknowns of producing reservoirs or in making conclusive decisions regarding the production mechanism, unless independently established geological control data are available for eliminating unreasonable values for the reservoir parameters, even though they may still satisfy the material-balance formulas. If, however, from core or logging data the initial oil in place and the gas-cap volume can be established in advance, the material-balance formulas can be inverted to find the water intrusion. Moreover, by determining by such calculations the water-intrusion coefficient, the iuture production performance can then be predicted by the aid of the materiaI-balance formulas for specified operating conditions. This type of application may be of particular value in predicting the results of Pressure-maintenance operations. Introduction The evaluation of the forces acting upon an oil reservoir is a problem of considerable interest to the operator as an aid in determining the proper method of operation for the reservoir to obtain an optimum recovery of oil. In many pools, the nature and magnitude of the forces acting upon the reservoir remain unknown until an appreciable amount of ultimate recovery is obtained. To be of value to the operator, a reliable interpretation of reservoir performance should be available in the early life of the pool to permit an optimum plan of operation. Progress has been made in an understanding of reservoir behavior and the importance of the different factors involved. The material-balance method of estimating oil in place has been proposed as a tool in analyzing reservoir-performance problems.l The solution of such problems by this method ordinarily involves two or more unknown values relating to the nature of the reservoir, and the results

Jan 1, 1945