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By J. S. Rinehart, W. C. Maurer

The mechanics of impact crater formation in rock, particularly sandstone, has been sutdied, the velocity range being approximately that normally associated with oilwell gun perforators. The bullets were small steel spheres having diameters of 3/16, 9/32 and 7/16 in; impact velocities ranged from 300 to 7,000 ft/sec. The craters have two distinct parts — a cylindrical hole (or burrow) with a diameter the same as that of the impacting sphere, and a wide-angle cup comprising most of the volume of the crater. The burrow is fornred as material in front of the projectile is crushed and pushed aside, forming a cylindrical hole surrounded by a high-density zone. The clip forms as fractures are initiated in front of the projectile and propagate along logarithmic spirals, approximaling maximum shear trajectories, to the free surface of the rock. A most significant observation (made for the first time) was that, below the base of the cup in one type of sandstone, there are a group of similar fractures, not extending to the surface, which are spaced uniformly a few millimeters apart. Each fracture follows roughly the contour of the base of the cup and appears to require a certain threshold impulse to initiate it. These fractures comprise a relatively high fraction of the total, newly exposed surface area. The volume of the material removed by crushing varies as the first power of the impact velocity and the volume removed by fracturing, as the second power of the impact velocity. Penetration varies linearly with the impact velocity and is inversely proportional to the specific acoustic resistance of the target material, the proportionality constant being dependent upon the shape of the projectile. INTRODUCTION Yield of oil from a producing well is frequently enhanced by firing bullets and shaped charges through the well casing into the oil-bearing rock, forming craters and fractures from which oil can flow more readily. The purpose of this investigation has been to develop a better understanding of the mechanics of impact crater formation in rock, particularly sandstone, the velocity range being approximately that normally associated with oilwell gun perforators. FORCES OPERATIVE DURING IMPACT When a projectile moving at considerable velocity strikes a- massive target such as oil-bearing sandstone, intense and complex transient stress situations develop within both the projectile and the rock or sandstone against which it is striking. Usually the struck rock fails, the missile or projectile penetrating into the rock to some depth where it comes to rest or is forcibly ejected from its burrow by expansion of a plug of target material compressed in front of it. When the impact velocity is very high, the projectile itself may fail, breaking apart or becoming distorted; this situation is not considered here, the discussion being limited to nondeforming projectiles. Many experimental studies'.' have been carried out to determine the nature of the mechanics of crater formation and the salient features of the forces coming into play, some of the earliest studies being the French Army experiments performed at Metz between 1835 and 1845.' The stratagem in most instances has been to make a post-mortem examination of the crater, measuring volume and depth of penetration and deducing force relationships from these observations rather than performing the more difficult (usually almost impossible) feat of measuring stresses during penetration. In many materials, the force acting during penetration of the projectile is found to be the sum of two components—(1) a constant force, independent of the velocity, representing some inherent strength of the target material; and (2) a component, proportional to the square of the velocity, representing inertial forces. For such materials, the average force per unit area acting on the projectile at any instant while it is in motion and being decelerated may be written F/A = a + bv2 . . . (1) where v is the velocity of the projectile at that instant, A is the cross-sectional area of the penetrating projectile taken normal to its trajectory, and a and b are constants which are dependent upon the target material and the shape of the projectile. It follows that the total penetration s is given by .........(2) where v, is the velocity of the projectile when it just strikes the target. Values of a and b for spherical projectiles impacting in a loose sand-gravel mixture and compacted earth were obtained in the Metz experiments. For sand-gravel, a and b are 620 psi and 0.0115 (psi) (ft/sec)', respectively; and for compacted earthworks, a and b are 432 psi and 0.0008 (psi) (ft/sec)'. Figs 1 and 2

By A. A. Venghiattis

This paper is discussed not because of its intrinsic value but because it has been related by its authors to the oilwell gun perforators. It is well known that conditions almost ever present in oilwell perforations are the overburden and the presence of the casing. Because of the lack of information in the paper on the dimensions or confinement of the target rocks, one is led to guess that they were not confined at all and, particularly, that no steel front plates were used on the impact face of the rocks to materialize the presence of the cemented casing. This situation, plus the fact that small steel balls have been used as projectiles instead of actual bullets, makes the whole thing unapplicable to oilwell perforation. When shooting is performed against target rocks confined (as shown on Fig. 1) in such a way as to give a fair image of the overburden applied to the formation to be perforated, as well as of the cemented casing, the following are found. 1. There is no cratering worthy of mention, even with bullets having 10 times higher impact energy per unit projected area than the steel balls mentioned in the article. This has been confirmed with sandstone as well as with other rocks (granite, limestone and chalk). See Figs. 2 and 3. 2. Penetrations vary closely as the logarithm of the impact velocity. On this matter I have established the relation

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

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

By J. B. Scott, J. L. Popham, H. F. Coffer, J. J. Reynolds

This paper concerns field experiments to define the areal extent, orientation and thickness of an artificial fracture in the Sacatosa field, Maverick County, Tex. The fracture was made by a sand-oil treatment of 176,-000 gal of lease crude containing a fluid-loss additive and 270,000 lb of 20-40 mesh subangular Poteet sand. The well was perforated with a jet gun, consisting of six shots in a single plane. Fourteen test holes were drilled at various locations around the fractured well. Drill-stem tests, Micro and Sonic Logs, coring and sampling of formation cuttings were used to determine the presence of the fracture in these holes. The test holes were drilled at distances up to 250 ft in a radial pattern around the fractured well. In addition to fracture areal extent and orientation, sand grain size before and after fracturing, erosion of perforations and fracture thickness were studied. INTRODUCTION The orientation,12 areal extent3, 4 and thickness5-9 of artificially induced fractures in reservoir rock by hydraulic means have been discussed in great detail in the oil industry in recent years. Methods for initiating vertical"' and horizontal" fractures have been tested in the laboratory and the field. Although the methods used give successful well stimulation, good field data on the physical characteristics of the fracture are lacking in the literature. It is recognized generally that properties of a fracture, such as thickness, sand placement in the fracture" and shape, may vary from reservoir to reservoir. This paper gives data on size, orientation and sand placement in a large fracture initiated in a single plane in Sacatosa field, Maverick County, Tex. It is not intended as a speculative study; rather, it is restricted to actual field data on fracture properties. No attempt is made to prove that the same type of fracture occurs in all wells. The field procedure was to drill 14 test holes at various locations around the fractured well. By employing several different testing techniques, the presence of the fracture and some of its characteristics were determined. These techniques as well as the results obtained are discussed in detail in this paper. DESCRIPTION OF FRACTURE TREATMENT N. J. Chittim Well No. 37-1, completed in the San Miguel No. 1 sand, Sacatosa field, Maverick County, Tex., was chosen for the field study. The San Miguel sand is a tight, well consolidated sandstone with an average porosity of 23 per cent. The permeability ranges from 0.1 to 10 md, with a median permeability of 2.3 md. The sand thickness averages 23 ft and is located at depths of 1,150 to 1,700 ft throughout the field.I3 The fracture treatment performed on Well 37-1 was as follows. 1. The well was drilled to a depth of 1,438 ft with native mud, and 51/2-in. casing was set and cemented to the surface. 2. The casing was perforated at 1,349 ft with a fracture-initiating jet gun. This gun consists of six shots, 7/16-in. diameter in a single horizontal plane. The jets were oriented in two groups of three, 180" opposed. The perforating device was designed to initiate a fracture perpendicular to the wellbore.

By H. J. Beach

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

By W. A. Walker, G. W. Ostroot

An increase in the number of deep wells being drilled where extreme bottom-hole temperatures are encountered, and the anticipated drilling of wells where temperatures in the range of 500°F or higher may occur, has brought about a comprehensive investigation of cementing materials and of the techniques involved in their proper usage at these elevated temperatures. Included are developments in cements, retarders, weighting materials and other cement additives which make it possible to formulate a variety of compositions to help resolve the cementing problems of these extreme well conditions. The problems associated with the selection and testing of cements are discussed, and a resume of field results is included. Previous studies on strength retrogression indicate that caution should be exercised in the selection of a cementing composition for use in high-temperature wells. It now appears that, by the addition of silica flour as a stabilizing additive to certain cements, compositions covering a wide range of slurry densities can be designed to meet extreme well conditions without strength retrogression. Improvements in cement retarders make it possible to produce a four-hour thickening time at static temperatures up to 500°F. This temperature is considerably higher than conditions presently being encountered in drilling and completion work. Inert weighting materials, used to produce 20-lb/gal or heavier cement slurries, are reviewed. INTRODUCTION As the search for oil continues, the number of wells being drilled to depths of 10,000 ft or below has continued to increase over the past decade. During 1959, there were 50,893 wells drilled in the United States for a total of 209 million ft of hole. Of this total, approximately 4.45 per cent were drilled below 10,000 ft and 0.30 per cent below 15,000 ft, with a record depth of 25,340 ft recorded (Table 1). With the drilling of this record-shattering hole comes the question, "How deep can wells be drilled?".' Limitations with respect to equipment (surface and subsurface), cementing materials and techniques would cause some concern; however, a panel of experts have agreed that the U. S. oil industry has the equipment and know-how to drill a 50,000-ft hole. The greatest deterrent would be the 700°F temperature they would anticipate encountering at this depth. Although the number of wells drilled under what is generally considered hot-hole conditions (230°F and higher) has been relatively high, each well often presents distinctly individual problems and requires separate consideration and selection of special materials, techniques and equipment. At the present time there are over 30 additives and special cements available for use in "tailoring" a cementing composition for a specific well. It is not uncommon to use three or four different additives with the basic cement to produce the desired slurry characteristics. A generally accepted procedure is to make laboratory tests on selected cementing compositions prior to pumping them into wells deeper than 12,000 ft, or where static temperatures are in the range of 260°F or higher. In some instances, it is recommended that laboratory tests be made where less severe well conditions are encountered. Prior to selecting a cementing composition for a particular well, key personnel representing the operator, drilling contractor and service company should meet to determine that each individual is acquainted with every detail which might influence cementing results and to discuss the execution of the job. For cementing hot-holes, a number of factors must be evaluated before proceeding with the operation. Consideration must be given to the following. 1. Thickening time—The slurry must remain fluid for a sufficient length of time to allow displacement down the casing and up the annular space in a primary cementing job or, in squeeze-cementing, adequate thickening time for both the build-up of a satisfactory squeeze pressure and the reversing out of excess cement. The thickening time of standard retarded cements will often be too short under extreme temperature conditions, thus involving special formulations and requiring laboratory tests to determine the proper amount of additional retarder to obtain the desired pumpability.

By F. C. Pittman, D. W. Harriman, J. C. St. John

This paper mentions briefly the history of hydraulic jetting as applied to perforating and fracture initiation. It points out the advantages of hydraulic perforation and undercutting as an aid for creating a fracture at the point desired rather than depending upon the weakest point in the formation for breakdown. It describes early experimental work with jet nozzles in search of better nozzle materials. The effect of splash-back damage and its subsequent influence on jet body and tool design during this work is discussed. A series of cutting-rate curves for jets cutting steel and steel-cement-formation combinations is presented to show the effect of hydrostatic head and the point of diminishing returns with respect to cutting time. There is a series of photographs showing various types of rock formation in which perforation and undercutting tests were made. These stones were drilled and the casing cemented in place as in an actual well. The casing was perforated and circularly cut as if preparing for a fracturing job. The conclusion reached in the paper is that hydraulic jetting with sand-laden fluid can be used for perforating and undercutting casing, cement and formation rock for the intended purpose of inducing the formation to fracture at a desired point. INTRODUCTION Hydraulic jetting as a means of cleaning a formation during acidizing has been used for many years. The acid-jet gun was used to clean formation and for drilling cement from casing with acid. This tool was dropped to a seating ring installed on the tubing and could be retrieved by reverse circulation or wire line. In this process, the fluids were directed against the formation to clean and penetrate beyond the mud-damaged area. After the development of the hydraulic fracturing process, interest in jetting the formation with abrasive-laden fluid was renewed. The cutting action of abrasive fluid on pumping equipment, which is a well known problem, has been utilized to perforate and undercut casing, tubing and formation. In this process, surface areas are provided in the formation on which the frac- turing pressures may work to produce a fracture at the location desired. EQUIPMENT The tools used consist of bodies containing two, three or four jets in a single horizontal plane equally spaced around the circumference. The body is threaded to the end of a string of tubing and run into the well. In addition, an expendable tool is available that may be left in the hole after perforating and produced through until necessary to remove the tubing. The bottom of each tool is equipped with a ball-type back-pressure valve. The ball can be reversed to the surface and recovered. This allows reverse circulation so that loose sand which accumulated below the tool while jetting may be removed before the fracturing job. The present jetting tools are of such length that, when screwed together, the jets fall on 12-in. spacing. ANALYSIS OF THE PROBLEM Early work with nozzles indicated that hardened steel was not a suitable material for jets and that more durable material would be required. Ceramics were tried and found to be superior to steel but still too shortlived for most applications. Tungsten carbide, which was tried and found to be the best material available, is now being used for jet nozzles. Analysis of the problems presented by this process indicated that the following information was needed. 1. The effect of submergence on a jet stream and the effect of submergence on the cutting rate of a jet stream. 2. The cutting rate and depth of a jet stream in steel. 3. The cutting rate in various formations and point of diminishing returns. 4. Size of hole or slot cut in a pipe by a given jet. 5. Fluids and sands used. 6. The flow of various weight fluids through the jet nozzle and the discharge coefficients. 7. The type cut formed in the formation by the jet stream. 8. The stretch and contraction of tubing due to temperature and pressure. The cutting effect of a jet stream on a target in the atmosphere is rapid and spectacular as most of the

By E. B. Hunt

Paraffin deposition has been studied in the laboratory under conditions simulating deposition in well tubing. A theoretical analysis has been made of the cooling of the oil and the precipitation of paraffin from the oil as it flows up the well tubing and through surface flowlines. It is proposed that paraffin deposits are initiated by the precipitation of paraffin directly on or adjacent to the pipe wall and grow by diffusion of paraffin from solution to the deposit. This mechanism is consistent with laboratory and field observations, and has proved useful in the design and interpretation of laboratory paraffin-deposition tests. Tests have been made of the effect of plastic pipe coatings and chemical additives on paraffin deposition. INTRODUCTION Paraffin deposits which form in well tubing and surface flowlines interfere with production and must be removed. Over the years much progress has been made in developing and improving methods of removing these deposits after they form. Much less progress has been made in developing methods of preventing or inhibiting the formation of paraffin deposits. This is due, it is believed, to the lack of knowledge of the mechanism of paraffin deposition, the absence of satisfactory laboratory testing methods and the difficulties in evaluating the results of field tests of preventive treatments. The present investigation was undertaken to elucidate the mechanism of paraffin deposition and to develop suitable laboratory tests for studying the inhibition of paraffin deposition in well tubing and surface flowlines. Current theories on the mechanism of paraffin deposition have been evolved from field observations, from laboratory studies of various factors which might be involved in paraffin deposition, and from laboratory paraffin-deposition tests.1-9 Paraffin deposits have been formed in the laboratory by immersing a cold finger into a hot wax-oil solution and by flowing hot wax-oil solutions through cooled pipe or over cooled plates. These laboratory conditions differ in important features from field conditions, and the observed deposition behavior is not entirely field-like." Thus, there is reason to question the field applicability of the results of these tests. The present investigation was undertaken to determine how to perform and interpret laboratory paraffin-deposition tests to obtain information on the inhibition of deposition in the field. The paraffin problem in the broadest sense encompasses the formation of any predominantly organic deposit in well tubing, surface flowlines and other equipment in contact with crude oil or gas. The present investigation was limited to paraffin deposition involving the precipitation of paraffin wax from solution by cooling and its concentration in a deposit on a cooled surface. This probably excludes its applicability to those problems arising from asphaltic-base crudes, but not those arising from paraffin-or mixed-base crudes. This also excludes its applicability to emulsion and congealing oil problems which are often included as part of the paraffin problem. The phenomenon of cooling appears to be the controlling factor in paraffin deposition involving the precipitation of paraffin wax and its concentration in the deposit. Deposits of this type are usually found in the field only where cooling occurs. Early in this laboratory investigation, it was not found possible to form deposits under constant temperature conditions from a wax-oil slurry, either by steady flow through pipe or by gas-lift up a pipe. Thus, the investigation was limited to situations involving cooling. THEORY The relationships involved in establishing the temperature profiles in an oil stream as it flows up well tubing with a linear (geothermal) pipe-wall temperature distribution or through surface flowlines with essentially constant pipe-wall temperature are presented in the Appendix. The relationship between radial distance in the pipe and the rate of cooling of the oil is then combined with a relationship between cloud point and rate of cooling to develop the pattern of formation of a wax cloud in the oil. The following discussion of paraffin deposition under various laboratory and field conditions is based upon this development which is presented in the Appendix. PARAFFIN DEPOSITION IN SURFACE FLOWLINES The average temperature of the oil coming out of a well is somewhat higher than the ground temperature. Thus, the oil continues to cool on its trip through the surface flowline, and wax deposition can occur. The temperature distributions calculated from Eq. A-4 are given in Fig. 1. As can be seen, almost all the cooling occurs in the first 500 ft from the wellhead. In addition, the radial temperature gradient near the wall decreases rapidly with distance and becomes very small after a few hundred feet. Thus, growth of a paraffin deposit would be expected to decrease rapidly with distance from the wellhead and become negligible after a few hundred feet, since growth is dependent on concentration gradient. Wax precipitation and diffusion of wax to the already

By L. C. Kern

This paper presents information on the use of a new propping agent (malleable aluminum particles) which has been used successfully for producing high-conductivity fractures. The conductivity of a packed fracture depends on the width of the fracture as well as the permeability of the propping material. It is significant that the flow capacity of a propped crack is often increased many fold by propping the crack with a sparse distribution of particles. However, the flow capacity of a sparsely propped crack can be limited by two phenomena: (I) crushing of the propping particles, and (2) embedment of the propping particles in the formation walls. Malleable aluminum particles exhibit interesting properties which tend to overcome these limitations. As high loads are applied to the particles they will deform slightly, rather than shattering. The deformation results in a greater bearing area against the formation wall. This reduces the stress on the particle and reduces particle penetration into the formation. The behavior of aluminum particles under load and the bearing capacities of serveral formation rocks have been measured in the laboratory. By properly using these data, as explained in this paper, the flow capacities of aluminum-propped cracks can be calculated for a variety of conditions. Aluminum particles have been used successfully in the field to prop fractures. Where high-conductivity fractures were needed, the aluminum-propped fractures have given greater well stimulation than could have been expected for conventional fracturing processes. INTRODUCTION The purpose of a hydraulic fracture treatment is to create a conductive channel from the wellbore out into the oil or gas formation. The word conductive is emphasized because we believe that the fracture conductivity (flow capacity) is one of the most important factors influencing fracturing results. Previous papers have pointed out the additional well stimulation that can sometimes be achieved by increasing fracture conductivity. Several years ago, we investigated in some detail the effect of fracture conductivity on productivity increases to be expeced from vertical fractures. Both electrical analog and theoretical studies of unsteady-state flow behavior were made. A discussion of the electrical analog equipment and some of the results of the study were given in a previous paper' by Dyes, Kemp and Caudle. Further details were given recently by McGuire and Sikora.5 Fig. 1 shows the remarkable influence of relative fracture flow capacity and length on well stimulation. Briefly, the study indicates the following. 1. High-permeability formations require high-conductivity cracks for best results. 2. The longer the crack, the higher the fracture conductivity required for best results. 3. If the conductivity of the crack is very large compared to the formation (i.e., flow is not being limited by crack conductivity), then the longer the fracture, the better will be the results. Judging from recently published articles,1,314 there is current interest in methods for obtaining high fracture conductivities. Hence, we would like to present in this paper a discussion of a new fracture propping process (use of aluminum particle) which we have used successfully to obtain highly conductive fractures. There are several factors which influence the conductivity of a propped crack. Conventional fracturing techniques frequently result in a crack completely packed with fracturing sand. For such conditions, the crack conductivity is the product of the width of the packed fracture and the permeability of the propping material. It is significant that a large increase in conductivity sometimes can be obtained by propping with particles which are distributed sparsely (less than a

By K. A. Slagle

Hydraulic analysis of the wellbore has become increasingly inzportant for designing cementing operations and selecting equipment, materials and techniques to complenzent modern well-c-ompletion practices. Non-Newtonian fluid technology has advanced beyond the point where former empirical methods of analysis adequately define the hydraulic system and fluid properties. In view of these factors, this paper describes a series of rheological calculations which have been found practical, through field usage, for assistance in selecting a cementing program. A relatively simple laboratory method using standard viscometric equipment is suggested for determination of the rheological properties of slurries, and clrrta are presented on some of the more common cementitrg conzposition.A. A criterion for divergence from laminar-flow characteristics has been proposed. Usefulness of the calculations is indicated by examples of cementing operations where they have been used. INTRODUCTION With the changing aspects of well-completion practices during the past few years, it has been increasingly important to have a relatively simple method of analyzing the flow conditions existing in the well during cementing operations. This is particularly true in view of the improved economics toward which most of the changes have been directed. Rheological characteristics of slurries used for cementing should be a major consideration in the trend toward smaller casing sizes, either single or multiple strings. Receiving increased attention is the practice advocated in 1948 by Howard and Clark' of attaining turbulent flow with the fluids circulated during a primary cementing operation. While there may still be a difference of opinion concerning this technique, most available information indicates that superior primary-cementing results are generally obtained when high displacement rates are employed. Fluid properties of the slurry to be used must be available, as well as calculation methods, to determine what flow rates should be attained and the probable consequences in terms of frictional pressure and horsepower utilization. It would certainly be inappropriate to attempt high displacement velocities if sufficient pressure might be developed to create lost circulation. Since cementing slurries are non-Newtonian fluids, it is not possible to define their rheological or fluid properties by the single factor of viscosity and then make calculations for the quantities just described. Because the shear stress-shear rate ratio is not constant: it becomes necessary to establish at least two parameters for adequate fluid-flow calculations. It is not the purpose of this paper to delve into the mathematical development of non-Newtonian technology, nor to discuss the arbitrary classification system under which a single fluid may resemble two or three different classes depending upon experimental conditions. Rather, the intention is to present a useful series of calculations based on a concept applicable to both Newtonian fluids and to the preponderance of non-Newtonian fluids encountered in the oil-producing industry. Development of this approach was begun some 32 years ago,' and has most recently been brought to fruition by Metzner and his co-workers at the U. of Deleware. Some non-Newtonian fluids encountered in the petroleum industry, other than cementing slurries, have also had the benefit of this method of analysis."' The two parameters required to define the fluid are usually denoted by the symbols n' and K' and, for the purposes of this discussion, are called "flow behavior index" and "consistency index", respectively. These two slurry properties permit calculation of the Reynolds' number and the "critical" velocity, or the velocity at which departure from laminar flow begins. EXPERIMENTAL DETERMINATIONS The two principal instruments used for rheological studies are the pipeline (capillary-tube) viscometer and the rotational viscometer. When conveniently possible, a capillary-tube viscometer (where the pressure drop and flow rate of the material can be measured) is the better method for rigorous determination of the flow behavior index and consistency index for non-Newtonian fluids. With pressure-drop data at various flow rates, it is then possible to prepare a logarithmic plot of shear rate as the abscissa-shear stress as the ordinate. For fluids which do not exhibit time-dependency, these data will usually produce a straight line. The flow behavior index n' represents the slope of this line, while the consistency index K' becomes the intercept of this line at unity shear rate in accordance with the mathematical derivations associated with this concept of rheology. Due to the difficulties anticipated in maintaining a uniform, pumpable cement slurry for the time interval required to obtain measurements from the pipe viscometer, the n' and K' data reported herein were obtained using a direct-indicating rotational viscometer (Fig. 2). The

By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,

By J. C. Wilhoit, E. M. Galle

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelastic-ity was used to determine the stresses within the model. Two separate problems were solved: (1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore, induced by an uneyual system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For uneyual principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. INTRODUCTION Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eeninkl have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. whitworth2 and woods3 have obtained numerical solutions. word415 obtained a three-dimensional photoelastic solution, Durelli and Deily 6 obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit7 determined the stresses around the bottom of a short cylindrical cavity. While Miles and McGuire, Harrison and Kieschnick and Hubbert and Willis 10 obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomo-geneous, permeable and anisotropic. Previous

By P. B. Baxendell, R. Thomas

Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poett-mann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 BID in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 BID for 27/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of % 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approxirnately ± 10 per cent clown to flow rates as low as 300 B/D in 27/8-in. tubing. INTRODUCTION Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert,' but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results cliscouraging. In 1952 a paper was published by Poettmann and Carpenter' which proposed a new approach. Their method was also based on an energy-balance equation. but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional 1osses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields" This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was 1 set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather 1imited data derived from low-rate observations in 23/8- and 27/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist—due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus. it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La. Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen. To obtain full pressure gradients, a special tubing string was installed which was equipped with electronic surface-recording pressure measuring devices,

By D. R. Wieland, A. N. Barron, A. R. Hendrickson

A definite relationship has been found between the reactivity of flowing hydrochloric acid and its shear rate in a carbonate fracture. Both flow velocity and fracture width affect the acid reaction rate. Laboratory studies were conducted on acid reactivity at different flow velocities through horizontal-linear fractures, using 15 per cent hydrochloric acid at 80' F and approximately 1,100 psi. Fracture width varied from 0.02 to 0.20 in. These data provide a new basis from which the spending time and penetration of the acid can be estimated. Equations were derived expressing the relationship between injection rate, fracture width, acid concentration, time and fracture height, for linear and radial fracture systems. Because the penetration of the acid before spending is closely related to the extent of productivity increase resulting from an acidizing treatment, these data provide a valuable insight into some of the controlling factors that must be taken into consideration during treatment preplanning. INTRODUCTION Acidizing of carbonate reservoirs to improve production characteristics has been widely practiced since 1932. Originally, it was assumed that the acid uniformly penetrated natural formation pores and flow channels, enlarging them and thereby increasing their flow capacity. Little consideration was given to the reaction rate of the acid, or how far it would penetrate away from the wellbore into the formation, before spending. It has been shown recently' that, unless fractures are present in the rock, very little penetration is attained before spending, and the benefits of the acidizing treatment are largely confined to the immediate vicinity of the well-bore. Therefore, acid treatments may be classified into two categories: (1) matrix acidizing, in which the acid flows through multiple: formation pores; and (2) fracture acidizing, in which the bulk of the acid travels through fractures in the rock, whether natural or induced. When acidizing treatments are conducted at pressures of sufficient magnitude to open and extend such fractures, it is often desirable to inject a propping agent to hold the fracture open after the treating pressure has been released, thus providing a highly conductive flow channel through the rock. In some cases where acid attack produces surface irregularities, the resulting flow passages can be sufficient to provide high conductivity without use of a propping agent. During injection, the acid dissolves the carbonate rock with which it comes in contact until it is spent. Deeper penetration of the spent acid into the formation produces no appreciable benefit (if no propping agent is used) because the unetched fracture faces will rejoin when treating pressures are released and the fracture will "heal", with negligible resultant conductivity. The spending time of the acid thus becomes important in determining how far from the wellbore the improved-conductivity zone extends. The spending time of acid after injection into carbonate rock depends on the rate at which the acid reacts with the rock. This in turn is controlled by a number of factors, as previously reported. 2-4 These include temperature, pressure, acid concentration, rock composition, injection rate and the area-volume relationship between the acid solution volume and the surface area of the formation flow channels through which it penetrates. Thus, in matrix acidizing, where an extremely large area is exposed to the acid, spending is rapid. In contrast, spending time is prolonged in open fractures, where the area-volume ratio is much lower. Thus, greatest penetration of the acid before spending will be achieved in acid-fracturing treatments where fractures are held open by hydraulic pressure. Perkins and Kern5 have presented equations for fracture-width determinations which, for hard formations such as limestone or dolomite, indicate that high injection rates and viscous fluids are required to create wide fractures. Increasing the injection rate will, in itself, produce faster reaction rates. Because this type of reaction can be considered to be first-order diffusion-controlled, '-' the rate of movement of fluid past the rock surface affects the thickness of the diffusion layer, in turn affecting the reaction rate. Staudt, et al,10 report the results of tests in which a rotating marble cylinder was immersed in acid, and the weight loss at different speeds determined. Such test conditions, however, are not truly indicative of the situation in a formation during an acid-fracturing treatment. This paper reports reaction-rate data obtained under

By J. E. Warren, J. H. Hartsock

Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, helve motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through. a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitcitions implied by the assumptions that were made, the following general conclusions were drawn. 1. For a radius of drainage at least four times us large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated. 2. The productivity of the hydraulically fractured system, relative to that of the unfructured well, can be determined from the apparent skin effect and can be used to establish design objectives. 3. In the evaluation of a fracture job, it is not Possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary. lNTRODUCTION Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years, it is only in the last few years that improvements in fracture design1-6 and fracturing technique' have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following. I. For a particular well in a given formation, what are the optimum design specifications for the fracture treatment? 2. Have the design objectives been achieved by the fracture treatment? The significance of these questions has been recoguized, and some attempts to obtain answers have been made. Howard, et al,8 endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy9 utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen10 to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al,11 attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner.12 These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should be sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments. Because this study is exploratory in nature, its scope

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by

By R. V. McAfee

The fundamentals of vertical-lift performance are examined with the aid of computer-calculated flowing gradient charts. Flowing and gas-lift well performance characteristics are determined from available well test data. The effect of tubing size, gas-liquid ratio and wellhead pressure is discussed for both flowing and gas-lift wells. The effect of gas-injection pressure, formation gas, bottom-hole pressure and valve spacing is also discussed for gas lift wells. From these studies conclusions may be reached for improving or prolonging natural flow, obtaining optimum lift efficiency when natural flow ceases and improving existing gas-lift systems. The techniques perfected satisfy the requirement that the time involved to conduct an evaluation be practical for operating personnel. INTRODUCTION Flowing pressure gradients furnish the key to successful evaluation of vertical-lift performance in producing wells. Command of multiphase flow gradients in some readily usable form is a necessity before operating personnel can competently include vertical-lift performance evaluation of both flowing and artificial-lift wells in their over-all consideration of production efficiency. A readily usable form cannot be overemphasized since most of the decisions which confront the production engineer with a problem well must be made quickly. In moving a barrel of oil from the reservoir to the stock tank, the major portion of energy generally is expended in the vertical-lift phase. This may or may not be of concern during the flowing life of a well, depending upon the production requirements. It becomes of some concern when the flow performance of the well becomes erratic, and a conscious effort must be made to maintain natural flow. It is at this time that the first steps may be taken to modify existing conditions to relieve unnecessary limitations to proper flow. When natural flow ceases and some form of artificial lift must be installed, the amount of energy expended in lifting liquids becomes quite obvious. It is at this time, if no other, that lifting efficiency becomes important because that part which must be supplied from an outside source is now related directly as a cost per barrel of oil produced. Ten years ago, the majority of gas-lift wells were produced with gas-well gas. Today, the majority are produced by closed rotative gas-lift systems. This permits a direct evaluation of well performance in terms of horsepower requirements and has resulted in mixed conclusions as to the success of gas lift based upon the relative efficiency of a particular system. An increased awareness of the need to resolve vertical-lift performance on a readily usable, scientific basis was inevitable. An indication of the need for better applied science in this field is the often-asked question of whether or not gas-lift can efficiently deplete a given well or reservoir. This question cannot possibly be answered without first evaluating reservoir, surface and vertical-lift performance both as encountered today and as anticipated throughout the life of the well or wells. The technique presented in this paper was originally developed to upgrade gas-lift installation design from an applied art to an applied science. It has since been successfully used not only for this purpose, but also for the whole field of vertical-lift performance in its broadest sense. Lift efficiency should be considered important while the well is still flowing, as well as after natural flow ceases. Correct interpretation and proper modification of the vertical-lift performance of a producing well can provide dramatic improvement in production performance and/or efficiency. STATEMENT OF THEORY AND DEFINITIONS Fig. 1 illustrates the three divisions of production which will be used in this paper. The terms are a modified version of those presented in the very fine paper by Gilbert.' The fields of reservoir and surface performance both have been greatly improved over the years. A study of those writings which may be found indicates that the field of vertical-lift performance has not progressed as well. There are two possible reasons for this lack of progress. 1. It has not been recognized as a scientific field in itself by the oil companies, as has reservoir engineering. 2. The equipment companies have confined their efforts to mechanical design research rather than the more basic study of vertical-lift performance of producing wells. Both organizations must have an economic stimulus for doing research in this field, and most of the results obtained in past work has been so erratic as to arouse little enthusiasm. The basic purpose of interpreting vertical-lift performance is to predict operating conditions below the surface of the ground from available data. The success of the interpretation depends upon the accuracy with

By F. W. Schremp, J. W. Chittum, T. S. Arczynski

This paper describes a laboratory study of causes of external casing corrosion and the test work that led to the use of oxygen scavengers to prevent this attack. External casing failures are classified as water-line, casing-casing, collar and body failures. A corrosion mechanism based on principles of differential oxygen availability is developed that is consistent with facts known about each kind of failure. The field use of oxygen scavengers is depicted as a direct result of the laboratory study. A part of the paper is devoted to reporting on the field use of hydra-zine to control external casing corrosion. Results of field measurements made over a period of several years are presented as evidence of the efectiveness of the hydrazine treatment. The first conclusion reached is that the use of hydrazine materially reduces the cathodic protection requirements for treated wells. This result is interpreted to mean that a reduction is taking place in the amount of corrosion on the casing. Results indicate also that hydrazine shows its greatest usefulness within the first 12 to 18 months after a well is completed when pitting corrosion is likely to be most active. INTRODUCTION According to surveys sponsored by the National Association of Corrosion Engineers,' the cost of repairing casing leaks caused by external corrosion may exceed $4 million per year. In addition, well damage and lost production resulting from casing leaks probably costs the petroleum industry an additional $5 to $6 million per year. Concern about the cost of external casing corrosion led to an extensive laboratory study of factors causing this external corrosion and to the development of a new approach to its prevention. This paper presents a discussion of various causes of external casing corrosion, details of laboratory studies and the results of the field use of an oxygen scavenger in well cementing fluids to prevent the external corrosion of oil-string casing. Measurements on test wells over a period of several years show that cathodic-protection current requirements are greatly reduced when hydrazine is used in cementing mud. Reduction of current requirements can be interpreted to mean that removal of oxygen by hydrazine has greatly suppressed corrosion cells on the external surface of the casing and thereby, has reduced corrosion. To date, hydrazine has been used by the Standard Oil Co. of California in more than 200 well completions. KINDS OF CASING FAILURES A survey of a large number of casing leaks disclosed four types of external casing failures — water-line, casing-casing, collar and body failures. These types are identified largely by their location on the casing. Water-line failures are found just below the surface of water or mud in the casing annulus. Casing-casing failures occur on the oil string just below the shoe of the surface string. Collar failures are found in the threaded ends of casing joints where they are screwed into casing collars. Body failures may occur at any point on the body of a casing joint. Ex- amples of each kind of failure have some of the general characteristics that are shown in Fig. 1. Water-line failures usually result in the circumferential severance of an oil-string casing. The corrosive action causing a water-line failure usually is sharply defined and is limited to a short length of the casing. Casing-casing failures usually are accompanied by pitting corrosion distributed around the oil-string casing for distances up to 100-ft below the shoe of the surface string. Casing-casing failures may also sever the casing. Collar failures seem to start on the first thread at the bottom of recesses between collar and casing joint. Corrosion proceeds across the threads by what appears to be a normal pitting mechanism. Both casing and collar are severely attacked. Body failures are the result of highly localized pitting at any point on a casing wall. Besides the pit that perforates a casing, a large number of other pits usually are found along one side of the casing joint. The pits occasionally are filled with corrosion products consisting largely of oxides and sulfides.' Frequently, the mill scale is largely intact on the rest of the casing. Examination of a casing failure does not always reveal the cause of the failure. Frequently, the necessary details are destroyed when the failure occurs. For example, formation water flowing through a perforation at high velocity may enlarge the hole and destroy any remaining evidence of the cause of the failure. One way to obtain undistorted information about a failure is to study the nature of other pits on the casing in the vicinity of the failure. A study of such pits frequently suggests that they are characteristic of an attack resulting from the differential availability of molecular oxygen.

By T. K. Perkins, L. R. Kern

A study of fluid mechanics, rupture of brittle materials and the theory of elastic deformation of rocks shows that, for a given formation, crack width is essentially controlled by fluid pressure drop in the fracture. Operating conditions which cause high pressure drop along the crack (such as high injection rate and viscous fluids) will result in relatively wide cracks. Conversely, operating conditions which cause low pressure drop (low injection rates and thin fluids) will result in relatively narrow cracks. Charts and equations have been derived which permit the estimation of fracture widths for a variety of flow conditions and for both horizontal and vertical fractures. INTRODUCTION There has been considerable speculation concerning the geometry of hydraulically created fractures in the earth's crust. One of the questions of practical importance is the width of fractures under dynamic conditions, i.e., while the fracture is being created and extended. Such width information could be used, for instance, to help estimate the area of a fracture generated under various conditions. Also, there has been a recent trend toward the use of large propping partiles.13, 15 Therefore is is desirable to know what factors can be varied in order to assure entry of the large particles into the fracture. There has been some work on fracture widths reported in the literature. In particular, there have been several Russian publications dealing with this sub-jeCt.1.31,3 These papers have dealt principally with the elastic theory and the application of this theory to hydraulic fractures. These studies have not led to an engineering method for estimating fracture widths under dynamic conditions. A recent paper3 has reviewed and summarized the Russian concepts. An earlier paper- from our laboratories also discussed the application of the elastic theory to hydraulic fractures. This first approach, based largely on photoelastic studies, has proved to be too simplified to accurately describe the fracturing process. However, these early thoughts have served as a guide during the development of more exact concepts. We would like to present in this paper our current concepts regarding fracture widths and some estimates of hydraulic fracture widths for several conditions. We believe that it is now possible to predict with fair accuracy the factors influencing fracture widths. Furthermore, the method of prediction has been reduced to a simple and convenient graphical or numerical calculation. CRACKS IN A BRITTLE, ELASTIC MATERIAL Many investigators2, 4, 30 have shown that competent rocks behave elastically over some range of stresses. Of course, if the tensile stress imposed upon a rock exceeds some limiting value, then the rock will fail in tension. In similar manner, there are some limiting shear stresses that can be imposed upon rocks. Hubbert and Willis11 have discussed the shear conditions which will lead to failure. Under moderate stress conditions (such as those likely to be encountered when hydraulically fracturing) and when stresses are rapidly applied, relatively, most rocks will fail in a brittle manner. Hence, for this discussion of hydraulic fractures in the earth's crust, we assume the rocks behave as brittle, elastic materials. Let us develop the discussion in the following way. (The following thoughts are applicable only to brittle materials.) 1. First we consider a brittle, elastic system. An energy balance will show the minimum pressure necessary to fracture rock, and from this pressure we calculate the minimum crack width resulting from extension of a hydraulic fracture. 2. Then we will show that, under ordinary fracturing conditions, fracture widths are appreciably greater than the minimum widths of extending fractures. In fact, we will find that crack width is controlled by fluid pressure drop in the fracture. 3. We will discuss pressure drops in fractures and resulting crack widths for various operating conditions and both vertical and horizontal fractures. 4. Finally, we will discuss the significance of these concepts, their relationship to fracturing pressures, etc. First, consider minimum fracture extension pressures. We can shed some light on this question by considering the theory proposed by Griffith7, 8 Yo explain the rupture of brittle, elastic materials. Griffith recognized that solid materials exhibit a surface energy8 (similar to surface tension in a liquid). The fundamental concept of the Griffith theory is that, when cracks spread without the application of external work (in the interior of an elastic medium which is stressed

By P. H. Royster

SOMETHING of a mystery has attached itself to the production of ferromanganese in the blast furnace. This alloy has been produced on the Continent almost continuously since 1876 and in very considerable tonnages, but little definite information concerning the practice is to he found in technical literature, and almost nothing in the way of a theory of the manganese furnace. In this country prior to 1904, bit one company had attempted its production in a serious way, and none of the operating data or other information from this company has been, or is, available to the public. In the last 5 years, as a result of the restriction of imports, a number of furnaces have been blown in on this alloy, with the result that in 1918 as many, as 18 furnaces were in blast. The majority of the men in charge of these furnaces had had little previous experience in such operations. Realizing the advantages both to the country and to the industry from a pooling of operating data and experiences, the Bureau of Mines, in the summer of 1918, undertook the collection of data from ferromanganese furnaces. Although the results of this investigation have already been reported to the companies cooperating, they may he of permanent metallurgical interest, so this paper attempts to give, briefly, the more important points brought out in the investigations. OPERATING DATA IN FERROMANGANESE PRACTICE Operating data were collected by the Bureau from 11 ferromanganese furnaces, which will be referred to throughout this paper as furnaces A, B, C, F, G, I, J, K, L, M, and P. The dimensions, of seven of the furnaces are given in Table 1. The companies from whom this infor-

Jan 2, 1919