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By J. B. Cheatham, R. B. Paslay

Rock stresses and steady-state flow rates induced by the pressure gradient associated with the flow of formation fluid into a borehole have been analytically determined for a permeable, elastic material saturated with an incompressible fluid. In this analysis, the material properties and loading are considered to be symmetric about the axis of the borehole and independent of axial position. For Case I the material is assumed to have uniform permeability in the radial direction, whereas for Case 11 the permeability is assumed to have been reduced in a localized region adjacent to the hole by either normal well completion and production operations or deliberate plugging during air drilling. Results of a numerical example indicate that, in the absence of plugging, the rock shear strength must be approximately two-thirds the formation fluid pressure in order to prevent rock failure. The required rock strength is high for small radial zones of plugging and decreases as the region of reduced permeability becomes larger; however, a depth of plugging can be reached beyond which there is no real gain in strength, although the flow rate can be further reduced. INTRODUCTION During normal production of oil from a well, it is often desirable to increase the production rate of the formation fluid by increasing the pressure gradient through the formation adjacent to the borehole. Depending upon the magnitude of this pressure gradient and strength of the rock material, this production-rate increase can cause sloughing of the hole wall. In many cases, the production - rate increase can result in excessive sand production, increased wear of production equipment, lost production time and expensive workover jobs. In addition, the phenomenon of increased rock bit penetration rate with the use of a gaseous instead of a liquid drilling fluid has been observed in oilfield drilling operations and experimentally demonstrated by various investigators for several years. The improvement obtained by employing this technique can be quite significant and offers apromising method for reducing drilling costs. However, air drilling is currently limited to geographical locations where high-capacity water-bearing formations are not encountered. This limitation has prevented widespread adoption of air-drilling techniques, because the water influx into the borehole interferes with efficient removal of the drilling cuttings and usually results in a condition such that the bit becomes "balled-up" or stuck in the hole. In an attempt to remove the water - intrusion limitation from air drilling, various chemical and mechanical water shut-off methods have been proposed. Goodwin and Teplitzl suggested one such proposal whereby the permeability of the water-bearing rock structure was reduced in the vicinity of the borehole. Although the development of a shut-off method based upon this approach would certainly be welcomed by the oil industry, it is conceivable that, under certain conditions of the pressure gradient, strength of the rock material and depth of the modified permeability zone, a stress field can be created that will result in an unstable hole. As part of their study, an analytical solution is given for stresses in an idealized model of a hole and the surrounding rock material. The purpose of the present study is to extend the analysis of Goodwin and Teplitz to gain more insight into the details and consequences of excessive production rates and formation water shut-off. In particular, simplified models of these problems have been analytically examined, which makes possible the evaluation of the type of stress fields that can be anticipated as a result of these production and drilling practices. Both problems solved concern the determination of the steady-state volume flow rate of the formation fluid and the resulting steady-state stress and displacement distribution in a hollow, cylindrical configuration. The cylinder of Case I, corresponding to the production-rate problem, consists of a material with a constant permeability from the inside surface to the outside surface; the cylinder of Case 11, corresponding to the water shut-off problem, consists of a material with a constant permeability from the inside surface to an intermediate concentric cylindrical surface and a second constant permeability from the intermediate surface to the outside surface-

By K. A. Slagle, D. K. Smith

weight obtained. Additives used in conjunction with salt in these slurries have included silica flour, calcium ligno-sulfonate and cellulose retarders, granular lost-circulation materials, bentonite and selected low-water-loss additives that are not significantly deteriorated by the presence of the chloride ion. In some other areas of South Texas, the salt-saturated slurries have been used quite extensively for improvement of the flow properties of slurries and attainment of better circulation characteristics at lower displacement rates. Concurrently with this property, the protection of shales and shaly sands is also realized, as well as useful retardation of the slurry. Resultant superior cementing jobs have been indicated by both communication tests and acoustic logs for bonding to pipe and formation.' In one section of Louisiana, a major oil company has been using salt-saturated API Class A cement with calcium lignosulfonate retarder for cementing through the Miocene at 9,000 to 10,000 ft. This is another of the situations where interbedding of sands and shales exists, creating difficulty in maintaining formation competency when a fresh-water slurry contacts the clay minerals of the formation. Further work has also been done in the shaly Miocene formation at 13,000 to 15,000 ft where fairly close water or gas contacts are encountered. Indications thus far are that better segregation of these various fluids is obtained by use of the saturated salt slurries because of their improved formation bonding characteristics. In addition to the properties of salt in this situation, attainment of turbulent flow at minimum displacement rates has also been accomplished by use of an additive to help provide exceptional dispersion and viscosity reduction of the slurry. Another oil company was encountering considerable expense in completing wells in Southwestern Louisiana due to extensive block squeeze requirements for effective separation of zones. A very effective mud program was being used to minimize washout in the shale sections and, apparently, a nearly gauge-size hole was being obtained. However, primary cementing results with fresh-water slurries were generally poor. On a few occasions when slurry was actually circulated to the surface, large pieces of shale formation were brought out of the hole with the slurry, indicating a severely water-sensitive, sloughing formation. Inhibition of shale heaving was being accomvlished in the drilling program, and immediately indone ipon circulation of the fresh-water slurry even though it contained a low-fluid-loss additive to reduce filtrate damage in the sands. The subsequent change to salt-saturated slurry yielded 11 successful primary cement jobs out of 12, compared to the previous success ratio of practically zero. Since these were deep, high-temperature wells in the range of 13,000 ft with high-pressure zones necessitating 17.5-lb/gal fluid densities, the slurry used was API Class E cement, silica flour, weight material, retarder, salt saturation (which also reduced the amount of weight material) and maintenance of low fluid loss by use of a salt-compatible additive. Other salt slurries have been used to a limited extent in this same general area for similar problems at depths ranging from 5,000 to 17,000 ft. In the shallower wells, the cement has usually been API Class A where the salt functions as a retarder, and in the deeper wells API Class E cement is used with the additional salt advantage being its increased slurry weight and inability to dissolve salt stringers. A considerable number of squeeze jobs have also been done on older wells using the salt-saturated slurries with very good results. MID-CONTINENT In North Texas, salt-water slurries have been used for cementing the Woodbine sand, Strawn sand, KMA sand and Pettit lime. Shales surrounding these formations have created the same difficulty in obtaining separation of producing zones that has been the problem in other areas. Depths in this area range from 3,400 ft for the Strawn to 7,400 ft for the Woodbine, and concentration of salt has varied accordingly. In the deeper wells, where retardation is desired, saturated salt-water cement is used; for the shallower wells, in order to provide shorter waiting-on-cement times, the amount of salt has been 18 per cent by weight of the mixing water. Results have been excellent with no reported failures on any of the salt cement jobs; where acoustic bond logs have indicated indifferent bonds previously, they are indicating very good bonding for the salt slurries. In Oklahoma various shales of Pennsylvanian age exhibit a high degree of sloughing in the presence of fresh water, causing severe washouts above and below sand formations which it is desired to isolate. This situation exists to some degree in practically all parts of Oklahoma and includes formations of other ages such as the Wood-ford shale. For the past few years, salt-saturated cements and displacement rates as high as practical have been used as a remedy for this problem, with very good results. The Layton and Bartlesville formations are two examples of shaly sands where saturated slurries have been helpful. In one area where five wells were drilled through this type of problem shale without obtaining a satisfactory primary cement job, a change was made to salt-saturated cement preceded by a suitable chemical wash for the drilling mud involved. Acoustic bond logging indicated excellent bonding, and final completion bore out this result by being trouble-free. This type of slurry has also been used extensively on squeeze jobs where shales have been heaving around the producing formations. Predominantly, the basic slurry has been either API Class A cement or a pozzolan cement—although, as deeper wells are being drilled, the use of salt in Class E cement is also increasing. Salt cement in West Texas has been used primarily to help prevent channeling through the shales around the Delaware sand, Queens dolomite and Hope lime. Many of the shaly and dirty sands of this area are sensitive to the filtrate from a fresh-water cement. Salt at 16 to 18 per cent by weight of mixing water has been added to centent, and has been effective in controlling formation damage and communication between zones in these formations. Use of these lower salt concentrations is dictated in this area by the relatively low formation temperatures where retardation of the slurry would create unduly long waiting-on-cement times. Also, quite a bit of cementing has been done in this area using salt concentrations in the accelerating range— that is, 2 to 5 per cent by weight of water. Specifically, these concentrations have been used in coiljunction with high percentages of gel to overcome the retarding effect of the calcium lignosulfonate dispersant, although there are probably several shales where these concentrations could provide some degree of formation stability. On several occasions, the salt has also been used to lower the critical velocity or rate for turbulence with the slurry, particularly in the pozzolan cements. On wells in the Hope lime, it has usually been necessary to squeeze the shale above and below the lime to get a water-free completion. Use of salt-saturated slurries has largely eliminated this

By H. A. Wahl, J. M. Campbell

This study extends our information on solid-liquid slurries to the flow of sand in horizontal fractures. Inasmuch as this is basically an unsteady-state process, a comprehensive photographic study was undertaken in a 10-ft windowed cell to determine if the basic flow regimes described for steady-state flow in pipes applied to the subject process. Since the number of potential variables far exceeds the capacity of a single study, emphasis has been placed on the effects of sand concentration, oil viscosity and oil flow rate. The extensive photographic evidence obtained has proven very valuable in gaining an insight into the basic flow mechanisms. Being able to follow visually the flow characteristics that accompany the quantitative data is valuable in the application of the results. Although the use of dimensionless parameters was carefully investigated. it was found that the data obtained could be more easily, and as accurately, correlated by judicious use of the dimensional variables investigated. However, a study into the feasibility of scaling slurry flow was made in the event this technique is justified in future investigations. The data presented show that the pressure behavior observed in solids transport in pipes basically applies to slurry flow in horizontal fractures. The roles of the parameters are altered but a basic equivalence exists. The most significant correlating parameter was the oil viscosity (µo) and the bulk velocity of the slurry (vn), expressed as ''µv" product. The most significant correlation expresses the rate of advance of the sand as a function of the variables investigated. There are many practical ramifications of this phase of the investigation that should aid in better treatment design. Evaluation of sand advance rates provides a means of estimating sand placement efficiencies during a treatment and the resulting sand distribution in the fracture. The results show that sand placement efficiencies are low under typical treatment conditions. A brief description of the effects of overflushing is also included. INTRODUCTION The flow of sand-oil slurries in fractures is an area in which little basic knowledge is available. This stems to some degree from the fact that it is impossible to duplicate fractures at the surface. They occur in various shapes and sizes with an infinite combination of irregularities. Unfortunately, we can never "see" these fractures except in cores and by indirect means of measurement. In spite of this inherent difficulty, it is desirable to develop some basic concepts that will provide a better understanding of the sand transport mechanism. An insight into the problem is provided by investigations of fluid flow in rectangular conduits. Several studies on the flow of liquids in non-circular conduits1,13 show that a Reynolds number-Fanning friction factor relationship can be written if the hydraulic diameter is substituted for the regular diameter in a circular pipe. This hydraulic, or equivalent, diameter is taken as four times the cross-sectional area occupied by the flowing fluid divided by the wetted perimeter. Eq. 1 expresses an extension of this same work when applied to infinite parallel planes b distance apart.' Eq. 1 is a theoretical equation expressing the friction factor as a function of the Reynolds number for laminar single-phase fluid flow. This expression has been verified experimentally. The equivalent expression for a smooth circular conduit differs only in that the value of the constant is 16 instead of 24. Numerous studies have related friction losses to Reynolds number in both circular and non-circular conduits. These results are widely used and are not reviewed here. Huitt' investigated the effect of surface roughness on fluid flow in simulated fractures. He concluded that fluid flow in fractures may be treated similarly to fluid flow in circular conduits. This work, together with that of Nikuradse,' shows that surface roughness has no appreciative effect upon the resistance to flow in the viscous flow region. In the region of turbulent flow, surface roughness is a prominent factor. Hydraulic conveyance literature is another important source of information. Durand3 has attempted to organize systematically the variables involved in hydraulic-solid transport in pipes. He has classified the modes of flow into three types according to the size of the particles in the mixture— homogeneous mixtures, intermediary mixtures and heterogeneous mixtures. With the usual concentrations and flow rates used in hydraulic transportation, particles with diameters of less than 20 or 30 microns form eszentially homogeneous mixtures with water. The data show, however, that even small materials will tend to settle out under laminar flow conditions. Mixtures containing solids over 50 microns in diameter do not achieve total homogeneity even under turbulent flow conditions. Particles from 50 microns to 0.2 mm in diameter may be transported in fully suspended flow at normal transport velocities although the concentration in the vertical plane is not uniform. Above 2 mm in diameter solid materials are transported along the bottom of the conduit at a velocity substantially less than that of the liquid itself. Between 0.2 and 2 mm in diameter, the particles tend to be in a transition zone between heterogeneous suspended flow and deposit flow at normal hydraulic transport velocities. The sand sizes used in fracturing usually fall in this size range. It is interesting to note that the grain size range designated by Durand for this transition zone corresponds closely to the transition zone between

By G. R. Countryman, G. H. Thomas, I. Fatt

Procedures are described for scaling up turbulent friction pressure drops of inelastic fluids and laminar friction pressure drops of inelastic/elastic fluids in circular ducts. The laminar scale-up calculation method does not require the use of arbitrarily defined flow models, and can be performed directly from laminar capillary viscometry data, or by means of a numerical solution of the integral equation for Poiseuille flow, inputing true shear rate-shearing stress data from other simple shearing experiments. e.g. Couette and plane Poiseuille flows. The turbulent scale up procedure, based on the Dodge-Metzner correlation for inelastic fluids, requires evaluating the characteristic rheological parameters at the existing wall stress under laminar flow conditions. Since the wall stress is the quantity sought in a pipe flow scale-up problem, a trial-and-err or solution is indicated, and therefore a calculation method has been developed and programmed for a medium-size magnetic-drum-memory digital computer. Laminar flow data from other somces may also be adapted to this turbulent scale-upmetbod for inelastic fluids. Comparisons between predicted and experimentally observed friction losses for generalized Reynolds numbers ranging from 3 — 32.000 indicate an error band width of less than 10 per cent in circular tubes ranging in size from 0.5 to 1.89 in. in diameter. INTRODUCTION Considerable effort has been devoted to the problem of establishing an accurate procedure for predicting the laminar and turbulent flow behavior of non-Newtonian materials in pipes from data obtained with small scale laboratory or pilot plant equipment, as evidenced by the variety of reviews on the subject.1-3 Although there does not appear to be a universally accepted scale-up method for laminar flow, the various methods currently employed can be divided into two principal categories depending upon whether a functional relationship between shear rate and shearing stress is assumed, or whether a generalized correlation is adopted. The methods of Hedstrom4 and of Weltmann are typical of the first category, while the generalized correlation of Metzner and Reed6 illustrates the second category. Under appropriate conditions either approach yields a reasonably satisfactory description of laminar flow behavior. In contrast, the prediction of non-Newtonian transitional and turbulent friction losses is much more complex. For example, certain types of materials have been observed to sustain laminar flow at much higher flow rates than Newtonian liquids. When turbulence does develop, the level of agitation is damped to such an extent that the friction factor is lower than that of the original low viscosity Newtonian medium. Extremely broad transition regions and "diameter effects" have also been noted in the turbulent flow of certain chemically complex materials.' Aside from the latter complications, which are attributed in part to viscoelasticity, the existence of a variety of scale-up procedures for predicting transitional and turbulent friction losses is due principally to the chioce of viscosity parameter used in the definition of the Reynolds number. In contrast, Dodge and Metzner have demonstrated that the friction factorReynolds number relationship for inelastic fluids can be satisfactorily generalized provided the fluid property parameters are evaluated at the existing wall shearing stress.* However, the quantity usually sought in a pipe flow scale-up problem is the wall stress, and hence a trial-and-error procedure is required when dealing with non-power law materials. In this report we discuss two calculation methods: (1) for determining the wall stress, and hence the friction pressure drop, for inelastic fluids under conditions of turbulent flow by means of an iterative procedure, and (2) for predicting laminar friction pressure drops without recourse to arbitrarily defined flow models.

By O. D. Gaither

This paper is an analytical study of the flow of fluids through small vertical conduits. Small conduits are defined as 11/4-in. nominal diameter tubing size and smaller, and approximately twice this area for annular conduits (i.e., 1- X 21/2-in. annulus and smaller). Experimental data are presented for the 1-X2-in. and 11/4- X 2%-in. annuli, and the I-in. and 11/4-in. tubing, since these represent the small conduit sizes and configurations generally encountered in oilfield applications. Data have been gathered for these conduits for single-phase water, single-phase gas and two-phase water-gas mixtures, with particular emphasis on high gas-liquid ratios. Water rates in excess of 2,000 BID and gas rates in excess of 2.5 MMcf/D, and two-phase flow ratios in between these two, represent the scope of the data gathered. Existing equations have been applied to predict flowing pressures and compared with experimental data. New correlations have been developed. INTRODUCTION The increased economic pressure on the domestic oil industry in the United States has constantly required the use of new techniques and equipment designed to reduce the cost of finding and producing oil and gas. Since tangible items are most readily apparent in economic analysis, the advent of lower-cost well completions was inevitable. One of the methods used to reduce costs which has received widespread attention is the slim-hole completion technique where tubing is used as the well casing and in which small conduits are used for tubing if necessary. Small conduits, defined by Kirkpatrick1 as "11/4-in. diameter nominal tubing and smaller for tubing flow and less than twice the 11/4-in. diameter nominal tubing internal flow area for annulus flow", have also found widespread usage as siphon strings for de-watering gas wells and as "kill" strings in deep high-pressure oil and gas wells. The growing use of small-diameter tubing has resulted in an increased need for development of improved methods to measure or predict flowing bottom-hole pressures since the physical dimensions generally preclude the use of subsurface-recording pressure gauges. Even in the cases where small bombs are available, the relatively high velocities encountered at nominal flow rates make it necessary to use excessive weight bars or special hold-down devices. Attempts to use recognized correlations to accurately predict flowing or gas-lift performance in wells equipped with small conduits have been generally unsuccessful. Insufficient field data were available to allow the development of a correlation on this basis, and an experimental approach was applied in an attempt to obtain a workable relation. The experimental approach used to obtain the data presented in this paper was actually a compromise between a field installation and a laboratory study. A test well 1,000 ft in length was used to obtain flow data on single-phase liquid, single-phase gas and two-phase water-gas flowing mixtures. Liquid rates up to 2,200 B/D and gas rates up to 3 MMcf/D were used in the single-phase flow studies. Two-phase flow rates from 100 to 600 B/D with gas-liquid ratios from 500 to 8,000 cu ft/bbl were recorded. Experimental data were obtained for single- and two-phase flow through 1-in and 11/4-in. nominal tubing, and through the annuli between 1- and 2-in. and 11/4- and 2%-in. nominal tubing strings. Experimental results for the two-phase flow are compared to the Poettmann-Carpenter correlation2 which is widely used as a comparative standard for development of multiphase flow predictions in flowing and gas-lift wells. Correlations developed by Tek,3 Baxendell and Thomas" were also investigated. The experimental data recorded herein fell in between the two flow regimes as defined by Ros," and this correlation also failed to yield satisfactory results. The fact that existing correlations failed to confirm the experimental data led to the need for development of a new correlation. Although a two-phase flow study was the primary objective of this investigation, data were also recorded for single-phase flow of water and gas, and constants were developed relating to pipe roughness and equivalent diameters for annular flow. These single-phase studies assisted materially in the development of certain of the two-phase flow results. Considerable previous work has been published which presented relationship of surface measurements to bottom-hole condition. The works of Buthod and Whiteley,6 Jones,' Poettmannb and the Texas Railroad Commission" are classic examples of the successful use of mathematical relationships which allow acceptable predictions of subsurface pressures, when gas is the flowing fluid. Darcy and others have derived relationships which may be used with minor modifications to predict subsurface flowing conditions in injection and water-supply wells. As previously stated, the application of the single-phase flow relationships

By J. Handin

Triaxial compression tests with independently applied external confining pressures and internal pore pressures show that the ultimate compressive strengths of representative oil well cements are nearly linear functions of effective pressure — the difference between external and internal pressures on the jacketed cylindrical specimens (to 15,000 psi). The strengths are little affected by the test temperature to 350F (not to be confused with the curing temperature). At an effective pressure of 15,000 psi, strengths are in the rage of 30,000 to 50,000 psi, comparable to those of sedimentary rocks under similar conditions. The cements become very ductile even under low effective pressures; permanent shortenings of 30 per cent or more are attainable without rupture. INTRODUCTION Since the pioneering work of Richart, Brandtzaeg and Brown1 on the failure of cement under combined compressive stresses, it has been recognized that ultimate compressive strength is greatly enhanced by the application of confining pressure. More recently, Mc Henry2 showed that the strength of concrete was a linear function of the effective pressure (the difference between the external confining pressure on a jacketed specimen and the internal fluid pore pressure), at least for a range of 0 to 1,500 psi. The effect of temperature had not been investigated, and no previous systematic triaxial compression testing of naterials used for oilwell cementing seems to have been done. The present work was suggested by the late J. hi. Bugbee3 who stated that "consideration of the common application of high-pressure hydraulic fracturing to the initial completion or recompletion of wells, and the large pressure drawdowns in some producing wells, particularly those in abnormally high-pressure gas-condensate reservoirs, raises the question of what is a suitable cement strength for various completions. The intuitive belief exists that cement strength need be no greater than formation strength. Tests should, however, be conducted at downhole conditions." The ultimate compressive strengths of rocks penetrated by the borehole must rise several fold with increasing depth.4 This marked enhancement of strength is due to the influence of the effective pressure, the total weight per unit area of the overburden less the hydrostatic pore pressure. (The effect of temperature due to the geothermal gradients is relatively small for depths to 30,000 ft.) .A significant comparison of the strengths of rocks and cements at downhole conditions requires knowledge of the confined compressive strengths of cements as well. EXPERIMENTAL PROCEDURES The theory and technique of triaxial compression testing are fully discussed in earlier reports.4-6 Briefly, cylindrical specimens 1-in. long and 0.5-in. in diameter are jacketed in thin copper tubes of negligible strength, placed in the test chamber and subjected to an external confining pressure of kerosene and loaded axially by the piston at a strain rate of 1 per cent per minute. Pore pressures of water (or kerosene) are applied independently through the hollow piston and are maintained constant during the shortening of the specimen, Tests at sensibly 0 pore pressure are arranged so that any free water in the cement can escape to the atmosphere. (If egress of water were denied, pore pressure would rapidly attain the value of the external confining pressure because of reduction of pore space.) The test chamber can be heated for high-temperature experiments. Unless otherwise noted, the cement samples were air dried for about a week. Recorded during a test are pore and confining pressures, shortening and axial differential force (total force less the product of the confining pressure and the area of the piston). True stress-strain curves are constructed by dividing the measured differential force by the actual cross-sectional area of the specimen at a given

Jan 1, 1966

By J. C. Savins, G. C. Wallick, W. R. Foster

The dual differentiation-integration method of rbeological analysis is applied to Couette flow. Using machine processing techniques, a spectrum of characteristic derivative functions for a variety of ideal Generalized Newtonian and viscoplastic models has been developed; As for the case of Poiseuille flow the functions for Generalized Newtonian models as a class are strikingly different from the corresponding functions for the class of viscoplastic models. It is shown that this dual scheme of analysis is a highly sensitive analytic method for dotermining the applicable range if a rbeoloaical model. The unique characteristics of this function in the case of viscoplastics may lead to a more precise detection and evaluation of the yield point or yield stress in these materials. INTRODUCTION It has been shown 1,2 that the dual differentiation-integration method of analysis is a discriminating and flexible method for interpreting flow behavior and determining the applicable range of a particular model from Poiseuille flow experiments. In the preceding paper3 the basic equations governing the Couette flow experiment were reviewed and the significance of changes in boundary conditions on data analysis in the case of the viscoplaaic discussed. In this paper the dual method of analysis is applied to Couette flow using the suites of rheological models considered previously.

By F. W. Jessen, C. C. Patton

Adsorbed films were formed on polished stainless steel specimens from dilute benzene solutions of two crude oil distillation residua. Although the two residua were extremely dissimilar in composition, contact angle measurements showed that the two films increased the wettability of the steel specimens to oil by equal amounts. Furthermore, the wettability of the films was essentially unaffected by the desorption techniques used. Paraffin deposits were formed from heptane-wax solutions on the same stainless steel specimens. These deposits definitely adhered to the surface. Presence of an adsorbed crude oil film on the metal surface increased its free surface energy and resulted in increased deposition of paraffin. The addition to the heptane - wax solution of small amounts of the same distillation residua that were used to form the adsorbed films resulted in decreased cohesive strength in the deposits formed, which resulted in decreased deposition. The presence of a crude oil fraction both in the solution and as a preadsorbed film eliminated the adherence of a deposit of any kind. A mechanism of deposition is proposed which explains the results obtained. INTRODUCTION The natural formation of any predominantly organic accumulation in oilwell tubing, surface flow lines or other production and storage facilities is called a paraffin deposit. These deposits restrict the production of crude oil, causing a substantial increase in production costs because of decreased flow capacity, expense for periodic deposit removal and unproductive downtime. The conditions under which such deposits form, their physical characteristics and the nature and severity of the problem created are extremely varied. Over the past several years, much progress has been made in developing and utilizing methods to remove accumulated paraffin deposition. However, like so many other problems, the basic stumbling block appears to be a lack of understanding of the fundamental mechanism involved in the formation of such deposits. Crude petroleum is known to contain considerable quantities of polar, surface active substances which Doddl has shown to be present at the oil-water interface. Denekas, Mattax and Davis2 observed that the wettability of reservoir rocks was drastically altered by exposure to crude oil fractions; and Zisman, et a1.3 showed that the nature of the compounds adsorbed on a surface would determine its wettability characteristics. Cole and Jessen4 and Ehrig5showed that surface wettability can have a profound effect on the magnitude of paraffin deposition, and Parks6 demonstrated chat the presence of certain adsorbed films on a metal surface would reduce the adherence of paraffin to that surface. Zisman7 has since advanced the theory that the conditions for adhesion are the same as for wetting. Therefore, it was felt that there was adequate evidence to support the supposition that adsorption of compounds from a crude oil might play an important part in paraffin deposition. ADSORPTION-WETTABILITY EXPERIMENTS Initial experiments were conducted to determine the effects of adsorption from solution of crude oil residua on the wettability of a polished stainless steel surface. Distillation residua with initial atmospheric boiling points of 700F were used in preference to the whole crudes in order to concentrate on the molecular weight range of interest, and to eliminate the possibility of composition change due to evaporation of the light ends. Also, these high boiling materials would be expected to be adsorbed from the whole oil in preference to similar compounds of lower molecular weight.

Jan 1, 1966

By V. J. Sikora, W. J. McGuire

Several years ago, we used an electric analogue computer to study the effect of vertical fractures on the productivity of wells in expanding fluid-drive reservoirs. The results of this work were used both as a guide to research and as a basis for the design of actual fracturing operations. In 1958, Dyes, Kemp and Caudle' published portions of the data from this study. The results were released in 1959 to service companies for use in fracturing guides. The purpose of this note is to discuss the experimental conditions and assumptions which were made to derive the information which is already partially a matter of public record. ASSUMPTIONS This study applies to fractures which extend in a vertical plane symmetrically from the well. For simplicity, we chose to study the case of a well in a square drainage area with its fractures extending toward two of its nearest neighbors. We have assumed no migration of fluid across the boundary of this area. The quadrant shown in Fig. 1 models this system. We made the usual assumptions that the reservoir is homogeneous and isotropic, that the fluid is homogeneous and that production is effected by fluid-expansion drive. We also assumed that the fracture extends from top to bottom of the reservoir. Of more practical interest is our assumption that the fracture does not change the size of the drainage area. This premise is appropriate if all the wells in the reservoir are fractured in the same way. But where a single well is fractured, its drainage area may be enlarged at the expense of its neighbors. This could be of economic importance. The assumption that the fracture will not extend beyond the established drainage area of the well also limits the application of the results. Such long frac- tures will yield benefits in excess of those predicted here. When we assume homogeneity, we disregard the frequently observed zone of damage in the vicinity of the well. Where damage is severe, the benefits resulting from by-passing it will far exceed those predicted by this study. All comparisons were made of systems producing in the semi-steady state. By this we mean that equal volumes contributed equally to flow (pressure was dropping at a uniform rate throughout the system) when the rate of flow was observed. EXPERIMENTAL SET-UP We used the pool unit of an electric analyzer' in this study. The squase drainage system of a well was rep-

By J. O. Scott

Transient pressure behavior of wells intersected by a single vertical fracture has been examined by means of a heat pow analogy. Results are correlated in terms of dimensionless pressure change and dimensionless transient time. The resulting curves are found to lie between the dimensionless curves for a cylindrical well and a line source when effective well radius is expressed as one-fourth of the total fracture length. Results are also shown for various degrees of afterflow. Use of the curves provides a means of determining reservoir permeability, wellbore radius, and thereby fracture length, even when the final slope of the transient curve is not obtained. Superposition of curves may be used to confirm existence of vertical fractures in the reservoir adjacent to the well or to indicate a damaged zone on the fracture face. INTRODUCTION Hydraulic fracturing has become a standard well completion practice for the purpose of increasing flow. Results are normally gauged in terms of some sort of "stabilized" flow rate established before and after the treatment. This procedure may be misleading because pressures in or around the well do not become "stabilized" during the test period. Transient pressure tests on fractured wells can overcome the objections to stabilized flow tests by indicating when a stable pressure gradient is reached. In addition, the transient pressure tests can be used to determine formation flow capacity and effective wellbore radius. The effective wellbore radius may be used as a measure of the success of the fracturing operation. The slope and position of the transient pressure-log time curve may be used to determine the flow capacity and wellbore size after sufficient lapse of time so that the pressure gradient in the vicinity of the fractures becomes constant. However, in tight reservoirs or in short tests this condition may not be reached. Presence of the fractures in tight reservoirs may cause a constantly increasing slope to the transient pressure curve. If this slope is picked too soon, formation flow capacity will appear high and the fracture size will appear too small. This paper is intended to clarify the early transient behavior of vertically fractured wells. It shows how formation flow capacity and wellbore size can be determined even though the maximum slope of the transient pressure curve is not obtained during the test. Development of the techniques of transient pressure analysis for wells has been summarized by Perrine.' He reviews the various definitions of wellbore effects such as skin effect, productivity ratio, damage factor and condition ratio. In the present paper, use of these terms is avoided by defining an effective wellbore size. For the fractured well this effective wellbore size is larger than the actual wellbore. Assumptions made are constant flow rate at the well, constant fluid compressibility, constant fluid mobility and uniform porosity and formation thickness. From the basic differential equations of flow, two different solutions may be obtained. The first, the line source solution, is commonly used in transient pressure analysis.' It expresses the change in pressure at any radius due to withdrawal or injection of fluid at the line source from an infinite reservoir at uniform initial pressure. This equation, in oil field units: is

By R. H. Kolb

A long term project at Shell Development Co.'s Exploration and Production Research Laboratory has been the improvement of the accuracy and the ease of BHP measurements. As a result of these efforts, two complete and separate systems have now been built for the automatic logging of BHP variations. The first of these is a small-diameter instrument suitable for running through production tubing on a single-conductor well cable. During the development of this instrument, as much emphasis was placed on providing a high degree of usable sensitivity and repeatable accuracy as on obtaining the advantages of surface recording. The second system combines the benefits of automatic, unattended recording with the convenience of a permanently installed Maihak BHP transmitter.' THE CABLE INSTRUMENT For many years the standard instrument for BHP determination has been the wireline-operated Amerada recording pressure gauge or one of several other similar devices. This gauge records on a small clock-driven chart carried within the instrument, and although relatively precise readings from the chart are possible, they are difficult to ob-tain. a Both the maximum recording time and the resolution of the time measurements are limited by chart size, and when a slow clock is required for long tests, the precision of the time measurement is often inadequate. Since it is impossible to determine the data being recorded until the gauge has been returned to the surface, wasted time often results when a test is protracted beyond the necessary time or when it is terminated too soon and must be re-run. Clock stoppage or other malfunctions which would be immediately apparent with surface recording remains undetected with down-hole recording; the test is continued for its full term with a consequent loss in production time. As new uses for subsurface pressure data evolved, the shortcomings of the wireline instrument became increasingly apparent, and the concurrent development of a surface-recording pressure gauge and the associated high-pressure well cable service unit' was undertaken. Description of the Instrument Because of its ready availability and advanced degree of development, the Amerada bourdon-tube element was chosen as the basic pressure-sensing device. This element converts a given pressure into a proportional angular displacement of its output shaft, and a suitable telemetering system was designed to measure accurately the extent of this displacement and to transmit the measurement to the surface and record it. The telemetering system furnishes a digital record printed on paper tape by an adding machine-type printer. The present arrangement provides a resolution of one part in 42,000 over the angular equivalent of full-scale deflection, giving a usable sensitivity of better than 0.0025 per cent of full scale. An additional refinement simultaneously records on the tape the time or the depth of the measurement, also in digital form. When the instrument is placed in operation, an adjustable programer can be set to initiate a read-out cycle automatically at selected time intervals. When subsurface pressures are changing rapidly, readings may be recorded as frequently as once every 10 seconds; when pressures are more nearly stabilized, the period between readings may be extended to as much as 30 minutes. Because the instrument is surface-powered as well as surface-recording, the maximum period of continuous logging is (for all prac. tical purposes) unlimited. The subsurface instrument is a tubular tool, 1 1/4-in. in diameter and 6.5 ft in length, operating on 12,000 ft of conventional 3/16-in. IHO logging cable. The transmitting section, mounted above the bourdon-tube element in place of the regular recording mechanism, contains no fragile vacuum tubes or temperature-sensitive transistors. This unit has been laboratory-tested to 1 0,000 psi and 300°F and has performed dependably during a number of field operations. The down-hole transmitting arrangement can be fitted to any standard Amerada pressure element, regardless of range and with no modification of the element itself. Calibration To obtain a repeatability commensurate with the sensitivity and resolution of the instrument, it was necessary to develop a special calibrating technique. The manufacturers of the Amerada recording pressure gauge claim an accuracy of only 0.25 per cent of full scale, which is a realistic figure for normal calibrating and operating procedures. An exhaustive investigation was made of the errors inherent in the bourdon-tube element, itself, independent

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

An asymptotic solution to the equation that describes the flow of a slightly compressible fluid in an infinite porous medium has been used to estimate the interaction between two adjacent wells producing from a common reservoir. A direct method for approximating the interference time defined by Stevens and Thodosl has been suggested. An alternative definition for the time of interference, based on the minimum pressure change in the interference region, has been proposed; also, a direct method of determination has been prescribed. Examples have been employed to illustrate the use of both methods.

By E. A. Ernst, N. F. Carpenter

The benefits derived from an acidizing treatment are a function of the penetration achieved by the acid before complete spending. Additional penetration may be achieved by (1) controlling acid leak-08 into formation pores in the channel faces, and (2) retarding the reaction rate of the acid. A recently developed chemical additive consists of a synthetic polymeric material which absorbs hydrochloric-acid solutions, when suspended therein, swelling up to 40 times its original volume. These swollen particles have the ability to deform and seal-08 formation pores, providing fluid-loss control. In addition, they provide a diffusion barrier between the fracture face and the acid solution, prolonging the spending time of the acid. Field applications of this new technique have shown promising results. A method of conducting acid fluid-loss tests, using carbonate cores, is believed to provide fluid-loss data that are more representative of formation conditions than the conventional filter-paper determinations. INTRODUCTION The concept of oilwell acidizing has changed since its first commercial application, 30 years ago. Originally, it was visualized that the acid penetrated thousands of tiny pores and flow channels in the matrix rock, enlarging them by dissolving the carbonate walls. The resultant permeability increase was assumed to be the responsible factor in increasing production from the well. Recent laboratory studies,' however, have shown that this does not provide the complete picture. Although this type of individual pore penetration by the acid does take place during acid "soaks", designed to overcome "skin effect" due to mud invasion in the immediate vicinity of the wellbore, many years of experience have shown that considerable pressure is required to attain any appreciable injection rate into the fine capillary pores of the rock. During most acidizing treatments, the bottom-hole pressure build-up due to the restriction of flow into the formation exceeds the "breakdown" pressure of the rock so that a fracture is induced. In most cases, such fractures open up along natural, incipient fissures and zones of weakness in the rock and, therefore, tend to follow the natural stress pattern of the rock—whether it be horizontal, vertical or inclined. Because of the comparatively greater permeability of the channel in relation to that of the matrix, the bulk of the acid volume is diverted into the newly opened fracture. Here it quickly penetrates the formation, opening and ex- tending the fracture in much the same manner as a conventional fracturing fluid. Unlike the fracturing fluid, however, most acidizing solutions contain no propping agent; thus, the open fracture will again close when the injection pressure is relieved. Laboratory studies2 have shown that in many cases the etching of the fracture faces, resulting from the reaction between the acidizing solution and the carbonate rock, is nonuniform due to the heterogeneity of the rock structure. As a result, the two fracture faces no longer match when pressure is released, and support pillars and intermediate voids remain, forming a high-conductivity channel for well fluids. Unfortunately, this is not true over the entire area of the fracture, but only over that portion of the fracture where the rock has been partially dissolved by the acid. The acid solution spends as its travels away from the wellbore; once it has completely spent, even though it may provide additional mechanical fracture extension, no additional benefit due to etching of fracture faces can be expected. Studies of acid reaction rates under formation conditions,3 observing the effect of different variables upon spending time, have shown that the reaction was often so rapid that very little penetration of the formation occurred before the acid was spent. Study was undertaken to devise methods of increasing the penetration of the acid before spending, so as to provide greater benefit from the acidizing treatment by etching a greater portion of the fracture faces. Several techniques were devised to accomplish this purpose. First, chemical additives were developed which were designed to retard the reaction rate of the acid, causing it to penetrate a greater distance from the wellbore before finally becoming spent. Another method was to increase the injection rate of the acid. However, it was found that the resultant increased shear tended to accelerate the reaction rate of the acid, partially offsetting the benefits of the higher injection rate insofar as achieving increased penetration before spending was concerned.' Another approach to the problem of achieving increased penetration was the development of fluid-loss additives for acid solutions, which would minimize the volume of acid lost into formation pores in the fracture faces and provide maximum fracture extension for the volume of acid injected during the treatment. The use of fluid-loss additives is now considered the most effective method of providing maximum fracturing-fluid efficiency.~ Unfortunately, this latter technique does not solve the problem of rapid reaction rate, with consequent limitation of the fracture area benefited by reaction with unspent acid. A newly developed acid additive overcomes many of these limitations by providing the dual benefits of fluid-loss control and mechanical retardation of acid reaction

By R. E. Zinkham, R. J. Goodwin

A mathematical study has been made of the amount of support a cement sheath could provide to casing cemented into the earth. Several assumptions were required to make the analysis, but only two of them are limiting: (I) the pipe must be completely surrounded with cement, and (2) any mud filter cake between the cement and formation has the same physical properties as either the cement or formation. The calculations showed that little support would be provided to the pipe before an unsupported cement sheath failed in tension; however, when the cement is confined between the pipe and wellbore and is loaded in compression, the pipe could receive a considerable amount of support. In fact, the theoretical results indicate the lower grades and larger sizes of pipe could have their working pressures doubled when reasonable compressive loads were applied to a surrounding cement sheath. These data are shown in six charts. Other down-hole conditions such as setting the cement under pressure, increased temperature and cement confinement all tend to increase the potential usefulness of the sheath. Because of size limitations, a laboratory program to verify the most important results of this mathematical study would be very difficult. However, small-scale field tests would be practicable. This paper shows that, if a solid cement sheath can be obtained in the field by either primary cementing or by repair after detection of flaws by surveys such as the new cement-bond logs, the use of this approach to reducing pipe costs merits further consideration. INTRODUCTION A modification in casing design practices is proposed which may either reduce the amount and grade of steel required to contain a specified internal pressure or permit the working pressure to be increased for a specified weight and grade of pipe. One of the more important considerations in casing design is its resistance to collapse; however, Bowers' and, more recently, O'Brien and Goins' have shown many casing programs are unnecessarily conservative in this respect, and they have indicated how savings can be made by designing for more realistic down-hole conditions. Earlier, Saye and Richardson howed that pipe costs could be reduced by considering the cement sheath as a part of the casing string when collapse resistance was being calculated. More recently, Rogers4 has raised the question as to whether a cement sheath might be considered in the design for burst resistance of the cemented casing. Calculations have been made for the increased burst resistance a cement sheath would provide for casing in a wellbore, and the results show that a sizable amount of support could be obtained in some instances. These data are presented in addition to a discussion of several other factors that are considered to affect the burst strength of pipe supported by cement. Two types of support are treated: Case I for tensile loading of the unconfined cement sheath, and Case for compressive loading of the confined cement sheath. ANALYTICAL TREATMENT AND RESULTS CASE I—TENSILE STRESSES IN AN UNCONFINED CEMENT SHEATH Conditions like this would most likely occur in a greatly enlarged portion of the hole where the cement was not in immediate contact with either the formation or a thin and hard mud cake. The mathematical analysis for this condition, as shown in the Appendix, rests on the following concepts. Pressure inside a unit length of pipe causes: (1) a tensile or tangential stress to be exerted over the longitudinal cross-sectional areas of the pipe and cement; and (2) an equal amount of strain in both the pipe and cement that is uniformly distributed over the wall thickness of each. This analysis was then used to make several calculations for a cement sheath around 51/2-in. OD pipe. The results are illustrated in Fig. 1, which shows that a tensile stress of 500 psi is imposed on a 5-in. thick sheath when the casing contains a pressure of only 1,450 psi. It also shows that a 10-in. thick sheath would be stressed to 500 psi in tension when the pipe contained a pressure of only 2,350 psi. Alternatively, if the stress analysis is made by means of the Lame thick-wall cylinder theory, the inner fibers of the 10-in. thick sheath will be stressed to 500 psi in tension when the pressure in the pipe is only 990 psi. This, of course, reveals that an unconfined sheath is of little support to the pipe in burst; however, an entirely different result is obtained when the cement is confined between the pipe and formation.

By K. E. Brown, F. W. Jessen

By utilizing an 8,000-ft experimental field well equipped with 10 gas-lift valves and 10 Maihak pressure recorders, gas-lift tests were conducted with port sizes ranging from 5/16 through I in. The well was equipped to provide accurate means of measuring surface pressures, temperatures, quantity of injection gas and fluid production. The tests were conducted in 2%-in. OD tubing, and the well was making 95 per cent water. A complete evaluation of gas-lift-valve port sizes shows the relationship of per cent recovery, gas-liquid ratios, minimum pressure created at the operating valve and horsepower requirements for each port. The length of time necessary for the fluid in the tubing to reach equilib.rium conditions after each cycle was recorded. Fallback of fluid at depths of 477, 969, 1,685, 2,493 and 4,290 ft was noted. For each port size, pressure loads of 2.50, 300, 350, 400 and 450 psi were lifted with a valve operating at approximately 550 psi at 6,000 ft. Gas-liquid ratios for each load were varied from excess gas to a gas volume per cycle whereby the load failed to reach the surface. Numerous curves are presented in evaluating the accumulated dara. The results show a 1-in. port to be the most efficient under all conditions. The production of intermittent liquid slugs against different-sized surface chokes was evaluated. These tests were conducted from a 7/16-in. ported valve at 4,072 ft. Tests indicate that, when possible, a %-in. in diameter choke or larger should be used at the surface. In the past few years most of the advancement in gas-lift operations has been made in continuous-flow operations. Yet, it is estimated that at least 70 per cent of the wells on gas lift in the United States are of the intermittent type. Since the term "slug flow" is sometimes used in both intermittent- and continuous-flow operations, it would be well to distinguish between the two types of flow. Continuous-flow gas lift is defined as a method whereby the fluids are produced at a continuous rate at the surface. This generally requires a continuous injection of gas through a surface choke; however, various other control devices sometimes are installed to eliminate freezing, to shut-off gas during natural flow periods, etc. The actual flow of fluids in the tubing may be of the slug type (one of many flow patterns known to exist in continuous flow). Intermittent flow is defined as a method of gas lift whereby the liquid is produced in separate piston-type slugs. Perhaps this type of flow could best be thought of as a ballistic-type flow where the liquid leaves bottom as a piston, propelled by a slug of expanding gas. Gas generally is injected through some type of control at the surface at predetermined intervals. However, the valve may have characteristics whereby gas can be injected through a small choke and still result in a ballistic-type flow. The purpose of the experimental work was to evaluate the most efficient port size to be used on the operating valve for the ballistic type of lift and, in addition, to establish the importance of utilizing a surface choke large enough to allow slugs to be produced without detrimental effects. This work is part of a compre- hensive study of both intermittent-and continuous-flow gas lift, representing a joint project conducted by the Ohio Oil Co., the Sun Oil Co., Otis Engineering Corp, and The U. of Texas. The problem of evaluating port sizes has been given little previous attention. Some work undoubtedly has been done which has not been published to date. Some tests were conducted when the wireline, mechanically-opened valve (Nixon) first came on the market. This valve was capable of utilizing full tubing area as its port size. It is known that this was a very efficient valve, but to the authors' knowledge the results of tests have never been published. EXPERIMENTAL EQUIPMENT These tests were conducted on an actual field well, the Ohio-Sun Unit Well No. 2-E, in the North Markham-North Bay City field, Matagorda County, Tex. The well incorporated 23/8-in. OD tubing and produced 95 per cent water. Since the running of equipment was to be quite elaborate and expensive, a well was selected in which both intermittent- and continuous-flow tests could be conducted. This particular well was capable of producing in excess of 1,000 B/D of liquid (95 per cent salt water), yet with a 3/64-in. in diameter bottom-hole choke, production was controlled to 82 B/D. Most of the intermittent tests were conducted at this low rate. Figs. 1 and 2 show all the surface and down-hole equipment. As can be seen, every attempt was made to insure that ample equipment was available for reliable testing procedures. Fig. 1 shows the surface testing equipment. The input gas was controlled first by a regulator, then

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.