Search Documents

By R. J. Blackwell, J. R. Rayne, W. M. Terry

This paper presents results of an experimental investigation of factors that control the efficiency with which oil is displaced from porous media by a miscible fluid. The study was made to elucidate the relevant processes both on microscopic level (within individual or between neighboring pore spaces) and on macroscopic level (within a large sand body). Mixing of miscible fluids on the microscopic level was studied in sand-packed tubes. It was found that molecular diffusion is the dominant dispersion mechanism for reservoir conditions of rate, length and pore sizes. Macroscopic channeling was studied for various mobility ratios in reservoir mode1s scaled to relate viscous, gravitational, and diffusional forces. The formation of channels was due to viscous firzgering, gravity segregation and variations in permeability. With adverse mobility ratios, it was found for reservoirs of realistic widths that diffusion will not be effective in preventing the formation and growth of fingers, even in homogeneous sands. At sufficiently low rates channeling was eliminated by gravity segregation in tilted reservoirs. The dependence of recovery on mobility ratio, length-to-width ratio, flow rate and angle of dip is presented. INTRODUCTION Oil recovery by solvent flooding is finding increasing application in the field. While the process promises high recoveries from the region swept by solvent, under adverse conditions only a small fraction of the reservoir volume may be swept at the time solvent breaks through to the producing well. Further, the high cost of the solvent encourages its use only as a bank whose size must be kept at a minimum. Thus, two important questions arise: (1) what fraction of the reservoir can be swept, practically, by solvent? and (2) what is the minimum size solvent bank that can be used to carry out the displacement? The answers to these questions require knowledge of both macroscopic channeling processes and microscopic mixing processes. The studies described here were carried out to gain this knowledge. Microscopic mechanisms which cause mixing will be discussed first, because an understanding of these mechanisms is necessary for proper interpretation of the experimental work on channeling described later. INVESTIGATION OF MICROSCOPIC DISPLACEMENT PHENOMENA FOR MISCIBLE FLUIDS The questions to be resolved concerning microscopic displacement behavior are: (1) how much mixing occurs between oil and solvent in the direction of flow? and (2) does the solvent completely flush the oil from the pore spaces in the region invaded by solvent? The classic work of Sir Geoffrey Taylor' and its extension by Aris2 have shown that it is possible from theory to describe the amount of mixing in single straight capillaries when solvent displaces a fluid of equal viscosity and equal density. Aris showed that the lengths of the mixing zones, 81, corresponding to the 10 per cent and 90 per cent concentration levels of the solvent can be calculated from the formula, 81 = 3.62 \/Kt, .........(1) where 8l is the length of the mixing zone, cm; t is the time, sec; and K is the effective dispersion coefficient, cm2/sec, given by K/D = 1 + (1/48) (au/D)2......(2) where a is the radius of the capillary, cm; D is the molecular diffusivity, cm2/sec; u is the average velocity

By H. D. Outmans

A method has been developed for determining the relative water wet-tability (fraction of the surface wet by water) of porous media. This method involves the adsorption of methylene blue dye from an aqueous solution onto the solid surfaces of rock contacted by the injected dye solution. Experiments on Berea snndstone cores have shown that water-wet cores adsorb a large amount of dye from solution. In oil-wet cores, however, the injected aqueous dye solution is prevented from contacting the adsorptive surfuces by a film of oil and virtually no dye is adsorbed. This method was tested by experiments on mixtures of water-wet and oil-wet sand. Using the dye adsorption method, it was possible to determine quantitatively the fraction of water-wet and oil-wet sarzd in such mixtures. The dye adsorption test is readily applied to determinitrg the relative water wettability of fresh oilfield cores. The cores are not extracted before testing. Observed values of the wettability of field cores tested to date have varied from 100 to 6 per cent water wet. INTR OD UCTIO N Recent articles1 ' have emphasized the important role that wettability plays in almost all phases of reservoir rock behavior. It has been shown that wettability has a profound effect on the interstitial water saturation, residual oil saturation, capillary pressure, relative permeability, waterflood behavior, and resistivity index of oilfield cores. A quantitative investiga- tion of the effect of wettability on these core properties is severely handicapped by the lack of a simple technique for measuring the wettability of a porous medium. If such a technique were available, it would provide investigators with a means of gaining insight into the distribution of phases within a core. A number of qualitative methods of estimating wettability are known. These include contact angle measurements, flotation tests and studies of displacement pressure: imbibition7 and relative permeability data.' Using these tests, it is usually possible to classify a core as water-wet, oil-wet, or some intermediate degree of wettability. One recently proposed method involving measurement of nuclear magnetic relaxatione offers promise of determining quantitatively the fractional wettability of cores. The equipment is rather elaborate and necessary treatment of the cores before testing probably alters the natural wettability. This latter point also applies to most of the cited qualitative methods. This paper presents a new technique for determining water wettability of cores; it is based on measurements of the dye adsorption capacity of the core. This method has the advantage of requiring relatively simple equipment and involves minimum handling of the core before testing. It is important to distinguish between the various concepts of wettability referred to in the literature. The term "wetting" is defined by Bartell as that phenomenon which occurs when a solid and liquid phase come in contact in any manner so as to form a solid-liquid interface. A preferentially water-wet solid is defined by Jennings in terms of the advancing contact angle in the solid water-oil systems. Brown and Fatt regard fractional wettability as the fraction of the total surface area that is preferentially oil-wet or water-wet. However, none of these definitions adequately describes the type wettability measured by the dye test. This calls for the introduction of a new term, "relative water wettability", which we define as the fraction of the total surface area of a core contacted by injected water. DESCRIPTION OF METHOD The ability of a porous medium (especially the clays) to adsorb large quantities of surfactants, dyes, etc., is well known. It is reasonable to assume that a substance can be adsorbed from solution onto a solid surface only if the solution contacts the surface. In this connection Shapiro" has shown by experiments on silica gel that completely dry gel will adsorb methyl red dye from a benzene solution. On the other hand, if a film of water more than several molecules thick is present on the silica gel, the adsorption capacity of the gel for the dye is drastically reduced. Thus, a study of the dye adsorption capacity of cores should give some clue as to the fluid distribution on the surface of the core. TEST OF METHOD As a qualitative check on this theory, dye adsorption tests were run on similar Berea sandstone cores (Table 1, Cores 1-5). Cores saturated initially with water and flooded with 0.01 per cent aqueous methylene blue adsorbed 0.58 mg dye/gm of core. Similar cores saturated initially with water, driven to irreducible water with oil, and then flooded with the same dye solution also adsorbed 0.58 mg dye/gm of core. Another core, treated with a 5 per cent Dri-Film solution, dried and saturated with oil (Soltrol) adsorbed no dye when the dye solution was injected. These tests confirm

By L. W. Holm

Laboratory flooding experiments on linear flow systerns indicated that high oil displacement, approaching that obtained from completely miscible solvents, can be attained by injecting a small slug of carbon dioxide into a reservoir and driving it with plain or carbonated water. Data are presented in this paper which show the results of laboratory work designed to evaluate this oil recovery process, particularly at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi. Under these conditions CO2 exists as a dense single-phase fluid. It was found that a bank, rich in light hydrocarbons, was formed at the leading edge of the CO? slug during floods on long cores. Formation of this bank is probably due to a selective extraction by the C02 and, it is believed, partially accounts for the attractively high oil recoveries. In crddition to the efficient displacernerlt of oil from the pores of the rock by this process, the favorable rnobility ratio related to a C0 2-water flood also contributes to high oil recovery. A further advantage of this process is noted on limestone and dolomite rock, in that the CO1 reacts with the porous medium increasing its permeability. Flooding experiments were conducted on sandstone and vugular dolomite models. The results of this experimental work show the effect on oil recovery of type of porous medium, pore geometry, flooding length, and flooding pressure. The porosity of the cores and rilodels varied from 16 to 21 per cent and their pern~eabilities ranged from 100 to 200 md. A reconstituted West Texas reservoir oil, a West Texas stock tank oil, an East Texas stock tank oil and Soltrol were used to represent reservoir oils in this study. Oil recoveries ranging from 60 to 80 per cent of the original oil in place in these cores were obtained by CO2,-carbonated water floods at pressures between 900 and 1,800 psi, compared with conventional solution gas drive and water-flood recoveries of 30 to 45 per cent on the same cores. Oil recoveries greater than 80 per cent resulted frorn f1oods at pressures above about 1.800 psi. There high recoveries were noted from both the sandstone and the irregular Porosity carbonate cores. In all floods, additional oil was recovered by a solutiorr gas drive resulting from blowdown following the flood. Oil recoveries of 6 to 15 per cent of the original oil in place were obtained during this blowdown period. This additional recovery was found to be a function of oil remaining after the flood, decreasing with decreasing oil saturation. It was also noted that highest oil recoveries by blowdown were obtained when carborlated water rather than plain water followed the CO, slug. INTRODUCTION Miscible phase or solvent flooding processes, which are designed to increase oil recovery -from petroleum reservoirs, involve the injection of small quantities of a petroleum solvent into the reservoir, followed by an inexpensive scavenging fluid which is miscible with the solvent. Essentially complete displacement of oil from the pores of reservoir rock has been obtained by this technique. CO,, although not completely miscible with most reservoir oils at moderate pressures, is highly soluble in these oils at pressures above about 700 psi; there is appreciable swelling and reduction in the viscosity of oil when CO, is dissolved in it. Therefore, CO, could be expected to perform similarly to other oil solvents as a displacing agent. CO, is also highly soluble in water at elevated pressures, so water should be a satisfactory material to drive a slug of CO, through an oil-bearing reservoir. A favorable mobility ratio would be obtained through the reduction in viscosity of the oil and the use of water as a final displacing agent. A number of investigations of the use of CO, to improve oil recovery have been reported in the literature.2,3,4,5,6 These studies, however, have been conducted on uniform porosity sandstone at relatively low temperatures and pressures. The behavior of CO1 as a flooding agent at temperatures above its critical temperature could not be predicted adequately from these studies, particularly for the case of non-homogeneous rock. The purpose of this work was to evaluate the oil recovery efficiency of a process involving the injection of a CO2 slug followed by carbonated water, at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi, and to compare this process with conventional water flooding. The investigations were primarily designed to provide information on the efficiency of the process in irregular porosity carbonate rock. The effects of flooding path length, the presence of free gas, the type of oil to be recovered, and the amount of solvent required were also determined. The essential results of static phase behavior studies and experimen-

By Dwight K. Smith, Greg Carter

Studies have been conducted on The properties of many deep well cementing compositions to determine their Strength behavior over curing periods to 180 days at elevated tem-peratures and 3,000 psi pressure. This pressure results in essentially the .vat, compressive strength as that obtained with much higher pressures in ac-cordance with the findings of an API subcommittee ' These different compositions include API C1asses A, E, and F cements containig additives such as retarders, berrtorlite, heavy weight materials and pozzolans. All compositions except mixtures of Poz-zolrrrts and hydrated lime show from mild to severe degrees of strength lass over a temperature rang from -730 to 320" F after setting. Pozzolatl-time compositions actually gain in strength with time at these high temperatures. Other chemical find physical properties evaluated to observe their inter-relation.ship with Strength loss show very little correlation except in per-meability. As retrogression in strength increases, the permeability of set cement increases. X-ray difraction patterns on the set products indicate the formation of certain compounds having little or no strength value in those cementing compositions where strength loss was more severe. INTRODUCTION As a result of the growing trend toward deep well completions, a study has been made on the properties of the various cementing slurries presently in use at elevated temperatures and pressure. The strength of these compositions is of prime importance in selecting the most suitable material for use at high temperatures, to determine WOC time and the proper time to perforate with a minimum of shattering. Of primary interest in this investigation was the strength behavior of various compositions currently in use, and the effect of additives on cement after long periods of curing under severe conditions. Earlier investigators have pointed out that the strength of some cements will increase with increasing curing temperature to about 220 to 340" F, but at higher temperatures a loss in strength occurs at extended time intervals. Studies by the API Mid-Continent District Study Committee on Oil Well Cements' outlined a testing procedure whereby field conditions of temperature and pressure could be simulated in the laboratory.' It was observed that retarded cements undergo changes at elevated temperatures and some lose as much as 50 per cent of their early strength when cured at high temperatures. The scope of these tests was limited to curing periods of 1 to 28 days; additives were not covered in this study. Saunders and Walker' found that the use of additives influenced the strength behavior of cements at high temperatures, but studies were conducted only to a seven-day curing period. Ludwig and Pence' conducted an investigation of two types of cements under elevated pressures and temperatures in an effort to explain the causes of this loss in strength phenomenon. It was observed that with retrogression in strength there were other physical and chemical changes which took place as the cement aged. Today there are a number of cementing compositions available for use at well depths below 10,000 ft. Since all these earlier investigations were limited in curing time as well as the number and type of compositions studied, it was believed that a more extensive study should be conducted on the properties of cements at elevated temperatures, and this work should include those compositions actually in general field use at this time.

By Kenneth E. Gray

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton's equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?' lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.' It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By I. Fatt

Study of a model which contains "dead-end" pore volume indicates that pressure transients are influenced by the amount of dead-end pore volume and by the resistance of the flow path between the dead-end pore volume and the main flow channels. A semi-empirical method is demonstrated that makes possible measurenment of the volume in the dead-end pores and the total pore volume. The difference between these two volumes is the volume of the flow channels. An indication of the flow resistance between the dead-end pore space and the lain flow channels is also obtained. INTRODUCTION In some engineering calculations the distribution of pore volume in a petroleum reservoir need not be known. For example, a material balance calculation treats a reservoir as an oil-filled tank. In other calculations the distribution of pore volume appears implicitly through use of the porosity and the relative permeability and capillary pressure characteristics. It is the purpose of this paper to point out that under certain conditions the exact distribution of pore volume must be known in order to interpret correctly transient flow behavior. Pressure transients during single-phase flow in porous media are usually said to obey differential equations of the form

By Carl Gatlin, S. Srini-Vasan

It is shown thar k k ratios cornputed on the as.sutnption that the average sandstone reservoir has a pore-size distribution characrerized by a linear 1/P saturatioN plo are in good agreewient with correspotlding k,,/k,, ratios obfairzed by Wahl, Mul-/ins and Elfrink by correlatiotz of field measurements. Methods of calculating relative permeability data have recently been reviewed and extended.' It was shown that for sandstone reservoirs where ' is approximately a linear function of effective saturation (as suggested first by Corey') it is possible to express relative permeabilities in very simple terms. For systems wetted by connate water and producing oil and gas (gas saturation growing at the expense of oil) the expression for the The accuracy of Eq. I has been frequently confirmed in our laboratories; because of its simplicity we make routine use of it in the analytical solution of proble~ns in reservoir engineering. Nevertheless, comparisons of the k,,,/k,, ratios yielded by Eq. 1 with appropriate reservoir data have been few. The publica- tion by Wahl, Mullins and ElfrinkV of an empirical equation for k,,/k,, ratios is thus of interest since this equation is specificalljl stated to be Vased on the correlation of field measurements made on sandstone reservoirs. Not surprisingly these authors found that it was necessary to

By J. E. Fox Jr., J. L. Lummus, J. P. Gallus

Fresh water or brine drilling fluids may be kept free of suspended drilled solids by the addition of a water soluble acrylamide-carboxylic acid copolymer at the flowline. Addition of from .01 to 0.2 lblbbl of the polymer solution to drilling fluids containing less than 5 per cent clay solids by weight causes the solids to flocculate and settle rapidly to the bottom of the pits. Solutions of the polymer injected at the pump suction reduce the loss of water to permeable formations without impairing the permeability to oil. The use of drill-itlg fluids clarified with the polymer has resulted in increased drilling rates, extended bit life, and lower drilling fluid costs. INTRODUCTION Field experience and the results of a number of investigations have established that the accumulation of solids in drilling fluid reduces drilling rate.'-' Drilling with water makes possible higher drilling rates than can be achieved with mud but in many areas drilling with water may not be feasible because of the possibility of encountering high formation pressures or by-dratable formations. To combat these conditions, the drilling fluid must possess certain physical properties such as viscosity, density, fluid loss, etc., which require the presence of solids. The current trend in drilling fluid treatment is to maintain as low a percentage of solids as is possible without harmfully affecting the mud properties needed for drilling. Mechanical separating devices such as wet cyclones and decanting-type centrifuges are proving to be an economical means of controlling the percentage of solids and thereby maintaining low solids muds. Also: special muds have been developed for the purpose of retarding the hydration of drilled solids so that they may be more easily removed by shale shakers or settling pits. In some areas, such as West Texas, the characteristics of some formations will permit drilling with water. However, because of the dispersion of drilled solids, it is usually not possible to maintain clear water even with the aid of mechanical separators, or by utilizing large settling pits. For this reason the commonly used term "water drilling" is a misnomer since the water usually contains some solids. Because of the improved drilling rates and other benefits which might be effected, a laboratory and field study was made of the use of flocculating agents for maintaining clear water for drilling. PROCEDURE Laboratory—Solids Settling Two techniques were employed to determine the effectiveness of flocculating agents in settling solids from drilling mud. First, the rate of fall of solids was measured in graduated beakers containing mud treated with various flocculating agents. Natural gum, oil-in-water emulsions prepared with ethoxylated nonyl phenols and diesel oil. and a powdered synthetic acrylamide-carboxylic acid copolymer* (hereinafter referred to as "polymer") were tested as flocculating agents in both fresh water and salt saturated muds containing 4 per cent solids. The polymer was not added in the powder form directly to the muds but was first dissolved in water in a concentration of 3.5 lb/bbl. The polymer solution was then added directly to the mud. The concentration of the flocculating agents, including the polymer, was varied. High rates of fall of the solids indicated high flocculating efficiency. A second technique consisted of measuring the time in minutes required to obtain clear water at the pump suction after addition of the various flocculating agents at the flowline. These tests were made using a model mud circulating system having a total volume of approximately 10 gal. The natural fresh water and brine muds used contained 4 per cent solids. A sketch of the circulating system appears in Fig. 1. The circulating rate

By M. R. Tek, K. H. Coats, D. L. Katz

The performance of a gas reservoir su,bject to water drive is often affected by interference due to gas procluction or injection in neighboring reservoirs adjacent to a common aquifer. Field data available on production-pressure behavior of several reservoirs indicate that prediction of reservoir performence must include the effects due to mutual interference. A method developed to predict the performance of two or more interfering gas reservoirs, subject to specified production-iniection .rchedule.s, is presented. The method involves the comhinatiorz of the theory of unsteady-state water movernent with appropriate meterial balance consideration.s. The procedure which extends M. Mortada's treatment for interfering oil reservoirs makes use of his dimen-.sionless pressure drop quantities. prevented graphically in the literature. In order to evaluale the predictive accuracy and practical field applicability of the theory, the method has been applied to analyze the performance of two actual gas reservoirs in mutual interference. The calculations were performed on an IBA4 704 computer. The predicted performances were alro calcltlated with the interference effects ignored. The results show that considerably better agreement between calculated and observed behavior ic. obtained when the interference effects are included. INTRODUCTION Fluid communication between any number of oil or gas reservoirs adjacent to a common aquifer results in mutual interference effects on their production-pressure behavior. The theory, application and interpretation of pressure build-up behavior of oil wells, drawdown tests on oil or gas-producing formations and behavior of several storage reservoirs indicate ample experimental evidence of mutual interference. A method developed to compute the behavior of interfering oil reservoirs was published several years ago by Mortada.4 Studies conducted during the recent years on underground storage of natural gas clearly indicated the need for extending Mortada's work to the case of interfering gas reservoirs. The adoption of appropriate material balance equations in conjunction with the unsteady-state pressure interference theory yields pressure-explicit equations. Their solution, their application to a specific case history and an over-all evaluation of the developed method through the comparison of predicted and observed field performances were the main objectives of this study. DEVELOPMENT OF MATHEMATICAL RELATIONS The diffusivity Eq. 1 governs planar, radial, unsteady-state compressible liquid flow through a porous medium. ?p/?r2+1/r ?p/?r=µFc/k ?p/?t (1) The 1iterature1,2,3 contains derivations and solutions of

By J. B. Cheatham, J. G. Yarbrough

Although adequate removal of cuttings from beneath a drill bit is important for efficient drilling operations, very little basic data are available relative to the fundamentals of chip removal by hydraulic jets. A discussion is presented in this paper of an experimental investigation of the jetting action of hydraulic jets in removing loose particles from the bottom of a cylindrical hole. Conditions for which the jet is no longer capable of removing chips from the bottom of the hole are determined. This situation represents equilibrium between the chip removal force and chip Bolddown forces such as gravity and pressure. In most of the tests loose particles were jetted with water or a water-glycerine mixture to determine the dependence of chip removal on hole size, jet size, height of jet off bottom of hole, flow rate, particle density and fluid viscosity. ,A test with a pressurized mud system indicated that relatively low pressures can completely overcome the removal action of a hydraulic jet. Although the system studied herein is not directly applicable to a rotary drill bit, the work with such simplified systems can provide a better understanding of the chip removal action of jets, and with logical extensions it may provide a reasonable basis for the best use of fluid jets in drilling. INTRODUCTION The primary deterrent to maximum drilling rates is the inability of the drilling system to remove rock cuttings efficiently enough to prevent interference with the drilling action.1-2 The objective of chip removal studies is to permit predicting and controlling removal forces under downhole drilling conditions. Conditions at the bottom of a hole during rotary drilling are exceedingly complex and are not likely to be described in a quantitative way by investigations in terms of the total drilling action until a better understanding is developed of the simplified components of the problem.3 The present study is concerned with the elementary condition of removal of chips by a single central jet. Even this relatively simple model provides mathematical difficulties because of the turbulent nature of the flow from the jet and because of the shape of the bottom of the hole beneath the jet. Theoretical and experimental studies have been made of turbulent jets impinging normally on an infinite body and deductions based on analytical solutions to simplified problems can give some insight into the problem of cutting removal by a jet. However, because of the present lack of understanding of the behavior of the interaction between the fluid jet and the chips being removed, an experimental approach was chosen for the present study. Methods have been developed for maximizing hydraulic horsepower, impact force and jet velocity; but whether maximizing these parameters maximizes chip removal with present drilling bits has not been demonstrated. Simplifying the problem of chip removal may make it possible to develop some understanding of the manner in which the jet velocity is dissipated. Better understanding of a simple case should materially assist in extending analysis to more complicated cases. Thus, we are not concerned in the present study with the rock fracturing process itself but only with the removal of the debris from the bottom of the hole. A problem which is quite similar to the chip removal problem is the suspension of solids in stirred vessels. This problem has been studied by the chemical industry and correlations have been obtained by dimensional analysis which permit the design of mixing vats7 An approach similar to that used in the mixing vat problem is used in the analysis of the jetting data in the present paper. EXPERIMENTAL PROCEDURE The test equipment arrangement shown sche-matically in Fig. 1 allows the jetting action to remove particles until an equilibrium height is attained for each combination of hole size, jet size and flow rate.*** Equilibrium conditions require that the removal force is unable to remove additional particles. This balance between holddown and removal forces implies a relationship between the two forces which is constant for the particular system. When the holddown forces are constant,

Jan 1, 1965

By R. H. McLean

Jet impingement produces two mechanisms to clean the bottom of a borehole during jet-bit drilling operations. One is an impact-pressure wave in the immediate area of jet impingement. The other is crossflow, which spreads across the bottom away from the pressure wave. Measurements of the vertical distribution of the cross-flow at several positions beneath a 4 3/4-in. tricone jet bit in a laboratory model show that the maximum velocity in the crossflow is directly proportional to the square root of the product of the rate of flow and the velocity of the jets through the nozzles (QV). Other measurements in the laboratory model show that gradients in the impact-pressure wave are directly proportional to the jet QV if the diameters of the nozzles are held constant. Consistency of the basic relationships through changes in the Reynolds numbers of the jets from 31,000 to 93,000 suggests that the laboratory results should be representative of typical flow in field operations having higher Reynolds numbers. Estimates of the impact-pressure waves under conditions other than those in the jet-bit model may be made by comparison with a less complex model—impingement of a jet against an unrestricted flat surface normal to the jet. Equations derived from current jet technology describe the wave in this simple system for a wide range of conditions. INTRODUCTION The efficiency of rotary drilling operations is strongly linked to the efficiency with which cuttings are removed. Cuttings remaining on the bottom of the borehole will impede further penetration by the bit until they are removed. Wasteful regrinding is prevented if the fluid circulated past the bit removes cuttings as rapidly as they are made. Most investigations of bottom-hole cleaning under bits have been concerned with the rate-of-penetration effects of bit type, nozzle configuration, fluid properties, pressure gradients and utilization of hydraulic horsepower. These investigations have shown that drilling muds, weighted to keep the pressure in the borehole greater than in adjacent formations and carrying material which forms a filter cake, apparently plaster cuttings against the bottom, making them difficult to remove. In addition to a demonstration of the factors causing poor cleaning, the most significant result of these previous investigations has been the increased use of jet bits accompanied by better hydraulic programs and better selection of drilling fluids. Undoubtedly, these practices have improved bottom-hole cleaning, but rates of penetration when drilling with muds are still often lower than would be expected with perfect cleaning." Although there is general agreement with the concept that increasing hydraulic energy at a jet bit often increases the rate of penetration by improving cleaning, research workers have differed as to the best criterion for evalyating hydraulics. Some lean toward maximizing the product of the rate of flow and the velocity through the nozzles (QV) others prefer to maximize the hydraulic horsepower at the bit;'"-' "till another says that neither criterion is universally suitable."' This controversy shows that conclusive field evidence has not established the superiority of either of these criteria. Analysis of the fluid flow which cleans the bottom should contribute to resolving the controversy. Impinging jets clean the bottom by creating two mechanisms capable of dislodging cuttings. One is the impact from the momentum of the jet and the other is the flaw parallel to the bottom away from the area of impingement. The impact force appears in the form of a pressure wave on the bottom and, in this paper, is called the impact-pressure wave. The flow parallel to the bottom is called crossflow. Fig. 1 illustrates these two mechanisms. This paper describes crossflow and the impact-pressure wave beneath jet bits and relates them to controllable parameters. Through these relations, criteria for use in designing hydraulics to achieve maximum use of the mechanisms of cleaning are derived. PROPERTIES OF CROSSFLOW CONCEPTS DEVELOPED IN PREVIOUS INVESTIGATIONS Concepts of scavenging the bottom by crossflow have been well discussed by Bobo, et al." They examine the means by which crossflow may create forces on cuttings and conclude that the cleaning action of crossflow can be increased by increasing the velocity of the flow stream close to the bottom. Using boundary layer theory, they indicate that a reduction in the viscosity of the drilling

Jan 1, 1965

By A. Lubinski, J. E. Hansford

Jan 1, 1965

By C. D. Hall, F. E. Dollarhide

Conventional static tests of fluid-loss agents do not realistically simulate conditions in a fracturing treatment. The dynamic tests reported here show that fluid-loss volume is better represented as proportional to time, rather than as the square root of time. This leads to a different equation for fracture area. The leak-off rate increases with increasing shear rate at the fracture wall, but appears to approach a limiting value. Pressure effects are minor. Spurt loss ordinarily is not affected by the flow velocity in the fracture and is inversely proportional to concentration of agent. The filter cake, once it is well established, is resistant to damage by the flow of plain fracturing liquid (without fluid-loss agent). The latter two findings indicate that a treatment employing a high-concentration spearhead followed by plain fluid can offer a more economical treatment under suitable conditions. INTRODUCTION The successful design of hydraulic fracturing treatments depends on accurate knowledge of the fluid-loss properties of the fracturing fluid. Howard and Fast,' in giving the basic equation relating fracture area to fluid and treating parameters, described three mechanisms which might control the rate of fluid leak-off from the fracture. One mechanism usually is dominant in a given well treatment. For each mechanism, the leak-off velocity is inversely proportional to the square root of time, and the proportionality constant is designated as the fracturing-fluid coefficient. For the wall-building type of fluid-loss agent, the coefficient is determined by a filtration test in a pressure cell, usually with a rock wafer or core as the filter medium. In these static tests, the cumulative volume generally is proportional to the square root of time, after an initial spurt volume. The static-fluid-loss test is not representative of the con,-&tions under which a fluid-loss agent performs in a fratturing treatment. The marked difference between the dynamic- and static-fluid-loss behavior of drilling fluids reported in the literature2,3 implies that dynamic testing is also needed with fracturing fluids. We have therefore undertaken a study of the dynamic-fluid-loss behavior of fracturing fluids. The testing apparatus has also afforded opportunity to evaluate the resistance of the filter cake to removal or damage by flowing fluid containing no fluid-loss agent, with and without sand. The results of these studies offer a means for more accurate evaluation of fluid-loss agent performance, and point the way to a "spearhead" fracturing technique which may offer more economical treatment for some wells. EXPERIMENTAL METHODS The dynamic-fluid-loss testing method is applicable to any type of wall-building fracturing fluid. The present study aimed first at finding what phenomena are involved, and therefore has been limited in the number of materials tested. All of the results specifically reported herein are for kerosene containing a commercial solid fluid-loss agent, which is commonly used at 50 lb/1,000 gal of oil. Another agent in liquid form, used usually at 20 ga1/1,000 gal oil, has shown all the same phenomena in dynamic tests, and generally the same level of fluid-loss control as the solid agent. The dynamic-fluid-loss core cell used in all tests is shown in Fig. 1. The fracture was simulated by the an-nulus between a 2.03 in. OD sandstone core and the surrounding pipe. Annulus widths of 0.234 and 0.117 in. were used, and the core was 3.5 in. long. The annular geometry provides a uniform fluid velocity and a well-defined shear rate over the entire filtering surface, and permits a large filter area (144 sq cm) in a reasonably compact cell. The leak-off fluid passed into a 0.5 in. diameter axial hole in the core. A hollow steel rod through this hole was threaded into a rounded "streamliner" upstream of the core, and into a mounting stud downstream. The streamliner and the stud had the same outside diameter as the core. In all tests except those where sand was circulated, the mounting stud had protruding rings which constricted the annulus, to minimize any tendency for channeling of the fluid to the side exit port. The ends of the core were sealed by Neoprene, steel and Teflon washers. The leak-off fluid was conducted from the hollow rod to an exit tube, through a metering valve (a fine-pitched needle valve) and a quick-opening toggle valve in series, and into graduated cylinders for volume measurement; Two separate circulating systems were used in the experimental program. The extensive initial testing was done at 50 to 150 Psi. The fluid was circulated by a variable speed Moyno pump, and the flow rate was read by a rota-meter flow meter. The filtration Pressure was supplied by holding a back-pressure with a throttling valve. The discharge streamcould be diverted into any of four sections

Jan 1, 1965

By A. Heim, M. Gondouin

Invasion experiments were run on Berea sandstone cores to get laboratory measurements of resistivity and saturation profiles characteristic of water and oil sands invaded by mud filtrate. Injection rates were as low as 1.13 cm/D, and the cores were 30 to 36 in. long, cut parallel to the bedding planes. In the water-sand case, the resistivity profiles revealed the existence of an extensive transition zone between flushed and uncontaminated zones. In the linear geometry of the experiment, the width of the transition zone increased as the square root of the injected fluid volume. For the oil-sand case the core was prepared by displacing the formation water with kerosene to minimum water saturation. During the subsequent invasion experiment. oil saturation was measured directly by means of an oil-soluble radioactive tracer, and resistivity profiles along the core were taken at the same time. These data were interpreted in terms of an oil-water front, followed by a formation water bank, a zone of mixed waters, and finally, invaded mud filtrate near the borehole. Micro-fingering and capillarity seemed to affect considerably the resistivity profiles observed in the invaded oil-sand experiment. Beyond the regular conductive annulus or "low zone", it was found that a resistive "anti-annulus" could also be formed. As a result of these experiments, some simplified invasion profiles have been accepted and are being used in Grand Slam* interpretations. INTRODUCTION The importance of the mud filtrate-invaded zone in interpreting electrical logs has long been recognized.',* In trying to account for its effect, only very simple models of the resistivity profiles in the radial direction from the borehole have been used. In fact, most log interpretation charts have been based on resistivity models consisiting of two media of uniform resistivity (R, and R,) abruptly separated at the diameter of invasion. Such a clean separation of the media of different resistivities seems unrealistic, since flushing may not be perfect and may vary with radial distance into the formation.3** The nature of the transition zone, when it is within the radius of investigation of the surveying devices, may affect the log readings. Campbell and Martin' verified that a conductive annulus containing a high percentage of formation water may be formed when mud filtrate invades an oil-bearing sand. Interpretations which are to include the effect of such an annulus require the addition to the model of a conductive zone located at the outer rim of the invaded zone.' Using the Buckley-Leverett relations,6 aturation profiles may be derived, from which resistivity profiles can be calculated. Results of such computations by K. S. Kunz and J. H. Moran were given in a paper by Dumanoir. Tixier and Martin,7 and led to the construction of log interpretation charts which were based on a representation with three media of resistivities R, R0 and R1. Fig. 1 shows a schematic representation of a resistivity profile which includes an annulus. Campbell and Martin realized that, during the invasion of an oil sand, both capillarity and mixing would contribute to rounding of the profile shown in Fig. 1. Capillarity tends to draw some of the formation water from the annulus into the uncontaminated (Rt) zone, whereas mixing of the mud filtrate with formation water of the

Jan 1, 1965

By S. J. M. van Leeuwen, R. Feenstra

The effect of jets on bit penetration has been investigated by means of a 50-ton drilling machine and 8½-in. commercial jet bits, drilling under representative bottom-hole conditions. The conclusions apply to the drilling of impermeable rock only. Penetration rate is in all cases primarily hampered by a differential pressure effect, known as dynamic hold-down. Jet action can reduce this slightly. Major gain in penetration rate, up to 25 or 50 per cent, is already ohtained at medium-high jet power. At high bit load, penetration by soft to medium-hard-formation bits is further hampered by bit-balling. Its alleviation requires intensive tooth scavenging, which is best performed by slanted nozzles with trailing, high-velocity, high-volume jets, hitting bottom in front of the teeth. Penetration may then improve by a 100 per cent. At high bit load, bottom-balling limits the penetration of insert-type bits. In this case bottom scavenging is required, which is most effectively performed with high velocity jets from nozzles extended close to bottom. As a result of this measure, penetration may improve 70 per cent in non-friable rock, and less in friable rock. This will make the insert-type bit more versatile. Toothed hard-formation hits suffer at high bit load from both bit- and bottom-balling. Slanted nozzles, possibly much extended, with high-velocity, high-volume jets then have best prospects. INTRODUCTION For years the use of jet bits in oil well drilling has been increasing, in conjunction with ever greater hydraulic horsepower. To the same extent, the need for efficient use of the horsepower has grown.' This paper, it is hoped, will contribute to an understanding of how effective jet action may be obtained. It deals with the effect of jets on phenomena that are known' " to hamper bit penetration. To study this effect, laboratory drilling tests were performed with 8½-in. commercial bits under bottom-hole pressures representative of deep wells. The investigation has been restricted to the drilling of practically impermeable rock. In the following sections, the increase in bit penetration rates due to jetting is discussed for conditions which made the troublesome phenomena stand out one at a time. A brief definition and interpretation of these phenomena is given in Appendix A. Appendix B gives the results of measurements of fluid velocities along the hole bottom, performed in stationary flow tests. Descriptions of equipment, bits, rocks and mud are collected in Appendix C. Unless otherwise mentioned, drilling conditions were kept standard as given in Table 1. CUTTING TRANSPORT TO THE ANNULUS Jet action was for some time believed to merely improve the transport of cuttings from bottom to annulus, resulting in a clean hole bottom. Flow tests performed in 1954 at the Battelle Memorial Institute6 showed, however, that jet velocities of the order of 40 ft/sec sufficed to clear even large (0.4-in.) chips from bottom in the time between two successive tooth actions. In the field, optimum jet velocities are appreciably higher, indicating that other effects must be involved. This much is confirmed by the results of our drilling experiments in soft rocks performed under atmospheric pressure, i.e., in absence of pressure-differential effects. Fig. 1 shows that variation in the nozzle velocity from 40 to 330 ft/sec had no effect on penetration rate, unless the bit penetrated more than 7 mm per revolution, which is about half the tooth height. At such high rates—150 ft/hr at 100 rpm—cuttings would be caught in the tooth cavities, leading to bit-balling, which was noticed on inspection of the bit. The jets thus assisted in keeping the tooth cavities clean. This is just perceptibly reflected in the penetration-rate curves of Fig. 1: Much the same results were obtained in hard rocks with hard-formation three-cone bits. The conclusion is that transport of loose cuttings towards the annulus does not require a powerful jet action. In the following sections we shall see that in deep-well drilling other phenomena are of greater importance. DYNAMIC HOLD-DOWN It is generally accepted that, in deep-well drilling, bit penetration is hampered primarily by the existence of a difference in pressure between the fluid in the hole and that in the rock at the depth of cutting.2-5 In the drilling

Jan 1, 1965

By W. C. Browning

The influence of the hydroxyl factor is more damaging to formations penetrated and causes greater consumption of drilling mud additives than previously realized. This hydroxyl effect on clays is essentially independent of the cations present in the drilling fluid and thus differs from the base exchange reactions that have preoccupied mud chemistry with sodium and calcium bentonite concepts for nearly two decades. The new organic polyelectrolyte-con-ditioned muds haw made it possible to use materials other than sodium hydroxide to maintain the alkalinity of such muds. The properties of silicates, as indicated by their dissociation characteristics and buffering action, are such that they can control he pH and alkalinity of drilling muds at the desired level and, at the same time, minimize undesirable hydroxyl effects associated with sodium hydroxide. This use of silicate compounds is different and distinct from prior applications of silicates as deflocculants or shale preservers. Laboratory and field data presented in this report show that silicate compositions can be utilized to adjust the alkalinity of drilling muds and, at the same time, minimize hydmxyl-promoted clay cleavage. INTRODUCTION Studies for improving the efficiency of rotary drilling techniques must consider the chemistry of drilling fluids and of the formations being penetrated. The chemical aspects of drilling must be studied in conjunction with and in relation to the mechanical factors if, for example, penetration rates are to be optimized. Drilling fluid technology has been largely influenced by chemical reactions of the montmorillonite (bentonite) clay minerals. Most of the literature of mud chemistry concerns the properties of bentonite. Clays of the kaolin or illite type, which are nonswelling, are not generally regarded as sources of drilling mud problems. If these nonswelling shale clays are considered, they are commonly regarded as inert solids. Particularly noteworthy is the fact that the relation of surface and colloid chemistry to massive shale bodies has received only scant attention from drilling technologists. Clay studies reported in the drilling mud literature have dealt, for the most part, with the properties of clays in a finely divided state, and often in very dilute suspensions. Yet frequently during drilling, shale problems not related to the rheology of clay suspensions develop in massive non-bentonitic shale sections of zero or near zero permeability. This paper is concerned with surface chemical reactions that can influence the behavior of these non-bentonite clay masses in such a manner as to adversely affect drilling operations. Browning and Perricone1,2 have pointed out that some of the most troublesome shales to drill, such as the Atoka, contain no montmorillonites. They also pointed out that mud problems can frequently be mitigated by reduction of clay cleavage achieved by using drilling fluids with a minimum of available hydroxyl ions. If pronounced clay cleavage occurs during drilling, the borehole may soften, increasing the possibility of sloughing. In addition, the resulting increased incorporation of high-surface-area clay solids into the mud system can reduce penetration rates and necessitate greater chemical treatment. This increase of shale, of colloidal or near-colloidal dimensions, into the drilling mud is due to clay aggregate cleavage and not to base exchange or swelling reactions, such as occur with bentonites. Searle and Grimshaw3 point out the difference between cleavage or slaking reactions of nonswelling clays (such as illite and kaolinite) and the swelling of bentonite. They further state that the speed of slaking is increased in alkaline water. Eitel1 cites Salmang and Becker, who recognized that clay surface reactions impart plasticity and workability to clay masses. Their results clearly show that all liquids which contain hydroxyl groups in their molecules favor the workability of clays. The ancient technique of aging clays in the moist condition to increase their "workability" is evidence that these clay cleavage phenomena are of considerable importance. The same hydration cleavage that occurs during the aging of nonswelling clays for ceramic use also acts to break up cuttings and soften the borehole during drilling operations. The mechanism of cleavage of the crystalline aggregates of illitic, kaolinitic and other nonswelling clays; and the chemical means of controlling this cleavage are therefore of considerable significance to the drilling mud chemistry. Inasmuch as there is little reference in the drilling mud literature to the cleavage reactions of nonswelling clays, the structure of these clays and certain properties that relate to the mechanism of clay cleavage will be reviewed briefly. STRUCTURE OF NONSWELLING CLAYS Clays such as kaolinite, illite and montmorillonite are compmed of alternate layers of (1) silicon-oxygen tetra-

Jan 1, 1965

By R. F. Burdyn

The inadequate use of centrifugation to economically recover solids from weighted drilling fluids reflects the need for better equipment and techniques for this putpose. Laboratory studies in the development of an improved separator are described in which an operating equation is derived and tested. Results show that the concentric cylinder geometry employed effectively separates bnrite from a suspension and that the operating equation provides a good approxinmtion for scale-up. INTRODUCTION Our current drilling technology frequently requires a high-density drilling fluid obtained by addition of barite. In the course of drilling, formation solids which are too fine to be removed either by screening or settling become suspended in the drilling fluid and gradually the volume of solids in the mud increases. The volume fraction of solids must be limited (if a satisfactory set of rheological parameters are to be maintained). A centrifugal separatorprovidesan economical way of accomplishing this. The barite recovery process can be considered as a separation of two solids. One, the light solids, composed of formation and added solids, has a specific gravity of 2.6 to 2.7; the other, barite, has a specific gravity of 4.2 to 4.3. This density difference, plus the fact that the average light-solids particle size is much smaller than the average barite particle size, permits separation by a centrifuge. In drilling fluids some of the coarse particles of the light-solids-range will settle faster than fine particles of the barite-particle range. As a result a complete separation of the two species is not possible. since the object of the process is not merely recovering the maximum amount of barite but includes as well removing the maximum amount of light solids, an optimum barite recovery efficiency exists. From a practical standpoint this optimum cannot be determined in the field for each drilling fluid system, and in practice the separation is less than optimum, with some sacrifice of barite. Drilling technology has included centrifugal separators for barite recovery for more than a decade. Results have been reported by a number of investigators indicating that the process is practical and economica1. l-4 The decision to use a centrifuge is based on economics in which direct cost savings and the indirect benefits in rig time derived from improvement of the drilling fluid are important factors. One would expect that centrifugal separation of barite from drilling fluids would significantly affect barite consumption; however, this is not the case. The Minerals Yearbook shows an annual domestic barite consumption in the drilling industry of nearly 1 million tons.5 By rough estimate there are perhaps 80 separators presently in field use. Assuming half of these in use at any one time, operating an average of four hours per day, at recovery rates averaging 3,000 Ib of barite per hour, total annual recovery is about 90,000 tons. This is less than 10 per cent of he total barite used. I conservatively estimate that barite consumption in drilling operations can be reduced by 30 per cent through greater utilization of centrifugal separators. To encourage more widespread acceptance of centrifugal separators in the drilling industry, improved equipment and techniques would be very desirable. The present paper, covering theory and results obtained from a laboratory model, is the first in a series on he development of an improved mud separator for field use. THE CONCENTRIC CYLINDER GEOMETRY AS A SEPARATING DEVICE Consider the geometry shown in Fig. 1, consisting of two concentric cylinders separated by an annular space. These are arranged so that the outer cylinder is fixed and the inner one can be rotated about its axis on shafts sealed against the ends of the outer cylinder. If the outer cylinder is fitted with openings at either end, the inner

Jan 1, 1966

By D. E. Hawk, R. F. Burdyn, F. D. Patchen

Earlier work on a mud separator for barite recovery is extended to the design and construct ion of a rugged field unit. Problems associated with scale-up for field use include the me of dilution water and its effect on capacity, power requirements and pressures developed. Equations for these quantities are derived and applied in maximizing the beneficial effects of dilution and minimizing the power required. Tests on the full-size rotor show that its performance can be predicted by theory. The completed unit is compact and lighter than current decanting types. Its capacity is from 10 to 22 gal/min with corresponding barite recovery efficiencies of 92 to 86 per cent. INTRODUC'TION In an earlier publication a new type of centrifugal device was described for solid-liquid separations.l In that paper an operating equation was derived, and its validity demonstrated in laboratory scale experimentation. Some of the features apparent in this new device seem particularly well suited to the conservation of barite in field drilling-mud systems, hence the development was extended to the design and construction of a field unit. In the present paper the design problems associated with scale-up are considered. A full-scale, rugged self-contained field unit is described, and test results discussed which verify that the performance of the large field unit can be described by a simple operating equation. PRINCIPLE OF OPERATION OF SEPARATOR In principle, the new device is simply a perforated cylinder rotating within a body of fluid which is contained within a stationary case, as in Fig. 1. The frictional drag generated by the rotating cylinder causes part of the fluid to rotate. At the surface of the cylinder, assuming no slip occurs, the angular velocity of fluid and of the cylinder are identical. If there are suspended particles present of greater density than the fluid, the centrifugal force acting on these particles causes them to move radially away from the cylinder at some velocity vp . Where the Stokes settling equation holds, this velocity may be expressed as:2 d2 ?p rw2 If the case is provided with openings at both ends, a suspension can be pumped in at one end at a fixed rate. Part of the suspension can then be removed at a fixed rate at the other end of the case as underflow, and the remainder forced through the perforations and hollow shaft of the rotor to appear as effluent, also at a fixed rate. The radial component of the flow velocity of this stream as it reaches the rotor surface, is simply effluent flow rate divided by cylindrical surface area: Because up is a function of particle size, for some particular particle size, the velocities vp and v, will be equal in magnitude. This is defined as the critical particle size and represents the size above which all particles appear in the underflow and below which all particles appear in the effluent. For this equilibrium condition at the rotor surface, Eqs. 1 and 2 combined give

Jan 1, 1966

By P. F. Gnirk, J. B. Cheatham

Single bit-tooth penetration experiments under static load were conducted on six rocks at confining pressures of O to 5,000 psi using sharp wedge-shaped teeth with included angles ranging from 30 to 120° In general, the force-displacement curves for all rocks exhibit an increasingly nonlinear and discontinuous behavior with decreasing confining pressure. The confining pressure at which a rock exhibits a macroscopic transition from predominantly ductile to predominantly brittle behavior during penetration vmies from about 500 to 1,000 psi for the limestones to greater than 5,000 psi for dolomite. The correlation between calculated values of force per unit penetration based on plasticity theory and experimental values is quite encouraging, even at confining pressures as low as 1,000 psi A qualitative correlation between volume of fragmented rock per unit energy input for a single bit-tooth and drilling rate for microbits appears to exist over a confining pressure range of 0 to 5,000 psi. INTRODUCTION Laboratory experiments utilizing a small-scale drilling apparatus have demonstrated that penetration rates are reduced considerably as a result of increasing the confining pressure from atmospheric to a few thousand psi?-3 This undesirable situation can, in general, be attributed to a combination of decreased efficiency of chip removal at the bottom of the borehole, increased rock-failure strength, and a possible change in the mechanism of chip generation and rock fragmentation with increasing confining pressure. To more fully understand the principles underlying the last circumstance, it is the purpose of this investigation to experimentally study the mechanism of single bit-tooth penetration into dry rock at low confining pressures and, in particular, to establish the confining pressure at which the penetration mechanism may undergo a brittle to ductile transition for various rock types commonly encountered in drilling. Confining pressure as used here refers to the differential pressure between the borehole fluid pressure and the formation-pore fluid pressure. EXPERIMENTAL PROCEDURE Using an experimental apparatus previously described: a single, sharp wedge-shaped tool was forced under a "statically" applied load into an effectively semi-in finite dry rock sample subjected to a prescribed confining pressure. To prevent the invasion of the con fining-pressure fluid into the pores of the rock sample during penetration, the exposed surface of the rock was jacketed with a layer of silicon putty.* Electrical instrumentation incorporated into the apparatus yielded a graphical plot of force on the tool as a function of penetration or displacement of the tool into the rock during an experiment. During the course of the experimentation the following conditions were maintained constant: (1) pore pressure — atmospheric (i.e., the rock was dry); (2) temperature — 75F; (3) rate of loading — essentially static (approximately 0.002 in./sec); (4) bit tooth — a sharp wedge-shaped tool loaded normal to the rock surface; (5) rock surface — smooth and flat; (6) drilling fluid — hydraulic oil; and (7) maximum depth of penetration — approximateiy 0.1 in. In addition, each experiment was performed on a different rock sample so the rock surface is free of a layer of cuttings and of any previous indentation craters. The influence of the corners of a borehole was neglected, since each rock sample was cemented inta a section of aLuminum tubing to simulate a semi-infinite body. Indentation experiments were made on a sandstone, two limestones, a marble, a dolomite and a schist with a 60' bit-tooth over a range of confining pressures from atmospheric to 5,000 psi and at a constant confining pressure of 1,000 psi for a variety of bit-teeth with angles ranging from 30 to

Jan 1, 1966

By H. Matlock

Beam-columns with continuous or discontinuous transverse and angular loads and elastic restraints are represented mathematically in a manner corresponding to finite-element mechanical models. Solutions for linearly elastic cases are accomplished by direct recursion-equation elimination of unknowns, and for cases involving nonlinear loads and supports, by repeated trial-and-adjustment of complete elastic-type solutions. Five practical applications are presented by which various capabilities of the general method are illustrated. The examples include simulation of a pipeline launching and the bending and collapse of a conductor pipe in deep-water drilling operations. INTRODUCTION The diversified and complex operations being conducted in support of the production of offshore oil have produced a wide variety of new problems in structural mechanics. Many of these problems cannot be solved by conventional analytical or experimental approaches and have therefore stimulated inquiry into new methods of solution. It is the purpose of this paper to give a brief description of an analytical method for solving nonlinear beam-column problems and to illustrate the generality of the method by applying it to several problems related to offshore operations. Although the data for all of the examples are artificial, the cases discussed will be recognized as being based on actual situations. DESCRIPTION OF METHOD The analytical approach which is to be described stems from research on offshore foundations, in particular, the study of lateral-load behavior of foundation piles. The method represents a generalization of a technique which was suggested by Gleser' and extended by Focht and McClelland2 and Reese and Matlock." To maintain generality and therefore versatility in the method, a considerable variety of input data is considered. Fig. 1 illustrates the various types of loads and restraints which might be applied to a short segment of a beam. Each of the terms illustrated in the figure is shown acting in a positive sense. Capital letters are used to designate concentrated quantities whereas the corresponding lower-case symbols indicate effects which are distributed in some way along the length of the beam. The transverse loads and the elastic restraints may be divided into two classes: (1) loads Q and q and springs S and s, which act normal to the axis of the beam, and (2) couples T and t and rotational springs R and r, which act in an angular sense. In addition, there is an axial force P which may be constant or may vary along the length of the beam. The bending stiffness of the beam (the product EI of the modulus of elasticity and the moment of inertia) is designated by the symbol F. The assumptions of conventional elementary beam theory provide the basis for the present method. Among these are the neglect of shearing and axial deformations and the limiting of consideration to straight beams of symmetrical cross-section. Lateral deflections are considered to be small compared to original dimensions. A deformed element of such a beam is shown in Fig. 2a. The curvature of the beam is approximated by the second derivative of the deflection y with respect to distance x along the beam. It is assumed that the material of the beam is linearly elastic and therefore the relation of Eq. 1 between curvature and bending moment M is the ordinary expression from elementary beam theory. A generalized beam element is shown in Fig. 2b. The element has been deflected in a positive direction by an amount y and tilted through a small positive angle dy/dx. The various loads and elastic restraint reactions are detailed in the figure. Temporarily, only distributed effects are considered; provision for concentrated loads and restraints will be made subsequently. Eq. 2 in Fig. 2b is obtained by summing the forces and moments acting on