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By W. C. Maurer

A study of bit-tooth penetration, or crater forniation. under simulated borehole condirions has been made. Pressure conditions existing when drilling with air, water and mud have been sirnulated for depths of 0 to 20.000 ft. These crater tests showed that a threshold bit-tooth force must he exceeded before a crater is .formed. This thresh old force increased with both tooth dullness and diflerenrial pressure between the borehole and formalion fluids. At low differential pressures, the craters formed in a brittle manner and the cuttings were easily removed. At high differenlial pressures, the cunings were firmly held in the craters and the craters were formed by a pseudoplas-tic mechanism. With constant farce of 6,500 16 applied to the bit reeth, an increase in differential pressure (sitnulated mud drilling) from 0 to 5,000 psi reduced the crater volumes by 90 per cent. A comparable increase in hydrostatic fluid pressure (simulated water drilling) produced only a 50 per cent decrease in volutne while changes in overburden pressure (simulated air drilling) had no detectable effect on crater volume. Crater tests in unconsolidated sand subjected to differential pressure showed that high friction was present in the sand at high pressures. Similar friction belween the cuttings in craters produces the transition from brittle to pseudo plastic craters. INTRODUCTION The number of wells drilled below 15,000 ft increased from 5 in 1950 to 308 in 1964. Associated with these deep wells are low drilling rates and high costs. High bottom-hole pressures produce low drilling rates by increasing rock strength and by creating bottom-hole cleaning problems. This paper describes an experimental investigation of crater formation under bottom-hole conditions simulating air, water and mud drilling. Although numerous investigators have studied bit-tooth penetration (cratering) at atmospheric pressure conditions, only limited work has been done on cratering in rocks subjected to pressures existing in oil wells. Payne and Chippendale2 have studied cratering in rocks subjected to hydrostatic pressure using spherical penetrators. Garner et aLJ conducted crater tests in dry limestone by varying overburden pressure and borehole fluid pressure independently and using atmospheric formation-fluid pressure Gnirk and Cheathem4,5 have studied crater formation in several dry rocks subjected to equal overburden and borehole pressure and atmospheric formotion pressure. Podio and Gray studied the effect of pore fluid viscosity on crater formation using atmospheric borehole and formation-fluid pressurc and varying overburden pressure. Although these studies have provided useful information on crater formation under pressure, they were limited in that the three bottom-hole pressures could not be varied independently and, therefore, that many drilling conditions could not be simulated. The prersure chamber used in this study allowed visual observation of the cratering mechanism and independent control of the borehole, formation and confining pressures. By using different fluids in the chamber, pressure conditions existing in air, water and mud drilling to depths of 20,000 ft were simulated. The mechanisms involved in cratering at these different pressure conditions were studied for teeth of varying dullness and at different loadins rates. High-speed movies (8,000 frames/sec) and closed-circuit television were used to visually study the crater mechanism under pressure. EXPERIMENTAT PROCEDURE PRESSURE CHAMBER The Pressure chamber in Fig. I was used to simulate bottom-hole pressure conditions. This chamber has been pressure-tested to 22,500 psi and is normally operated at pressures up to 15,000 psi. The chamber contains four lucite windows' used for illuminating and observing the crater mechanism under pressurc. A closed-circuit television and a Fastax camera (8,000 frames/sec) have been used in these studies. Cylindrical rock specimens (8-in. diameter X 6-in. long) were subjected to three independently controlled pressures simulating overburden, borehole fluid and formation-fluid pressures. Overburden pressure, which corresponds to the stress induced by the overlying earth mass, was applied by exerting fluid pressure against a rubber sleeve surrounding the rock. Borehole pressure, which is the pressure exerted by the column of mud in the wellbore, was simulated by applying pressure to the fluid overlying the rock in the chamber. Formation pressure was simulated by applying pressure to the water saturating the rock. The borehole and formation pressures were equal except when mud was used in the chamber, in which case the differential pressure between these fluids acted across the mud filter cake.

Jan 1, 1966

By H. A. Kendall, W. C. Goins

Several investigations in recent years have shown that drilling rates are increased significantly with increased hydraulic horsepower. But, there has been no over-all method of designing jet-bit programs that efficiently uses the surface power. A study of present practices indicates that frequently as little as 50 per cent of the possible effects at the bit are used. Some observers have indicated that the best utilization of hydraulic horsepower (maximum effect on drilling rate) occurs when the bit hydraulic horsepower is maximum; others have stated that jet impact force is more important, and others have believed that maximum jet velocity is required. Limited efforts to date have shown some optimum conditions for bit hydraulic horsepower and impact, but these conditions cannot exist during drilling of a large part of the hole and do not provide a basis for designing a complete jet-bit program. This paper shows the maximum obtainable bit horsepower, impact force and jet velocity at all depths, taking into account the limitations of the pump, piping, hole and minimum circulating rate for adequate cuttings removal. Ranges of operation are developed; and flow rates, surface pressure and bit pressures are specified for each range to provide a maximum of any one of the desired effects. It also is shown that, by proper selection of nozzle sizes and by following the rules presented, the maximum obtainable quantities can be effectively utilized from surface to total depth. Finally, a simple graphical method of selecting nozzle sizes and flow rates is presented which can be used with familiar bit-company hydraulic tables and calculators to design jet-bit programs for maximum bit hydraulic horsepower, impact or jet velocity, as desired. These programs make most effective use of the pumps. Heretofore, there was no method available for designing field tests which adequately separated the effects of bit horsepower, impact and jet velocity. The programs and procedures developed in the paper are dissimilar and, when used in future field testing, should demonstrate which program is the most important in obtaining the fastest drilling rate. INTRODUCTION During the past decade, rig hydraulics has come into increasing prominence. There has been a definite trend toward providing higher horsepower pumps, jet-type bits have had increased use, numerous investigators"" have reported increased drilling rates as a result of increased hydraulics, and bit manufacturers have provided tablesa-" and calculators that are now commonly used 10 design jet-bit programs. Opinion has varied as to the hydraulic quantity which has the great- est effect on drilling rate. Papers and data have been presented that show pump horsepower,'9 it hydraulic horsepower and jet impact force,' each to be the most significant factor affecting drilling rate. Examinatibn of jet-bit programs of the bit companies indicates emphasis on jet velocity. Only pump horsepower can be eliminated because it can be used to produce any one of the bit effects which, a priori, must be more relevant factors. This contradictory state of opinion and practice regarding the bit effects is unfortunate, but several published references have been concerned with making one or another of the factors maximum; and, because these in each case have given results applicable to only intervals of the hole drilled, there seems to be ample reason to complete the previous efforts. It also is believed that the differences in programs for each effect, where they exist, should be delineated so that future use may determine which hydraulic effect is the more relevant. It is the purpose of this paper to: (1) show the theoretical maximum bit hydraulic horsepower, jet impact force and jet velocity available at all depths, taking into consideration all necessary restrictions on operating conditions; (2) illustrate procedures by which the maximum available horsepower, impact force or veIocity may be obtained; and (3) present a graphical method for rapid selection of jet-nozzle sizes and flow rates to be used with conventional procedures to design jet-bit programs for maximum bit horsepower, impact force or velocity as desired.

By H. C. H. Darley

The influence of particle size and concentration on the development of chip hold-down pressure (CHDP) was studied in an apparatus designed to measure the change of filtration rate during the first second of the filtration process. CHDP is controlled by the "bridging" particles (i.e., particles in the 50 to 0.2 micron range), whereas filter loss is controlled by the colloid fraction. The results indicated that a fast drilling fluid with a low filter loss could be obtained if the concentration of bridging solids and the viscosity were kept very low. A novel group of drilling fluids, which we have named colloid emulsions, was developed to meet the above requirements. These colloid emulsions are made by dispersing art oleophilic colloid in oil and emulsifying about 5 per cent of this dispersion in water or a dense brine. Good results have been obtained in field trials with emulsions which use asphalt as the oleophilic colloid. INTRODUCTION In recent years it has been found that fast rates of penetration can be maintained in hard formations by using "clear" water as a drilling fluid. In some cases, however, water cannot be used because the very high down-hole filter loss creates various difficulties in drilling, in logging, or in producing the well. It then becomes necessary to "mud up", which results in a decrease in drilling rate. The reason that mud decreases drilling rates is a complex subject which has been well covered by such authors as Garnier and van Lingen, Cunningham and Eenink,' and van Lingen.3 One of the principal factors involved is the tendency of the drilling fluid to develop a filter cake on the bottom of the hole. The pressure differential which develops across this filter cake opposes the action of the bit in dislodging chips from the rock. This pressure differential is referred to by Garnier and van Lingen' as the chip hold-down pressure, which is denoted by the initials CHDP in this paper. The work described in this paper was undertaken to develop a drilling fluid which would minimize CHDP but which would still have a low filter loss—in other words, a fluid which would deposit a filter cake on the sides but would lay little or no filter cake on the bottom of the hole. EVALUATION OF CHDP EXPERIMENTAL Conditions governing the growth of filter cake on the sides of the hole are obviously different from those on the bottom of the hole. On the sides of the hole, cake will form continuously but at a decreasing rate, until eventually the rate of growth will equal the rate of cake erosion by the mud stream.' On the bottom of the hole, each time a bit tooth dislodges a chip the cake is removed, a fresh rock surface is exposed, and the filtration process must start over again. Thus the CHDP is determined by the amount of cake which can form in the interval between successive tooth strikes at a particular spot, normally a fraction of a second. Our first step therefore was to study filtration rates over the first second or so of the filtration process. These tests were conducted in the simple type of dynamic filter cell shown in Figs. 1 and 2. In this cell the mud was filtered through a train of rock cores while rotating blades kept the mud flowing over the surface of the core. The procedure was to evacuate the cores to 0.05 mm of mercury, saturate with brine, and assemble in the holder under brine. The permeability of the core train was then determined. A plastic seal was placed on the face of the core train, and a rip cord was attached from the seal to one of the blades. At the start of the test, 500 psi was applied to the mud, and the meniscus in the capillary measuring tube was adjusted to zero. When the blades were started, t,he seal was ripped from the face of the core, and filtration began. The filtration rate was at first measured by photographing the advance of the meniscus in the capillary tube. Using

Jan 1, 1966

By E. I. Radzinovsky, D. W. Dareing

This paper presents theory which is used to predict rock-bit bearing life reduction due to simple harmonic variations in bit forces. The theory is based on the premise that if a constant load acts for a certain fraction of the life which the bearing would have if that constant load were applied for its entire life, then the same fraction of thelife of the bearing is consumed. Total bearing life is related to simple harmonic variations in bearing life associated with instantaneous bearing loads. The results show that rock bit bearing life is not affected appreciably by forces commonly impressed upon a bit, but it is affecied appreciably by relatively large dynamic bit forces occasionally encountered during drilling. In addition, the results show that the life of sealed bearings is more sensitive to bit force variations than is the life of unsealed bearings. INTRODUCTION Roller bearings are important components in roller cone rock bits because they transmit a large portion of the drill collar weight to the formation being drilled. Unfortunately, they have a relatively short life under down-hole drilling conditions. Roller bearings are usually the first bit components to fail, and their failure leads immediately to failure of the entire bit. Short roller bearing life, and thus short bit life, is due mainly to high unit loads transmitted by the bit and to the adverse environment in which the bearings operate. The results of the study discussed in this report show how dynamic bit forces also affect roller bearing life. The purpose of this paper is to discuss theory developed to predict the effect of different magnitudes of periodic bit forces on roller bearing life. Theoretical results are used to compare the life of rock bit roller bearings subjected to steady forces to the life of rock bit roller bearings subjected to unsteady forces similar to the type of unsteady forces measured at the bit with a special downhole recording instrument. BACKGROUND AIanufacturers of bearings have conducted laboratory tests which show how bearing life is affected by steady bearing load. 1 The well-known empirical equation which defines bearing life follows from bearing test data. It is: where L = bearing life, hr P = bearing load, Ib C = constant q = exponent (constant). The effect of environment on bearing performance is manifested through the exponent q and the constant, C. King,2 in similar tests conducted on roller bearings used in rock bits, showed that, in addition to the load, the environment (abrasive materials, chemical components, etc.) greatly affects bearing life. His data, which show how the life of roller bearings in a 7-7/8-in. W7R bit rotating at 60 rpm is affected by bit weight and fluid environment, are displayed on a log-log plot by broken lines made up of straight line segments. Each broken line corresponds to a given environment. One segment (q = 1.4) of the broken line corresponding to a fluid environment of barite mud is shown in Fig. 1 along

Jan 1, 1966

By L. W. Legerwood

During the past three decades, the oil industry has expended increasing eflorts seeking improved drilling tools or systems to reduce drilling costs. The total cost of these efforts is unknown, but it certainly amounts 10 tens of millions of dollars. Most of the "new" system that past and present investigators have sought to develop actually are old public information. In seeking to implement new-systern concepts, investigators have tested the following: impact at frequencies ranging from 6 to 300 cycles per second; electrical, mechanical and hydraulic meam of actuating percussors; bit rotary speeds up to 2,000 rpm; electric and hydraulic bottom-hole means of rotating bits; bottom-hole machines with power outputs up to 400 hp; shock waves; explosives; high-velocity pellets; flame; arc; grinding wheels; abrasive jets; erosion by high-velocity gases; chemical attack; electric current; magnetic waves; retractable rock bits; reelable drill pipe; continuous coring with reverse circulation; and automation of drilling rigs. Table I shows how these investigations are grouped for discussion purposes in this paper. In spite of these efforts to discover new and improved systems, rotary drilling main;aim its economic leadership. Undoubtedly, rotary drilling costs will continue to be reduced by rigid application of the best available technology and by development of new rotary technology. In view of the extensive past development programs, however, significant long-range improvement appears to be a research, not a development problem. Research must postulate and prove theories and principles governing variour subsurface rock-failure processes pertinent to both rotary and new systems. Ah, research must produce physical and engineering data relative to these processes. When such information is available, earth boring will graduate from an art to a science. Major improvements in rotary drilling can then be expected, and the systematic evolution of an improved drilling method can be initiated—with a strong probability for success. Development of drilling methods other than rotary drilling has been one approach investigated by the industry as a means for reducing drilling costs. Major cost-reduction efforts, however, have been centered on engineering development work aimed at incremental improvements in rotary drilling. A relatively minor effort has been expended to establish basic physical principles and engineering data pertaining to the earth-boring process which can serve as a foundation for the development of cost-cutting drilling hardware. Current oil-industry economic trends have added impetus to the need for effective programs to reduce drilling costs. However, areas for expanded future efforts should be selected only after careful study of past investigations. It is the purpose of this paper to review past and Dresent industry efforts to develop new drilling tools or systems and to suggest areas where additional science is needed. Past reviews of drilling methods have been limited to a few processes prominent at the time the reviews were made. This paper seeks to present a concise, well organized review of all methods that have received actual development or test work. The preparation of a paper seeking to review all past developments is fraught with many difficulties, not the least of which are errors in or obsolesence of printed matter used as source material and the lack of data on industry developments which have not been published. Since de-

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By C. E. Hottman, R. K. Johnson

Fluid pressure within the pore space of shales can be determined by using data obtained from both acoustic and resistivity logs. The method involves establishing relationships between the common logarithm of shale transit time or shale resistivity and depth for hydrostatic-pres-sure formations. On a plot of transit time vs depth, a linear relationship is generally observed, whereas on a plot of resistivity vs depth, a nonlinear trend exists. Divergence of observed transit time or resistivity values from those obtained from established normal compaction trends rinder hydrostatic pressure conditions is a measure of the pore fluid pressure in the shale and, thus, in adjacent isolated permeable formations. This relationship has been empirically established with actual pressure measurements in adjacent permeable formations. The use of these data and this method permits the interpretation of fluid pres.rure from acoustic and resistivity measurements with an accuracy of approximately 0.04 psilft, or about 400 psi at 10,000 ft. The standard deviation for the resistivity method is 0.022 psi/ft, and for the acoustic method 0.020 psi/ft. Knowledge of the first occurrence of overpressures, and of the precise pressure-depth relationship in a geologic province, enab1es improvements in drilling techniques, casing progroms, completion methods and reservoir evalzmtions. INTRODUCTION CENKRAL STATEMENT Operators engaged in the search for and production of hydrocarbon reserves in Tertiary basins are more and more frequently confronted with complications associated with over pressured (abnormally high fluid pressure) formations. This is particularly true in the Texas-Louisiana Gulf Coast area. The problems associated with these formations are of direct concern to the combined activities of all phases of operations, i.e., geophysical, drilling, geological and petroleum engineering.' - Knowledge of the pressure distribution of a given area of operations would greatly reduce the magnitude of many of these complexities and in some cases would completely eliminate specific problems. his pape; presents techniques developed for estimating formation pressures from interpretations of acoustic and electric log data. Specifically: the acoustical and electrical properties of shales, reflected by conventional acoustic and electrical surveys, can be used to infer certain reservoir properties, such as formation pressure, at any level in a well. It has been possible to develop these techniques because of a firm understanding of the basic principles that govern and apply to such overpressured provinces. NORMAL PRESSUKES Normal pressures refer to formation pressures which are approximately equal to the hydrostatic head of a column of water of equal depth. If the formations were opened to the atmosphere, a column of water from the ground surface to the subsurface formation depth would balance the formation pressure. On the Gulf Coast, the shallow, predominantly sand formations contain fluids which are under hydrostatic pressure. These formations are said to be normally pressured or to have a normal pressure gradient.* Experience has shown that the normal pressure gradient on the Gulf Coast is approximately 0.465 psi/ft of depth. OVERPRESSURES Formations with pressures higher than hydrostatic are encountered at varying depths in many areas. These formations are referred to as being abnormally pressured, abnormally high pressured, or overpressured. Formation pressures up to twice the hydrostatic pressure have been observed. These formations require extreme care and much expense to drill and to exploit. COMPACTION-FLUID PRESSURE RELATIONS THEORY The generation of overpressured formations in Tertiary sections of the Gulf Coast and several other Tertiary sedimentary basins is, in general terms, considered to be primarily the result of compaction phenomena.' This portion of the paper presents a brief review of the theory which associates compaction and fluid pressure relations, and should thus provide the necessary background for an understanding of the techniques presented. See Hubbert and Rubey' for a more comprehensive treatment of this subject. The theory of the consolidation of a water-saturated clay' has been well established by workers in soil mechanics. The concept is explained by a model with perforated metal plates separated by metal springs and water and enclosed in a cylindrical tube. Fig. 1 is a schematic representation of such a model (see Ref. 5, Fig. 27, page 74). The springs simulate communication between clay particles, and the plates simulate the clay particles. Mano-

Jan 1, 1966

By R. F. Krueger

Results are presented from tests of dynamic fluid-loss rates to cores from clay-gel water-base drilling fluids containing different commercial fluid-loss control agents (CMC, polyacrylate or smt,ch), organic viscosity reducers (quebracho and complex metal lignosulfonate) and oil at several different levels of concentration. In the dynamic system the most effective individual additives to the clay-gel drilling fluid, based on cost-equalized concentrutiom, were found to be starch and the viscosity reducers. These results do not conform with the rankings determined by API fluid-loss rests, which indicate CMC, polyacrylate and starch to be the most effective and comparable. Generally, minimum dynamic fluid-losr rates were attained at cost-equalized concentrations of additive (including thinner) of about $1.00/ bbl, or less. For chernically treated clay-gel drilling fluids, both the standard and the high-pressure API filter-loss tests were found to he inaccurate indicators of trends in dynamic fluid-loss rates under the test conditions used, particulurly for drilling muds containing viscosity reducers. From a practical field viewpoint, restrictions on the applicability of the API fluid-loss test are such that it is open to question whether or not results of this test can be used routinely with confidence as an indicator of control of down-hole fluid loss under field treating conditions. INTRODUCTION The petroleum industry spends large sums of money during drilling operations to control the fluid-loss properties of drilling fluids based on the standard API filter-loss test,' which is a static filtration system. Laboratory studies' ' of dynamic filtration have shown that in a given time period filtrate loss from a circulating mud stream is greater than from a static system and that it is a function of linear mud velocity, pressure and the properties of the drilling fluid. Ferguson and Klotz' and Horner, et al," observed that (I) the dynamic fluid-loss rates for the drilling fluids used were not related to the extrapolated API filter loss and (2) the drilling fluids with the lowest API filter losses did not have the lowest dynamic fluid-loss rates. However, there has been no published information on the relative effects on dynamic fluid-loss rate as a given drilling fluid is treated with increasing amounts of chemical additive to reduce the API filter loss. Such information is economically important because drilling-fluid costs rise rapidly as chemical requirements increase. This paper presents the results of a study of dynamic filtratioi rates to cores from a clay-gel water-base drilling fluid treated with various commercial viscosity reducers and chemical fluid-loss control agents. The dynamic fluid-. loss rates to cores are compared with the standard API filter-loss values at several different levels of additive concentration. Dynamic filtration rates were obtained in each experiment under two different simulated wellbore conditions: (1) filtration just above the bit through a new mud cake laid down dynamically on a freshly drilled formation and (2) filtration up-hole through a mud cake formed by deposition of a static filter cake on top of the initial dynamically formed cake. The latter case corresponds to the bottom-hole conditions existing above the bit when mud circulation is restarted after a stand of pipe has been added or a round trip has been made to change the bit. Except for the short-duration, high-rate filtration beneath the bit where no mud cake can form, these two conditions probably represent the two extremes of dynamic filtration. Because thickness of a dynamic mud cake formed on freshly exposed formation is limited by the shearing action of the mud stream, the filtration rate for this condition is high. On the other hand, once circulation is stopped and a static mud cake forms on top of the dynamic cake, re-starting circulation has only a small effect on the cake properties and filtration rate is much lower thereafter. A discussion of the mechanics of mud-cake deposition and dynamic filtration is outside the scope of this paper but may be found in more detail in publications by prior investigators. APPARATUS AND EXPERIMENTAL CONDITIONS The test equipment used to simulate the dynamic flow conditions existing during drilling was a modification of that described previously by Krueger and Vogel: A schematic flow diagram is shown in Fig. 1. In general, a power-driven, high-pressure mud pump capable of delivering up to 60 gallmin was used to circulate drilling fluid parallel to the faces of 1-in. diameter sandstone cores mounted in a 2 3/4-in. ID high-pressure test cell. Pump rates were controlled by means of a magnetic clutch to maintain an average axial fluid velocity of 110 ft/min in the annular space between the cell wall and a 1 1/2-in. rod positioned on the center line of the cell. The core specimens were Berea sandstone plugs sealed with plastic inside 1 1/8-in. OD tubes and were fluid-saturated prior to use. Burettes were used to accumulate fluid discharged from the cores. The mud sump shown was used for treatment and storage of the drilling-fluid samples during a particular test. The valve arrangement permitted either (1) circulating drilling fluid through the by-pass line while treating with

By C. Gatlin, N. E. Garner, A. Podio

Experimental data from single chisel blows on Leuders limestone are presented. A pressure chamber, similar in design to well known microbit drilling chambers, was utilized to impose variorcs stress states on the sample. Confining pressure of zero to 10,000 psi and borehole pressures from zero to 5,000 psi have been used in the studies. Pore pressure was zero and the rock samples dry in all instances. Force-displacement records and visual examination of the craters indicate that the mode of failure depends on both confining and borehole pressure in certain ranges, ranging from brittle, through a transition, to near plastic. The mode of failure is reflected in the observed blow force and energy data, as well as the shape of force-penetration curves. INTRODUCTION A previous paper' presented initial data from the project on which this paper is the second report. While the first paper dealt with impact studies on synthetic rocks, the literature cited there is also pertinent to this paper, but will not be listed again in order to avoid needless repetition. This paper presents experimental data from single chisel impacts on limestone at certain simulated wellbore stress states. Specific variables investigated were combinations of borehole and confining pressure, crater geometry, a narrow range of impact velocity and the forces required to drive the chisel into the specimens under the varying conditions. EXPERIMENTAL PROCEDURE The same basic apparatus described in our earlier paper, except for the pressure vessel, was used in this study. Fig. 1 shows the complete experimental system. Fig. 2 shows details of the pressure cell, which is quite similar to the well known microbit drilling chamber. The confining (overburden) pressure system provides independent pressure control over the sample except for two, 21/4 in. diameter areas located on the sample ends. These two areas provide a pore pressure entrance on the bottom and a striking surface on the top where borehole pressure can be controlled. The ends are isolated from the confining pressure by O-ring seals. The borehole and pore pressures are related through the striking surface; they will be the same unless a seal is deposited on the borehole surface, either a mud cake or some other impermeable membrane. In these studies pore pressure control was not used, as the rocks were dry and unsaturated in all cases. Rock samples were prepared from 4-in. cubes as illustrated by Fig. 3. The circular disks of adhesive vinyl plastic protected the impact surface from the resin coating (Scotchcast No. 2) and were removed just prior to each test. This procedure insured a fresh uncontaminated surface for the impact. Fig. 4 shows the dimensions and loading of the sample, including the concentrations around the "borehole" periphery (O-ring seal). The rock used in this study was Leuders limestone, of Permian age (Leonard), quarried near Leuders, Tex. Geologically, Leuders limestone is a light gray, fossili-ferous limestone (oolitic foraminifera1 biosporite). Its fossil content is 80 to 90 per cent and consists primarily of calcitornellid, ostracods, pelecypods and oolites with the remaining part intraclasts. There are hematite or limo-nite rims on some of the intraclasts. The porosity is approximately 20 per cent, but the permeability is less than 1 md. There is no apparent orientation in the structure. Triaxial tests have been conducted to determine the variation of the physical properties of Leuders limestone in three orthogonal directions', and it is known to be unusually isotropic and uniform. Physical parameters for this rock are: uniaxial compressive strength = 9,700 psi; F = 32 and C = 2,700 psi; where + and C are Coulomb equation values (t = C+u tan +). Impact tests were run under the combinations of confining and borehole pressures shown in Table 1. Samples were dry with atmospheric pore pressure in all cases. Tests, in which elevated borehole pressures were applied, used a single layer of household Saran-Wrap to prevent horehole fluid invasion into the sample. This proved to be simple and reliable. The blunt wedge used in all the tests was 0.75 in. long and had an included angle of 60" with a 0.05-in. flat. In addition, a sharp 60" wedge was used for all confining pressures at zero borehole pressure. The chipper speed

By L. H. Robinson

A proposed method of drilling utilizes sequential detonation of two types of explosive charges delivered to the hole by a conventional drilling fluid through pipe. A shaped charge first produces a long thin hole. A second charge, called a gauging charge, is pumped into the thin hole, explodes, and enlarges it to full gauge. In one suggested configuration, the explosives are contained in cylindrical capsules 4- to 5-ft long. A drilling head is positioned 2- to 3-ft off bottom. When a capsule is pumped to the bottom of the hole and stops, pressure inside the drill pipe increases and differential pressure detonates the explosive. Primacord along the length of the capsule disintegrates the capsule. The debris circulates out of the hole with the drilling fluid. The gauging-charge action was examined using 2-ft cubes of Berea sandstone. The sandstone (18 per cent porosity) was vacuum-saturated with water and surrounded by concrete. To prevent reflected tensile pulses, the acoustical impedance of the concrete matched that of the sandstone. A 750-psig pressure was applied to a drilling fluid within a shaped-charge-formed hole before detonating the gauging charge. In these tests, 190 gm of rock were removed for each gram of explosive detonated. A similar series of experiments on low-porosity (0.40 per cent) metamorphic limestone provided a more rigorous test. Extensive fracturing from the gauging-charge action prevented an estimate of the volume of the expanded hole. The diameter of the hole was irregular, ranging from about 2 to 4 in, or about fivefold larger than the hole created by the shaped charge. INTRODUCTION In the past, explosives have found a varied but somewhat limited use in the oil field. An early well stimulation technique, still in use today, in vo lves shooting ni troglycerin to en large the borehole and to increase matrix permeability near the wellbore. Bullets and jets are now the conventional method of perforating casing and tubing. Detonations are frequently used to "back off" or "shoot off" stuck pipe and, of course, seismo-graphic work has long depended on explosive-generated pulses to find attractive earth structures. Efforts to use explosives in drilling operations have received limited examinations1-3 which, in one respect, is surprising because explosives offer one way to transmit large amounts of energy directly to the bottom of the hole. Recently, Ostrovskii l described a Russian method of drilling with explosives that utilizes small capsules containing explosives which are pumped into the mud stream to the bottom of a borehole. As the capsules leave the end of the drill pipe, a detonation mechanism is armed. Impact detonates the explosive. In another configuration, two liquids (an oxidizing agent and fuel) in the capsule are separated by a frangible membrane. Separately, the liquids are nonexplosive. Near the bottom of the drill pipe, the capsule passes through a narrow constriction which ruptures the membrane. The mixing of the liquids produces an explosive. Impact is again used to detonate the explosive. About the time Ostrovskii was developing his method, Humble Oil & Refining Co. was independently doing research on another explosive drilling concept based on the sequential detonation of two types -of explosive charges. The proposed technique consisted of alternately pumping a shaped charge and then a "gauging charge" down a well. The shaped charge should drill a long, tapered hole, and the gauging charge should expand it to full gauge. This paper presents the visualized drilling concept and gives results of laboratory work which showed that sequential firing of charges can form hole at an attractive charge-to-rock removal ratio. An important finding was that increased environmental pressure, which is to be expected in wells, increases rock removal efficiency of the gauging charge.

Jan 1, 1966

By D. J. Weintritt, R. G. Hughes

Statistics show arz increase in the average depth of wells drilled in recent years. As a corollary to this trend, drilling fluids have been improved in an effort to meet the problems inherent at temperatures approaching 500°F. Of importance are (1) deterioration of mud components and (2) the effect of solids on filtration and rheological properties. High-temperature, stable water-base and oil-bare muds are discussed. Those areas in which differences exist are pointed out. Results are based on data taken from the Fann consistotneter, rheometer and shear-strength measurements, static and dynamic filtration tests, methy-lene blue test for bentonite solids and specific heat measLrrenlents of muds. INTRODUCTION Higher well temperatures go along with the fact that the average depth of wells continues to increase. Recent data by Gardner' lists 137 completions deeper than 15,000 ft for the first half of 1964 with a record second-half total of 167 wells drilling or proposed. In addition, there has been an increase in drilling for steam for power production or mineral recovery. In this application the depths are modest, but the mud may approach the critical pressure and temperature of water. Scearce and Magnon' report drilling mud used at temperatures of about 700°F in the Salton Sea area of California. Most deep wells have been drilled with water-base muds. In recent years, however, there has been a substantial increase in the use of oil-base muds because of technological advances in effective additives. The significance of this development was dealt with in considerable detail by Simpson and his co-workers.3 Additiona1 field data have now been obtained to indicate that oil muds are competitive in control, performance and cost with the best types of water muds for use at high temperaturc. This parallel offer of two very different fluid systems, each offering a similar variability in performance, cost and convenience, has created the need to evaluate the merits of these fluids under specified conditions so that the advantages and disadvantages of each can be weighed in relation to the over-all drilling program. This paper is not intended as a review of all the factors. Rather, it attempts to emphasize: (1) important condltions and facts peculiar to high-temperature drilling muds, (2) that more than one imposed test condition or testing method is necessary to describe the quality of a mud at high temperature and (3) that elaborate experimental precautions are necessary whenever laboratory data are used in selection of a mud for field use. WHAT IS A HIGH-TEMPERATURE DRILLING FLUID? For the purpose of this discussion, a high-temperature drilling fluid is any system so formulated or treated to economically minimize the effects of temperature on the properties of the fluid. Our experience in drilling fluids suggests that these effects become obvious for many mud materials at temperatures of 300F or higher. It is understood that hydrolysis of starches, depoly-merization of certain organic thinners, or irreversible chemical reactions (such as that of clay and lime) can affect filtration, viscosity and shear strength at less than 300F. However, the temperature level is not a serious point and in no way affects the precautions and techniques used in this study. An up-to-date review of the literature on high-temperature drilling fluids and the many variations was treated by Rogers'in 1963. EXPERIMENTAL REQUIREMENTS TESTING EQUIPMENT AND PROCEDURES With the advent of deeper drilling and increased demand for temperature-stable drilling fluids, new testing equipment and laboratory techniques were devised for the evaluation of drilling fluids subjected to elevated temperature and pressure. While the equipment has not been standardized, it is in widespread use. Milligan et al. Qescribe a filtration cell for determining the filtration properties of drilling fluids at temperatures in excess of 300F. They showed the effect of variations in temperature and pressure on oil and water muds filtered in the 300 to 400F range. The dynamic filtration apparatus described by Simpson6 permits the study of the filtration properties to temperatures of 350F for drilling fluids circulated over sandstone cores. Watkins et al.' describe the use of pressure bombs for studying the effect of prolonged periods of elevated temperature upon the gelation or solidification of drilling fluids. Chisholm et a1.' describe the use of a modified cement consistometer adapted for use in drilling fluid evaluations. A similar consistometer is used in this study, although the application and data-recording method have been changed. The consistency of a mud sample is measured by timing the movement of a soft iron bob which is magnetically moved up and down in the sample container.* Changer in the time of travel and the temperature of the mud at that moment are plotted with a two-point Brown Elec-tronik Recorder. A 10-in. chart with a speed of 4-in./hr is used. Fia.- 1 is a generalized internretation of the data ob-

Jan 1, 1966

By A. Satter

Studies of wellbore heat transtnission during the injection of a hot fluid, as either gas or liquid, have appeared in he literature. The present investigation takes into account the effect of condensation, which is of practical sig-nificance when considering steam injection operations. Calculation procedures are given for superheated and for saturated and undersaturated steam. Effects of injection rate, time, pressure, temperature and depth of a well on heat losses have been analyzed. The benefits of using a packer are discussed. Also presented are correlations for estimating heat losses involved during injection of saturated steam. INTRODUCTION Studies of wellbore heat losses during the injection of a hot fluid have appeared in the literature. Ramey' has presented a useful solution for calculating temperature of a heated gas as a function of depth and injection time. Ramey and others have also presented solutions for the hot liquid case.'. ' No method is available to take into account the effect of condensation, which is of practical significance when considering steam injection operations. This paper presents a method of estimating the quality of a condensing fluid as a function of depth and time. The approach is basically the same as that used by Ramey. The following injected fluids and conditions are considered in this study: 1. Injection of superheated steam A. Decrease in temperature until cooled to the saturated state B. Condensation until condensed completely into hot (saturated) water 2. Injection of saturated or undersaturated steam; condensation until condensed completely into hot (saturated) water. Although this investigation does not include cooling of water after steam is completely condensed, Ramey's solution for the hot liquid case can be used for this purpose. The effects of various process variables on heat losses During the injection of steam into a well are investigated. THEORY QUALITY OF CONDENSING STEAM Predicting the behavior of condensing steam flowing down the injection wellbore requires an estimate of the quality of steam, i.e., the mass fraction of vapor in the mixture. Let us divide the total depth of the injection well into several segments which might be, but do not have to be, of equal magnitude. Consider condensation within a given depth interval AZ, the bottom of which is located at a depth Z from the surface (Fig 1). The following equation, derived in the Appendix- relates the quality of steam at the bottom of an interval to that at the top of the interval:

Jan 1, 1966

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.' They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan'gin' using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy's law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy's law,

By F. D. Patchen

Changes in the properties of partland cement upon the addition of fine-ground silica are discussed. Data were collected from formulations cured for periods up to 60 days at temperatures varying from 180" to 350°F. Compressive strengths, permeabilities and thickening times are compared. It is demonstrated that addition of find-ground silica in proper proportion results in a hydrated cement with superior properties above 230°F; i.e., early compressive strengths are higher and increase with additional curing, permeabilities are significantly lnrver and thickening times are increased. X-ray analysis of hydrated cement samples have been used to determine more fully the complex chemistry of these systems. Dicalcium silicate alpha-hydrate was found in all neat cements cured above 260°F. A 10 weight per cent silica addition produced a maximum amount of this phase. Xonotlite and tobermorite have been identified as hydration products at 320°F in systems containing 35 or more weight per cent silica. Formation of these components appears to be primarily responsible for the gain in strength and reduction of permeability observed after the addition of silica. INTRODUCTION For several years it has been recognized that loss of compressive strength occurs when portland cement is cured at a temperature above 250°F. This phenomenon has been called "strength retrogression". More recently it has been recognized that increased permeability usually is associated with decreased compressive strength at these temperatures. At curing temperatures above 300°F, these factors reach serious proportions. A compressive strength loss of 50 per cent between curing times of 24 hours and 14 days has been reported,' and permeabilities as high as 10 md have been measured in neat cements cured at 320°F for seven days.' Earlier investigators,' although unsuccessful in eliminating strength retrogression, stated ". . . .it appears possible that by the proper selection of additives for cement, strength loss with age at high temperatures can be either eliminated or considerably lessened". One solution suggested was the use of a pozzolanic material, hydrated lime, and a retarder. Menze15 in 1934 discovered that portland cement containing finely divided silica possessed high compressive strengths when the curing temperature was 350°F. The use of such a composition is now an established practice in the manufacture of steam-cured cement blocks. It is reasonable to assume that the same beneficial effect can be used advantageously in high-temperature oilwell cementing operations. Ludwig first mentioned the use of sand for this purpose. Later, a portland cement containing moderate additions of silica flour and retarded with CMHEC, a cellulose derivative. was recommended for high-temperature application." These formulations have been successfully employed in the field."'" This paper presents the results of a research program to test the efficacy of finely ground silica in increasing the compressive strength and reducing the permeability of oilwell cement compositions containing portland cement. Included also are X-ray diffraction patterns of powdered samples which have been used to determine some of the important chemical reactions occurring in these systems. LABORATORY PROCEDURES AND MATERIALS All compressive-strength test specimens were prepared and cured from a slurry in accordance with API RP 10B, with two modifications. A final curing pressure of 5,000 psi was maintained for a one- or three-day period; but, for further curing, pressures were reduced to the vapor pressure of water at the curing temperature. Also, the water content was varied in samples containing silica to maintain the slurry viscosity within a range of 5 to 15 poise as measured on a consistometer. Test specimens at 180°T were cured in a water bath at atmospheric pressure. At higher temperatures the specimens were cured in a steam-jacketed high-pressure curing vessel at 5,000 psi for a one- or three-day period. cubes cured for longer periods were removed from the pressure-curing vessel after 24 hours, sealed in small bombs containing water and placed in an aging oven.

By K. H. Hiller

A rotational viscometer has been designed which perrnits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described. The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensiom at high temperatures and pressures, are presented. Data are also presented for the flow behavier of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. INTRODUCTION The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin.1 The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.' Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids. The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.3 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro- duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress 7 and the rate of shear D is given by the following equation: where is the plastic viscosity and 4 the yield point. If 4 = 0, the equation for simple Newtonian flow, 7 = pD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known. For this reason a high-pressure, high-temperature rhe-ometer has been designed to measure the plastic viscosity the yield point +, and the static gel strength S, at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress t at any given rate of shear D. This is possible only if t and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde." The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fie. 2. which revresents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. For measurements of dynamic flow properties, the rotating cup is driven by a 1/2-hp electric motor, which operates through a Vickers

By N. T. Burdine

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By W. C. Maurer

A study of the mechanics of shear failure of rock under pressure has been made. The transition from brittle to ductile failure occurs when the friction along the fracture surfaces exceeds the shear strength of the rock. A machine has been developed for measuring both the shear strength of rock and the friction along rock fracture surfaces. In this shear machine, the fractures are forced along definite planes; as a result, the rock is stronger than in compression tests where the fractures choose the weakest paths through the specimens. Friction is composed of several forces: (1) the forces to slide irregulurities on surfaces over each other; (2) forces to shear some of these irregularities; (3) molecular attractions across the fractures; and (4) forces required to break bonds resulting from melting and welding at the tips of irregularities on the surfaces. Friction along rock fracture surfaces is not proportional to contact pressure as usually assumed; instead, it increases as the contact pressure raised to the 0.4 to 0.8 power. INTRODUCTION It is difficult to produce tensile stresses under the high compressive stresses present in the earth; therefore, in deep drilling and geological faulting, shear failure predominates. This shear failure mechanism is complicated because rock is a heterogeneous material containing pore spaces, microfractures, elastic discontinuities and other imperfections. A study of shear failure of rock under pressure has been made to obtain a better understanding of this complex mechanism. A machine has been developed and used to measure the shear strength of rock and friction along sheared surfaces. This machine has certain advantages over the compression test — shear properties can be measured under low normal stresses and shear stress and normal stress can be varied independently. The first part of this paper is a description of shear failure of rock under pressure. The role of shear strength and friction along fracture surfaces in the shear failure mechanism will be discussed. The second part consists of a description of the shear machine and a discussion of the shear strength and friction data obtained using this machine. It will be shown that shear strength depends upon the size of the stressed zone, and that friction does not increase linearly with contact pressure as usually assumed. Attempts are made to relate some of the new concepts to tectonic failure and to dril ling. SHEAR FAILURE IN ROCK TRIAXIAL TESTS The shear failure mechanism is illustrated by the triaxial test shown in Fig. 1. In this test, a cylindrical rock specimen is subjected to a confining pressure, PC, and an axial pressure, pa. These external pressures produce normal a and shear T stresses on inclined planes within the specimen equal to1 where 0 is the angle between the specimen axis and a normal to the inclined plane. Fig. 2 shows how triaxial specimens deform as the axial pressure is increased. The pressure is

Jan 1, 1966