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By H. D. Outmans

The paper presents a theoretical approach to the drilling problem based on rock mechanics and drilling fluid hydraulics at the bottom of the hole. The volume of the fractured rock around the vevtically penetrating bit tooth is expressed as a function of the tooth pressure, included tooth angle, drilling fluid pressure and formation characteristics on the assumption that fracturing is preceded by plastic flow. This assumption is verified by comparing the stress-strain state in the rock around the tooth to that in equivalent tri-axial compression tests described in the literature. An expression similar to the above is derived for the tooth penetration in the cuttings which have been retrained at the bottom. Combination of these two expressions leads to a relation between depth of tooth penetration in the virgin rock, the amount of cuttings retained and the other variables. By relating the cutting volume to the drilling rate, the hydraulic bit horsepower and the drilling fluid pressure, it is possible to arrive at formulas which express the drilling rate for viscous or turbulent flow at the cutting surface, for instant clearance, for retained cuttings, or for false tooth foundering as functions of such variables as the drilling fluid pressure, hydraulic horsepower at the bit, rotary speed and bit weight. Plotting the results as drilling curves and comparing them to published field and laboratory data justify the conclusion that the drilling model presented in this paper approximates the actual mechanism. The drilling curves serve to explain some characteristic features of the rotary drilling operation, and the equations may be used for numerical evaluation of the effect of changes in the magnitude of some of the variables on the drilling rate. INTRODUCTION Published laboratory data have established that consistent and relatively simple relations exist between the drilling rate and any one of the important variables. For instance, the drilling rate usually increases at an increasing rate with the bit weight. It increases at a decreasing rate with the rotary speed, decreases at a decreasing rate with increased drilling fluid pressure and plots as an S-shaped curve against the hydraulic horsepower at the bit. This relative simplicity seems difficult to understand considering that the drilling mechanism is a continuous process of generation and removal of innumerable individual cuttings, under different conditions for each. On the other hand, the drilling rate (although determined by this complicated process) only expresses the average rate at which cuttings are produced and cleared away. Ignorance of the drilling mechanism as far as individual cuttings are concerned, therefore, does not exclude the possibility of arriving at a concept of the drilling rate provided the mechanism is properly evaluated for the average cutting. It then may be concluded from the first sentence that this concept also should be rather simple in its final form, although not necessarily in its derivation. Two aspects of the drilling mechanism are difficult to evaluate — (1) the effect a penetrating drilling fluid has on the stresses around a bit tooth entering the formation and (2) the volume of rock fractured by a penetrating tooth which moves both vertically and horizontally. Thus, the scope of this paper has been limited to an evaluation of the drilling mechanism in formations which have a low permeability and are drilled with hard-formation bits. In the following sections, the drilling mechanism is analyzed in three steps. First, the effect of tooth pressure on the volume of fractured rock around the tooth is evaluated, assuming initially that the bottom of the hole is free of cuttings and, then, determining the effect of a layer of these cuttings. In the second section, the thickness of this layer is related to the drilling rate and the chip clearance time, and the latter to the hydraulic horsepower at the bit under conditions of laminar and viscous flow at the cutting surface. In the third section. the previous results are combined with the rotary speed into drilling equations which are then plotted and compared to experimental drilling curves. This section also contains some numerical examples of drilling rate computations. Some mathematical details are given in the appendixes. Finally, it should be mentioned that, although some drilling equations are already available, these equations (with the exception of one' which attempts to relate drilling rate to drilling fluid pressure) are all mathematical expressions for observed laboratory data; none considers the effect of delayed drill-cutting removal, an essential feature of the drilling mechanism.

By J. W. Clark, C. T. Sims

Wrought chromium-base alloys containing yttrium, cubic monocarbides of the Ti(Zr)C type, and similay alloys containing manganese and rhenium have been melted and fabricated. Strength has been studied by hot hardness and elevated-temperature tensile and rupture measurements, low-temperature ductility by tensile testing, and surface stability by oxidation testing. In additiod, studies have been conducted of the carbide stability, and of aging behavior. The carbide dispersion generates effective elevated-temperature strength, which is further enhanced hv strain-induced precipitation. The dispersion exhibits classical dissolution and aging response. The ductile-to-brittle transition temperature of these alloys is above room temperature. The alloys reported show fairly good oxidation resistance, but nitrogen contamination can cause fortnation of a hard Cr2N layer under the oxide scale. Manganese does not appear to be a promising alloying element in chromium. In the years 1945 to 1950, the metal chromium was considered as a possible base for alloy systems due to its considerably higher melting point than superalloys, its low density, its high thermal conductivity, and its apparent capacity for strengthening. However, this interest in chromium was short-lived. It was found difficult to melt and cast, to be exceptionally sensitive to the effect of minor imperfections, to have a lack of ductility at both room and elevated temperatures, and to be subject to a deleterious effect of alloying elements upon the ductile-to-brittle transition temperature.' Since then, chromium, as a practical alloy base, has remained virtually unstudied. Further, purposeful ignoring of chromium has been promoted by statements that its bcc structure would not allow it to be strengthened to useful values, when compared to the "austenitic" alloys.2 Recently, a new look has been taken at chromium-base alloy systems. Study of the literature will show that chromium, providing some of its disadvantages could be eliminated or minimized, actually has a rather attractive potential as an alloy-system base. Analysis of rather scattered data suggests that chromium is quite capable of being strengthened to high levels. Also, significant strengthening of its two sister elements in Group VI-A, molybdenum and tungsten, has been demonstrated in a number of commercial and exploratory alloys. Chromium should be similar. Since chromium does not readily form a volatile oxide like tungsten or molybdenum, it offers a much higher probability of giving birth to alloy systems with useful oxidation resistance. Concerns about possible high elemental vapor pressure have been mitigated by recent data.3 In addition, the physical properties exhibited by chromium are attractive for application as a high-temperature structural material. For instance, its thermal conductivity varies from 49 to 36 Btu-ft/hr-sq ft-°F over its range of usefulness (which is two to four times higher than most superalloys), its density is about 7.2 g per cc (20 pct less than most nickel-base alloys), its coefficient of thermal expansion varies from 4 to 8 x 10-6 per OF, and it has a relatively high modulus of elasticity, approximately 42 x 10' psi.4 Alloying studies on a chromium base in the past have usually encompassed rather sweeping solid-solution alloy additions for strengthening. This is not consistent with contemporary alloying practice in Group VI-A. For instance, molybdenum, also in Group VI-A, is primarily alloyed for strength improvement by use of heat-treatable carbide dispersions.5 Chromium and molybdenum are similar in their chemical activity and other properties. Thus, strengthening of chromium by carbide dispersions was studied. Chromium-base alloys are plagued with room-temperature brittleness, although high-purity unal-loyed chromium can be made ductile.4,8 Use of yttrium as a scavenger has done much to improve ductility and resistance to nitrogen embrittlement in chromium systems,7 so it was utilized in this program. It has also recently been found8 that small rhenium additions (1 to 5 pct) create improvement in the ductility of Type 218 tungsten wire. This is apparently related to the remarkable effect of rhenium additions near its terminal solid solubility in all Group VI-A metals.9'10 Investigation to establish if dilute concentrations of rhenium would also be effective in chromium appeared to be logical for this program. Since rhenium is too expensive to be practical in alloys for application as structural components, ductility improvements through solid-solution alloying were also sought by substitution of manganese for rhenium; manganese, like rhenium, exists in Group VII of the periodic system. The optimum amount of carbide dispersion for chromium-base alloys was obtained by analogy with molybdenum. Strengthening in molybdenum is achieved by use of Ti-Zr carbide dispersions. A

Jan 1, 1964

By William Hurst

Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This nietkod of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined tern? for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and sec-ondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. INTRODUCTION The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent move- ment of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation. The type of depletion performance equation chosen for predicting the future performance of a reservoir depends on the amount of past history available. When the reservoir is somewhere past the halfway mark in depletion, some form of decline curve is often used. With less past history, material balance equations which incorporate empirical factors based on the past performance are often used. When, however, the amount of past history is small, the Muskat depletion performance equation will usually be used. The distinguishing feature of this type of equation is that empirical factors based on the over-all or macroscopic reservoir behavior are almost or entirely absent. Each parameter affecting the reservoir performance is ascribed an independent set of values based on measurements made on laboratory samples; that is, incorporating microscopic empirical factors. In establishing Muskat-type depletion performance equations, it is necessary to consider the reservoir as consisting of a number of associated blocks, in each of which the saturations and pressures may be considered uniform, and in each of which all substances have uniform pressure-volume characteristics. Thus, a primary gas cap can usually be considered as one block and an aquifer as another. Gravity segregation may be negligible for practical purposes when the rock and oil properties are adverse and/or the dip or thickness of the reservoir is too small. In this case the whole oil leg may be considered as one block, except in very large reservoirs. In very large reservoirs the fluid and rock properties may vary enough, particularly in the dip direction, for it to be necessary to divide the oil leg into a number of blocks, in each of which the relevant quantities may be considered uniform. When gravity segregation of the oil and free gas is not negligible, it is necessary to consider the space occupied by the initial oil leg as divided into two blocks, a secondary gas cap and an effective oil leg, in each of which saturations may be considered to be uniform. The total volume of these two blocks is thus constant, but the secondary gas cap grows continuously at the expense of the oil leg. Muskat1 derived depletion performance equations for the basic case of an oil reservoir with closed boundaries and without segregation, and for the case of an oil

By N. H. van Lingen

A laboratory stud], has been made to determine what factors affect the penetration rate of roller bits, diamond bits and drag bits in rock drilling with clay /water muds. The rather simple relations that exist when pressures in and around the borehole are equal become more conzplicated when under down-hole conditions the penetration rate is hampered by the existence of a pressure differential between the mud at the hole bottom and the pore liquid at cutting depth. Expressions that have been derived for both the penetration rate and the magnitude of the pressure differential in permeable rock together fully account for operating, rock, mud and bit variables. In impermeable rock a similar pressure differential is caused by the bit action itself. In all cases, the pressure difierential and the reduction in penetration rate increase with the effectiveness of the plastering at the bottom of the hole by mud particles. Where bits are employed whose action is largely that of crushing, however, the plastering may become even more effective owing to the addition of rock particles rubbed into the pores of the rock. With roller bits, a plastically hehaving layer may be formed, which causes a further reduction in penetration. In the case of bits whose action is chiefly scraping, moreover, penetration may be arrested by the bit's becoming balled-up. The various adverse effects are reduced by thorough scavenging of the hole bottom. This paper shows how with jet bits the efficiency of such scavenging may he improved by suitable choice of the position of the nozzles. INTRODUCTION The reduction in a bit's penetration rate with increasing depth of hole has been the subject of many investigations. Various investigators ',' have independently reached the conclusion that this reduction occurs not so much because the rock-breaking process becomes more difficult as it does because the lifting of the rock fragments is impaired by a fluid pressure differential holding the fragments down. When such a pressure differential can be avoided, as in air drilling and to a smaller extent in water drilling, penetration rates remain high. Although the range of applicability of these techniques is being extended, most oil wells still have to be drilled with mud. In this paper we present the results of laboratory experiments carried out to determine what factors govern the hold down effect encountered in mud drilling. In the course of this investigation, the well known importance of bottom scavenging came more and more into prominence. Not only may it reduce the magnitude of the hold-down forces, but also it appeared to be a means of preventing the accumulation of a plastic mass of cuttings and mud on the hole bottom and bit which may cause penetration to cease almost completely. So that the effects of fluid pressures may be more readily understood, the factors that govern penetration rate in the absence of these pressures will first be discussed. The effect of down-hole pressures will then be assessed for the case of permeable rock where fluid pressures are well defined, and it will be demonstrated how rock strengthening due to confining can be accounted for. Subsequently, fluid pressures in less-permeable rock will be examined; we will show that in impermeable rock it is the bit action that governs fluid-pressure distribution and hold-down. In the case of poor scavenging and/or high bit load. cutting cake manifests itself. The effect, like various others. appears to depend on the type of bit used. From the very beginning, therefore, we shall base our discussion on the three main types of bits used in rotary oil-well drilling— roller bits, diamond bits and drag bits. Since space is limited, it will be impossible to make more than a passing reference to many aspects of the problem. Moreover. certain relations that are not of primary irnportance to our argument will unavoidably have to be stated in a somewhat dogmatic fashion, and the experimental data on which these are based necessarily must be omitted. EQUIPMENT The drilling experiments were performed on three machines, of which one has been designed for the realistic simulation of down-hole pressure conditions. HIGH-PRESSURES MACHINE In this machine (diagramed in Fig. 1) the mud, pore and confining pressures can all be adjusted independently. The foil-covered rock sample contained in the inner pressure vessel is confined by oil that is pressurized by means of a hand pump. The pore space of the watersaturated sample is connected to an arrangement which keeps the pressure in the pore space constant regardless of the rate of filtrate flow through the sample.

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of liquid Mg-Ge alloys have been determined between 1000°and 1500°K by an isopiestic method. Germanium specimens, heated in a temperature gradient and contained in covered graphite crucibles of special geometry, were equilibrated with magrtesium vapor in closed titanium tubes. The crucible design allowed free access of magnesium vapor to the samples during the equilibration to form alloys of magnesium and germanium, but prevented magnesium losses from the crucibles on quenching the titaniuin tubes to terminate the experimental runs, thus preserving the equilibrium alloy compositions. The activities and partial molar enthalpies of magnesium and the integral thermodynamic properties of the system were calculated from the experimental data. THE Mg-Ge phase diagram' shows one congruent melting compound, Mg2Ge, of essentially stoichio-metric composition, two eutectics, and very limited terminal solid solubilities. Very little information is available on the thermodynamic properties of the Mg-Ge system. The free energy of formation of Mg,Ge was recently deter-mined2 by a Knudsen cell technique in the temperature range 610° to 760°C. The standard enthalpy of formation of Mg,Ge was measured calorimetrically by Bever and coworkers.3 The present study was undertaken as part of a general investigation of the thermodynamic properties of the homologous series of Mg-Group IVB systems, i.e., Mg-Pb,4 Mg-Sn,5 Mg-Ge, and Mg-Si. An isopiestic technique was used which was developed by the authors5 for investigating the thermodynamic properties of liquid Mg-Sn alloys. Specimens of the nonvolatile component, contained in covered graphite crucibles, are heated in a temperature gradient in an evacuated and sealed titanium reaction tube, and equilibrated with magnesium vapor of known pressure. The method employs crucibles of special geometry which preserve the high-temperature equilibrium composition of liquid alloys having a highly volatile component such as magnesium on termination of the experimental runs by quenching the crucibles to room temperature. EXPERIMENTAL PROCEDURE First reduction germanium of 99.999+ pct purity (Eagle-Pitcher Co., Cincinnati, Ohio) and 99.99+ pct magnesium metal (Dominion Magnesium Ltd., Toronto, Canada) were used. The graphite crucibles were machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non-reactivity of graphite with germanium at the temperatures used in this study had been previously established by Scace and Sleck.6 The experimental procedure has been previously described in detail.5 The selection of a particular crucible geometry for a run was determined by a combination of imposed experimental conditions, the principle being that more tightly covered crucibles were required to preserve alloy compositions during quenching when higher magnesium pressures and higher specimen temperatures were used. Depending upon the composition range of the equilibrated alloys the source of the magnesium vapor was either pure magnesium or a two-phase mixture of Mg2Ge + Ge-rich liquid of known magnesium pressure. The experimental runs can be divided into the following three groups on the basis of crucible geometry and magnesium source material. Crucibles with Small Holes and Pure Magnesium Reservoirs. The crucible dimensions were identical to those of the Mg-Sn investigation5 except that the hole diameters were reduced to 0.010 in. because of the higher temperatures and higher magnesium pressures involved in the Mg-Ge system. During an equilibration run, magnesium vapor diffused from the reservoir to each specimen through the small holes, one drilled through the crucible lid and two others drilled through graphite baffles positioned vertically inside the crucible between the lid hole and the specimen. Since the magnesium pressure was high, i.e., in the range 117 to 277 Torr, during the equilibration time of approximately 24 hr, equilibration was not impeded by these holes. A specimen composition at equilibrium was fixed by the relative temperatures of the specimen and the reservoir, and by the thermodynamic properties of the system. Upon brine quenching the titanium reaction tube to end a run the vapor pressure of magnesium above the liquid alloys decreased exponentially with decreasing temperature, and the small cross-sectional areas of the holes (4.9 x 10"* sq cm) drastically reduced magnesium losses from the crucibles. Because of its low vapor pressure, germanium losses from crucibles during a run were at most 0.2 mg for pure germanium and correspondingly less for the alloys. This crucible geometry satisfactorily retained the equilibrium alloy compositions on quenching for magnesium-rich (from 3 to 33 at. pct Ge) alloys provided their temperatures were below the melting

Jan 1, 1967

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

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

Fluid Ioss agent.s for crude oil and for water have been studied in dynamic tests. A treatment using a spearhead with a fluid loss agent followed by plain fluid appears feas ible in crude oil, but not in water. An equation for spearhead depletion shows that spurt loss relative to fracture width must be low, if the portion of spearhead fluid in the treatment is to be small. The presence of colloidal matter in crude oils aids the fluid Ioss agent. Unlike in kerosene, where flow limited the agent deposition, in crude oils the filter cake continually formed and leak-off declined. The volume-time relation varied somewhat for different crudes, but was best described by a square root of time function. Spurt loss was inversely proportional to agent concentration. After the fluid loss agent initiated the filter cake, the crude oil colloids built on it effectively. A 2-minute or a 5-minute spearhead with double the normal agent concentration gave the same fluid Ioss curve as the same concentration did for a 30-minute test. The agents tested in water gave fluid Ioss plots on which, for the first few minutes, volume was proportional to the square root of time, but later became proportional to time. For fracture area calculation the customary square root of time function is a satisfactory approximation. Leak-off rates and spurt losses were higher in water systems than in oils. The spurt Ioss tended to be inversely proportional to concentration. In spearhead tests, the filter cakes were not eroded by water flow. However, the rather high spurt loss values make spearhead treatments impractical for water-based fluids. Introduction The effects of dynamic testing conditions on the performance of fluid loss agents in kerosene have been studied previously.' We have extended the work to include crude-oil- and water-based fracturing fluids. An understanding has been gained of the mechanisms of formation and functioning of the filter cakes of fluid loss agents. The practical aspects of evaluating performance of agents in relation to fracture area calculations also are considered. The feasibility of using the fluid loss agent in a spearhead stage of the treatment is examined further for both types of fluids. Experimental Procedure The dynamic fluid loss tests were performed in an apparatus similar to the high-pressure apparatus described in a previous publication.' A fracturing fluid was circulated over a rock surface located in a closed pressurized loop. The fluid flowed axially over the cylindrical surface of a core 2 in. in diameter X 3.5 in. long, mounted (with the flat ends sealed off) in a pipe, with 0.117 in. annular clearance. The filtrate was collected in a central hole in the core and led through valves to graduated cylinders. Provision was made for changing quickly the circulating fluid during the test (spearhead runs) without interrupting the filtration pressure. The only modifications were to add heating tapes and water jackets for the tests with crude oils, all conducted at ISOF, and to change all parts exposed to the test fluid to stainless steel for the tests with water-based fluids. The latter tests were made at room temperature, 80F. Three crude oils were tested. A mixed crude, obtained from a local refinery, contained a considerable amount of light ends. For safety reasons, it was stripped to 250F vapor temperature before use in the fluid loss tests. The other two oils were used as obtained from lease tanks. One was a greenish-brown, 37" API paraffinic crude, and the other was a black, 32" API asphaltic crude. The fluid loss agent for oil, here designated for brevity as Agent A, was Adomite@ Mark II*, a granular solid commercial agent, the same as previously tested in kerosene.' Three different compositions of fluid loss agents were tested in Tulsa tap water. Agent B was adomit& Aqua*, a solid commercial fluid loss agent, comprising clays and hydrophilic gums principally derived from starch. Agent C was a mixture of three parts of Agent B with two parts of silica flour. Agent D was Dowel1 J137, a mixture of guar gum and silica flour. The test cores were cut from contiguous blocks of Berea or Bandera sandstones. For the oil tests, the cores were oven dried, evacuated, saturated with kerosene, and the kerosene permeability was measured. The cores used with the water-based fluids were pretreated by saturating with 3 percent calcium &loride solution to minimize pemeability damage by the fresh water due to clay migration. The

Jan 1, 1969

By J. E. Walstrom

While intensive research continues to promote a more complete understanding of the potential and resistivity measurements that comprise the electric log, it is believed that consideration should also be given to translating these numerous and often widely separated findings into a coordinated and readable body of fundamental facts designed specifically for the petroleum engineer and geologist. Although provision is made through publication for a ready exchange of new theoretical concepts. it is also desirable to provide reviews and appraisals of the more established techniques and methods from the operating standpoint so that an economic and practical application may be realized concurrently with the theoretical progress. With these basic premises as a guide the author reviews the presnt state of electric log interpretation. The paper is directed not so much to the logging or research specialist as to the petroleum engineer and geologist to whom the electric log is only one of the many tools which he employs. Frequently, these persons do not have the time to follow in detail the many specialized contributions that appear and, as a consequence. are not in a position to place these contributions in proper relation to each other, or to the art as a whole. The paper reviews the basic steps in making quantitative determinations from the electric log of the amount of oil or gas present in subsurface formations and also discusses the degree of reliability of these determinations under various conditions. The paper also indicates the trend of future developments in electric logging systems and methods of interpretation. INTRODUCTION The electric log has been used about 20 years as a means for studying the formations penetrated by a well bore. The first half of this period is characterized by the development of suitable logging techniques and equipment. Although progress in this direction is continuing at a satisfactory rate, the last ten years are characterized more by an increasing interest in methods of electric log interpretation. During this period, a large number of fundamental papers have been published, expounding various logging techniques and particular phases of the interpretation problem. Many of these papers represent important contributions, and a few are classic. This paper is an effort to outline as concisely as possible and in simple terms the main course of progress in electric log interpretation. More specifically, it is the purpose of the paper to review the necessary elements and basic steps used in making quantitative determinations of water saturation from the electric log; and to point out the degree of reliability of these determinations under different conditions. It is strongly advised that the operating staffs of the drilling and exploration departments of oil companies cooperate wholeheartedly with both the electric logging service companies and research organizations in the testing and development of new logging systems and interpretation methods. One purpose of the paper is. however, to indicate the degree of caution which must be exercised in placing confidence in new techniques and interpretation methods that have not been thoroughly tested in the field. It is entirely possible to be cooperative in trying new methods and yet reluctant to believe in the results until the methods are firmly established. It is important to define the meaning of quantitative electric log interpretation. In the most general sense, an interpretation of the log has been made when the electrical characteristics of the formations, as portrayed on the log, have been translated into terms describing the formation geometry, rock type, or any other physical characteristics of the formations. The determination that the top of a sand is at a certain depth is an interpretation of the log. Structural determinations made by correlating electric logs from a given area are also interpretations of the logs. The term quantitative interpretation, however, will be used in this paper in the restricted sense to indicate the determination of the water saturation of a formation. This determination defines the fluid content of an oil and gas productive formation only if the porosity is known, and it assumes that the remainder of the pore space contains hydrocarbons. This assumption is believed to be true for most oil and gas productive formations. The quantitative electric log interpretation may he said to be a determination of the fluid content only to the extent which the water saturation, under the conditions given above. defines it. THE BASIC STEPS The fundamental steps in calculating water saturation from the electric log are: 1. Determination of the true resistivity of the formations from the apparent resistivities as recorded on the electric log.

Jan 1, 1952

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.'a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.' However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By P. J. Dean

This Paper contains a comprehensive survey of the known electron-hole radiative recombination mechanisms in the family of III-V compounds. Because of space limitations, the luminescence properties of each III- V compound are not reviewed separately and exhaustively. Instead, the different known types of recombination processes are discussed in turn and exemplified with reference to the III- V compound in which they were first recognized, or are best understood. Electron-hole recombinations usually occur predominantly at impurities or lattice defects either introduced de1iberately or inadvertently present, but radiative intrinsic interband electron-hole recombinations, which occur in perfect crystals, have been observed. Recombination processes which involve the participation of impurities or lattice defects ("extrinsic" recombinations) considered include transitions in which a) free carriers recombine with carriers trapped at impurities ("free to bound" transitions) , b) electrons bound at donor impurities recombine with holes trapped at acceptor impurities ("donor-acceptor pair" recombinations), C) excitons bound to charged or neutral donor or acceptor impurities recombine radiatively (both "resonance" and "two-electron" "bound exci-ton" transitions have been observed), d) excitons bound to neutral donor or acceptor impurities recombine non-radiatively (an example of an "Auger" recombination), and e) excitons bound to impurities with the same number of valence electrons as the host atom which they replace ("isoelectronic " traps) recombine radiatively. In addition, Auger recombination processes involving one or more free carriers have been observed. These extrinsic processes all involve impurities which are present as point defects. Some apparently well-authenticated examples of the recombination of excitons bound to complex impurity-lattice defect centers including nearest-neighbor donor-acceptor pairs are also discussed. Identificalions of the transitions involved in stimulated emission from the direct gap III-V compounds are briefly reviewed. Although the examples of these recombination mechanisms are selected from the III-IV compounds ia this review, these processes have quite general relevance in semiconducting crystalline solids; irrdeed most of them have also been identified in the 11- VI compounds and elernental semzconductors. THE development of crystal growth and purification techniques in recent years and concurrent advances in the understanding of physical processes in solids has accelerated the development of a wide variety of solid-state electronic devices of proven utility. These de- vices are generally used for switching or amplifying operations in electrical circuits. Most solid-state circuit elements are very photosensitive. This photo-sensitivity is generally undesirable and the single-crystal chip forming the active portion of the solid-state device is mounted in an opaque container. The photosensitivity is made use of in phototransis-tors and photodiodes, which are among the most sensitive detectors of electromagnetic radiation particularly in the near infrared.' In these devices, light is converted into electrical power. The solid-state lamp utilizes the inverse effect, namely the conversion of electrical power into light. There is an increasing tendency to use single-crystal diodes rather than the earlier electroluminescent cells in which the active material is present as a powder embedded in a suitable dielectric.' The radiation is emitted at a rate far in excess of the thermal equilibrium rate for the frequencies and temperatures involved; i.e., luminescence occurs. The development of practically efficient solid-state lamps is at an early stage compared with solid- state circuit elements or even photodetectors. Considerable progress has been made in recent years, however.3 The present review is devoted to a survey of the radiative recombination processes in the semiconducting compound crystalline solids formed from elements in groups I11 and V in the periodic table. These materials exhibit the full range of known recombination processes in solids. In fact many of these processes were discovered in 111-V semiconductors. Nonradiative recombination processes, which control the lutninescence efficiency, are also discussed. Luminescence is efficiently excited in semiconductors through processes which produce large excess concentrations of free electrons and holes in the energy bands of the crystal. Transitions induced by lattice defects or impurities usually predominate in the recombination process. By contrast, luminescence in the conventional fluorescent lamp is excited by optical absorption at the luminescent impurity center itself (the activator) and/or at a second type of impurity center (the sensitizer). This latter type of photoluminescence process, occurring in doped ionic crystals with wide band gaps, is outside the scope of this review.4 I) ENERGY BAND DESCRIPTION OF ELECTRON STATES IN CRYSTALS The energy band description of the energy states available to an electron in a crystal forms the basis of our understanding of the empirical division of crystalline solids into metals, semiconductors, and insulators in accordance with their electrical and optical properties.' Nonmetallic crystals have a finite energy gap between the highest energy band which is

Jan 1, 1969

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By C. C. Miller, A. B. Dyes

The cost of finding and developing new reserves is continually rising. We must meet these rising costs with more economical operations. This can he accomplished if we revise our ideas of proper well spacing and well allowable to consider the concept of optimum well spacing. According to this concept, the optimum spacing is the one which leads to the maximum present worth for a reservoir when ail factors affecting total cost and total revenue are considered and when the wells are produced in the most eficient manner. Application of this principle efficiently utilizes available well potential and properly considers the recovery eficiency in addition to fixing the spacing on the basis of the amount and value of the oil to he recovered. This Study presents an analysis of one producing zone containing low gravity crude to illustrate the effect of these factors on the present worth and on the optimum economic spacing under two production drives—-evolved gas and water drive. The maximum present worth occurs when the optimum number of wells for open-flow operation is employed. Frequently, this optimum development cal1s for very wide spacing and the ideal field rates are not unreasonable. Under other circumstance. where proration is necessary, an optimum combination of well spacing and well allowable exists which permits production at relatively high rates. The optimum well density in a field depends on the recovery efficiency and the valule of the oil. In solution gas-driven reservoirs this optimum spacing for operation at high producing rates can vary from extremely wide spacing to handle viscous low gravity oil in thin formations to relatively close spacing in thick sands where good recoveries are expected. Because of the better recovery from water-driven fields, the optimum spacing in these fields is closer than in solution gas-driven fields. Also, the water encroachment pattern is dependent upon the well spacing, and an adequate numher of wells is needed to assure a good sweep eficiency. The economic optimum well density in a water-driven field is high enough for this purpose. INTRODUCTION From year to year domestic oil becomes more difficult to find. The fields we do locate are frequently smaller and deeper than older fields and the costs for men, material and equipment are continually rising. To replenish our reserves we must continue to search for and develop new fields, but experience has shown we cannot expect prices to rise in proportion to costs. Consequently, we must meet increasing costs by more economical operations. A vigorous effort is being made within the industry to improve exploration methods, to cope with the problems of deeper drilling, and to obtain a secondary yield from older fields. Many significant contributions have resulted from these efforts. The economic operation of new fields can be further improved by developing these fields on optimum spacing and producing the wells at higher rates. This would avoid the drilling of unnecessary wells and provide additional capital for seeking new oil. While the benefits of these practices are obvious, the problem of defining the optimum development of a field for natural depletion can become very complex. A study of the effect of well spacing and several reservoir variables on economic worth of a specific field is reported here to illustrate the problem and to show the magnitude of the benefits to be realized. This study is necessarily limited to the field conditions selected and is not intended as a general solution of the well spacing problem. It does, however, indicate factors to be considered, the trends to be expected, and the direction in which we should proceed in developing new fields. NO consideration is given to land and legal considerations which might arise. METHOD OF ANALYSIS The optimum method of developing and producing a field is to use the combination of spacing and prora-tion which gives the maximum return. In addition, we do not want to lose recovery. These considerations of maximum return and maximum recovery present no serious conflict. The value of each method of operation is conveniently expressed in terms of its present worth. According to the present worth method of evaluation,' an acceptable annual percentage return is assigned to the operation, and all incomes, capital costs, and expenses are discounted at this rate to the start of the operation. This net value is the present worth. If we apply the same discount rate to several alternate methods of operation, the one yielding the greatest present worth is the best method. If we express net income in terms of price per barrel of oil produced, drilling and equipment costs on a well basis, and expenses as cost per well year, this evalu-

By C. S. Matthews, H. C. Lefkovits

Drilling progress is often delayed by sticking of the drill string. The development of preventive and remedial methods has been hampered by incomplete understanding of the sticking mechanism. A recent lahorntory investigation hns indicated that one type of sticking may be attributed to the difference in pressure between the borehole and formation. This paper shows, by means of soil mechanics, that the primary cause for differential pressure sticking is cessation of pipe movement, whereas diflerential pressre and stanrtding time determine the severity of the sticking. The analysis stresses the importance of using low-weight muds with low solids content and low water loss to alleviate diflerential pressure sticking and describes why packed hole drilling, long strings of drill collars, and a large deviation from the vertical are conducive to sticking. Finally, preventrve and remedial methods ore evaluated, and a theory is presented on the release of stuck pipe by spotting oil. INTRODUCTION Since drilling with long strings of oversize drill collars has become standard practice in many areas, the incidence and severity of the stuck pipe problem has increased. It has been noticed that in the majority of these cases the sticking could not possibly be attributed to key seating or caving of shales. It appeared that, due to the differential pressure between the mud column and the formation fluid, the collars were pressed into the wall and so became "wall stuck". Points to note about differential pressure sticking are: (1) sticking is restricted to the drill collars, (2) the collars become stuck opposite a permeable formation, (3) the sticking occurs after an interruption of pipe movement, (4) circulation, if interrupted, can be restarted after the sticking is noticed, and (5) no large amounts of cuttings are circulated out after restarting circulation. Helmick and Longleyl investigated pipe sticking by differential pressure in the laboratory and found an empirical relationship between the differential pressure, the sticking time and the required pull-out force. In this paper an explanation of the mechanism is given based on Terzaghi's theory of clay consolidation. A qualitative description is given in the following paragraphs while the derivation of fonnulas is given in Appendices. This paper is a first attempt to explain pressure differential sticking and many points will require additional theoretical and practical investigation before the problem can be fully understood. PRESSURE DIFFERENTIAL STICKING AS A CONSOLIDATION PROBLEM In any borehole, where the mud pressure is higher than that exerted by the formation fluids, a mud cake is formed opposite the permeable sections of the hole and a continuous flow of filtrate takes place from the mud, through the cake and into the formation. This radial flow pattern requires a certain distribution of the hydraulic and the effective (grain-to-grain) stresses inside the mud cake. Any quantitative or qualitative change in the external pressure conditions will produce a change in the flow pattern and, consequently, also in the internal stress distribution inside the cake. In view of the low permeability and the high compressibility of a clay mud cake, the adjustment of the internal stress distribution is slow and is accompanied by a change in volume. Time dependent stresses are thus created which gradually diminish as the new state of equilibrium between internal and external pressures is approached. Some 30 years ago, Terzaghi developed his "Theory of Consolidation" to account for the time-dependent stresses and settling of clay formations under the influence of external loads. He derived a differential equation by which the time-dependent hydraulic stress and the consolidation can be computed for any point inside the layer during the consolidation process. His theory is based on the assumption that the change in stress is solely due to a change in water content and it may only be applied to one-dimensional consolidation phenomena. Other investiga-tors5,10 have expanded his theory to include processes of more than one dimension. The difference between the external pressures on the mud cake before and after sticking is a qualitative one (isolation of part of the cake by the static contact with the drill collars after pipe movement has been stopped)', and the time-dependent stresses thus created may be investigated by means of Terzaghi's theory. By this analysis the changes in the nature of the contact surface between the drill collars and the mud cake during the sticking can be explained; and the friction force between the two may be computed as a function of the sticking time, the borehole dimensions and the mud cake characteristics.

By L. H. Robinson

Triaxial compression tests have been performed to determine the strength characteristics of limestone, sand-stone and shale rocks subjected to controlled stress conditions. This control tuns exercised by varying the liquid pressures within and around a plastic-encased rock specimen. The pressure in the pores of the rock was varied throughout the range from atmospheric to 15,000 psig; the external pressure was changed over the same range with various positive pressure differences between is and the intertnal pressure. The data show that the rock strength increased and the mode of failure changed as the pressuire. surrounding the rock became greater than the pressure in the pores of the rock. These observations and the resu1ts of microbit drilling experiments indicate that the increased rock strength under pressure may bc an important effect in reducing drilling rare, but that other factors are probably of even greater importance. INTRODUCTION A large part of the research conductcd to reducc thc cost of drilling is directed toward improving present drilling technology and dcveloping new drilling methods. In spite of the fact that drilling is essentiaIly the act of making rocks fail, many details of the mechanism of failure are not known. It seems probable, therefore, that continuing studies of the fundamentals of rock failure can lay a foundation for future improvements in drilling technology. One of the factors which affects rock failure is the stress applied to the rock. This effect has been known for many years.'.'.; As an example, stress studics have been published by engineers' concerned with the strength characteristics of concrete in large dams. More recently, a number of investigators4-12 have explored the effects of stress on the strength of geologic formations and the geologic implications of their findings. During the last few years some research'" on rock strengths has also been conductcd in an attempt to gain additional insight into the factors which affeet rock drillability. In detcrmining the strength characteristics of rocks under different stress conditions, investigators have conventionally used triaxial compression equipment. wherein a jacketed rock cylinder is uniformly loaded from all directions and then compressed longitudinally. The results of this work have demonstrated that the mode of failure (brittle or malleable) is dependent upon the loading pressure, and that the strength of the rock increases as the loading pressure increases. These results clearly manifest that the stress, which is determined by the loading pressure, affects rock strength, and this implies that rocks under stress should be stronger and hence harder to drill. During the drilling of a porous rock the stress conditions are determined not only by the pressure surrounding the portion of the rock undergoing failure (confining pressure) but also by the pressure of the interstitial fluids within the rock (pore pressure). The importancc of both these pressures on the drilling rate of rocks has already been demonstrated by a number of investigators. Murray and Cunningham" found in microbit drilling expcriments that at constant pore pressures the drilling ratc decreased as the hydrostatic pressure surrounding an unjacketed, impermeable rock increased. Later Eckel" found that for jacketed Iimestone specimens the differcnce between hydrostatic (wellbore) pressure and formation (pore) pressure had an important effect on drilling rate. These observations of the effect of pressure on drilling rate emphasize that for drilling studies triaxial compression tests should be conducted under conditions of confining and pore pressure which simulate conditions underground. In the past, triaxial tests have been made under conditions which do not reproduce those underground. In particular, most of the tests on porous materials have keen made at varying confining pressures but with atmospheric pore pressures. In only one group of tests' was any data on the effect of pore pressurc reported, and these few data were on materials not representiltive of those encountered in drilling earth formations. The research described herein was initiated to deter-mine the importance of both internal pore pressure and confining pressure on failure characteristics of limestone. sandstone and shales. Triaxial loading equipment was used to obtain strength data at pressures up to 15,000 psig. An additional objective of this research was to apply these results to drilling rate studies by comparing them with the previously published drilling data of Murray and Cunningham" and of Eckel12. The work reported here is but one step in determining and evaluating the fundamental mechanisms which control drilling rate. Additional research is needed to clarify other aspects of the drilling process. The better

By S. J. Sindeband

Prior to discussing the metallurgy of sintered chromium borides, it is pertinent to outline some of the reasoning behind this investigation and the purposes underlying the work. This study was initiated as an aproach to the ubiquitous problem of a material for service at high temperatures under oxidizing atmospheres, and it was undertaken with a view to raising the 1500°F (816°C) ceiling to 2000°F (1093°C) or better. For the reason that no small, but rather a major, lifting of the high temperature working limit was being attempted, it was felt appropriate that a completely new approach be taken to this problem. A summary of the thinking behind this approach was published recently by Schwarzkopf.' In briefest terms, it was postulated that the following requirements could be set up for a material which would have high strength at high temperatures. 1. The individual crystals of the material must exhibit high strength interatomic bonds. This automatically leads to consideration of highly refractory materials, since their high energy requirements for melting are related to the strength of their atom-to-atom bonds. 2. On the polycrystalline basis, high boundary strength, superimposed on the above consideration, would also be a necessity. Since this implies control of boundary conditions, the powder metallurgy approach would hold considerable promise. Such materials actually had been fabricated for a number of years, and the cemented carbide is the best example of these. Here a highly refractory crystal was carefully bonded and resulted in a material of extremely high strength. That this strength was maintained at high temperature is exhibited by the ability of the cemented carbide tool to hold an edge for extended periods of heavy service. Nowick and Machlin2,3 have analytically approached the problem of creep and stress-rupture properties at high temperature and developed procedures whereby these properties can be approximately predicted from the room temperature physical constants of a material. The most important single constant in the provision of high temperature strength and creep resistance is shown to be the Modulus of Rigidity. On this basis, they proposed that a fertile field for investigation would be that of materials similar to cemented carbides, which have Moduli of Rigidity that are among the highest recorded. The cemented carbide, however, does not have good corrosion resistance in oxidizing atmospheres and without protection could not be used in gas turbines and similar pieces of equipment. It would be necessary then to attempt the fabrication of an allied material based upon a hard crystal which had good corrosion resistance as well. It was upon these premises that the subject study was undertaken and at an early stage it was sponsored by the U.S. Navy, Office of Naval Research. Since then, it has been carried on under contract with this agency. Chromium boride provided a logical starting point for such research, since it was relatively hard, exhibited good corrosion resistance, and, in addition, was commercially available, since it had found application in hard-surfacing alloys with iron and nickel. That chromium boride did not provide a material that met the ultimate aim of the study results from factors which are subsequently discussed. This, however, does not detract from the basis on which the study was conceived, nor from the value of reporting the results which follow. Chromium Boride While work on chromium boride proper dates back to Moissan,4 there has been a dearth of literature on borides since 1906. Subsequent to Moissan, principal investigators of chromium boride were Tucker and Moody,5 Wede-kind and Fetzer,6 du Jassoneix,7,8,9 and Andrieux." These investigators were generally limited to studies of methods of producing chromium boride and detennining its properties. Some study, however, was devoted to the chromium-boron system by du Jassoneix,7 who did this chemically and metal-lographically. This system is not amenable to normal methods of analysis by virtue of the refractory nature of the alloys involved, and the difficulties of measurement and control of temperature conditions in their range. Dilatometric apparatus is nonexistent for operation at these temperatures. Du Jassoneix made use of apparent chemical differences between two phases observed under the microscope and reported the existence of two definite compounds, namely: Cr3B2 and CrB. These two compounds, he reported, had quite similar chemical characteristics, but were sufficiently different to enable him to separate them. The easiest method for producing chromium boride is apparently the thermite process, first applied by Wede-

Jan 1, 1950

By A. S. Yue, A. G. Guy

A study was made of the effects of a prolonged flux of zinc atoms through the a solid solution of zinc in copper. The experimental arrangement consisted essentially of a copper disk about 0.01 in. thick, at one of whose surfaces a gaseous atmosphere containing zinc atoms was maintained, and at the other surface a gaseous atmosphere with a minimum of zinc atoms was maintained. During prolonged theothersurfaceexposure at high temperatures the zinc content of the copper disk gradually built up to the steady-state concentration distribution and then remained at this value. The concentration-distribution curves for various conditions were determined by chemical analyses. The results showed that the condition of steady-state diffusion was achieved. The diffusion coefficients calculated from the experimental data, although not of high precision, agreed with the values obtained by other workers using unsteady-state methods. Relatively slight porosity developed in the specimens in the course of diffusion. A LTHOUGH most diffusion studies have been made under unsteady-state conditions, it is known' that the steady-state method is often superior with respect to the directness and accuracy of interpretation of the data. Steady-state diffusion of gases through metal diaphragms is well known. Also, Harris' and Smith" have used the steady-state method in studying the diffusion of carbon in aus-tenite. The accepted mechanism in this system involves the motion of the interstitial carbon atoms in the rigid framework of the lattice of iron atoms. Thus, there is little difficulty in visualizing the steady flow of the small carbon atoms through the austenite. The situation in substitutional diffusion is quite different. Here the atoms are comparable in size, and it is not evident how a steady flow of one of the atoms through the solid solution might be achieved. At the time the present research was started, it was known that a previous exploratory attempt to produce steady-state diffusion in a substitutional alloy, the Au-Ag system,' had been unsuccessful and had indicated that perhaps there were basic difficulties that could not be ovei-come. Therefore, the present research began as a study of the effect of a prolonged flux of metal atoms through a substitutional solid solution. Eventua.lly, it was possible to produce actual steady-state diffusion in the system chosen for study, the a Cu-Zn alloys. Experimental Procedure The aim in the experiments was to maintain a high zinc content, about 30 pet, at one surface of a copper sheet, and to maintain a low zinc content, near 0 pet, at the opposite surface. The zinc would then diffuse into and through the copper, first building up to the steady-state concentration distribution and then maintaining this distribution. The three types of specimens that were used are shown in Fig. 1. In type A specimens the copper disk through which diffusion occurred was welded to the top of a cylindrical molybdenum tube, the bottom of which also was sealed by welding. At the diffusion temperature the brass chips in the molybdenum container were the source of the zinc vapor which maintained the lower surface of the copper disk at 30 pet Zn. The upper surface was maintained at 0 pet Zn by the vacuum in which type A, and also type B, specimens were diffused. Since the molybdenum container was impervious to zinc vapor, it was intended that the only path of escape for the vapor from the brass chips would be through the thin copper diffusion disk. However, it was found that small leaks often developed at the welded joints during the diffusion treatment, and in most specimens some of the zinc was lost in this manner. Although even small losses of this kind were a serious handicap in attempting to determine the flux through the disk, they did not prevent the maintenance of satisfactory boundary conditions for the attainment of the steady-state condition. Type B specimens differed from type A in having a weight of about 300 g supported on the copper disk by 15 to 20 short quartz rods. This change was made when it was observed that the copper disk was being bowed upward by the difference in the pressures acting on its two surfaces. Since the grain-boundary cracking which occurred in the bowed specimens could be attributed largely to the accompanying creep,3 it was desirable to minimize this effect. The counterweight was effective in significantly decreasing both bowing of the disk and cracking at grain boundaries. Type C specimens differed considerably from the others in that the low-zinc atmosphere at one sur-

Jan 1, 1959

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967

By Charles H. Grant

Some of the limiting factors relative to explosive crushing of rock and ways to overcome a few of these problems are presented. Relationships between borehole diameters, bench heights, and spacings, along with a review of the influence geometry has on energy as these are changed, are discussed. Efficiency in use of explosives and the decay of energy as it moves through rock and is absorbed and dissipated, is described, along with fragmentation as a function of spacings and energy zoning, etc. Communications are one of the major problems encountered. In an effort to provide a better understanding of the use of explosives, it is necessary to take a little different view of what explosives are, how to look at them as tools to fragment rock, and some of the problems encountered in doing so. First, take the explosive: although there are many factors involved, consider these as being reduced to only two — shock-strain imparted to the rock by the high early development of energy, and the gas effect which is a combination of heat, moles of gas formed, rate of formation of these gases which develop pressures, etc. First, consider shock energy by itself and assume there is no gas effect in the reaction. Fig. 1 illustrates a block or cube of rock, in the center of which is detonated an explosive charge which is 100% shock energy. Tensile slabbing would be seen on the surface and probably the cube of rock would generally hang together even though microcracks were formed. If the situation is reversed and an explosive whch has no shock energy and only gas effect (Fig. 2) is considered, the cube of rock would act as a pressure vessel and contain the pressure from the gas effect until it exceeded the rock-vessel strength; then the rock would break in a few large pieces. If these two kinds of energy are put together and the area of shock-strain around the explosive (Fig. 3) is considered, the two energies will be seen working together to furnish broken rock. The gas effect applies pressure to the microcracks formed from the shock energy to weaken the rock-pressure vessel and propagate these cracks to break the rock apart. It not only will be broken more finely, but will break apart at a lower pressure than the gaseffect case, since the shock energy has first weakened the rock vessel. Although tensile spalling from the shock-strain imparts momentum to the rock, the main source of displacement comes from the gas effect. The term "rock" is being used to mean any material to be blasted. These energies are absorbed by the rock in different ways. First, classify rock into two main categories: "elastic" and "plastic-acting." Elastic rock should be thought of as rock which can transmit a shock wave and is high in compressive strength, such as granite or quartzite. Since this elastic rock transmits a shock wave well, it makes good use of the shock energy from the explosive-forming cracks, etc., for the gas effect to work on. Plastic-acting rocks are rock masses which are relatively low in compressive strength and absorb shock energy at a much faster rate, thereby making poor use of the shock energy by not developing as extensive a cracked zone for the gas effect to work on. Rocks of this type are generally softer materials such as some limestones, sandstones, and porphyries. For the most part, the shockenergy part of the explosive reaction is wasted in plastic-acting rock, leaving most of the work to the gas effect. Since the ratio of gas effect to shock energy is different in different explosives, it is easy to understand why some explosives perform well in elastic rock and poorly in plastic-acting rock, and vice versa. Some of the most difficult blasting situations arise when mixtures of plastic-acting and elastic rock are encountered (Fig. 4). Fig. 4 shows an example of granite boulders cemented together with something like a decomposed quartz monzonite which is plastic-acting. The elastic granite boulders will transmit the shock-strain within itself, but when this shock tries to move through the monzonite to the next boulder, its intensity is absorbed by the monzonite and little shock-strain is placed on the adjoining boulder. In addition to this loss by absorbtion, shock reflection at the surface of the boulder will effect tensile spalling. The net effect is poor breakage of the boulders which do not have drillholes in them as they simply will be popped out with the muck. The same is true (Fig. 5) when layers and joints make

Jan 1, 1970

By M. A. Goudie

The deposits occur in a large salt basin of Middle Devonian age. The potash, the final deposit in the salt basin, results from several interrupted cycles of evaporation and dessication. The deposits are extensive, and, at first glance, relatively undisturbed. With more and more wells being drilled, it has now become evident that salt solution has played a large part in changing the original deposits, resulting in some cases in partial to complete removal of the potash and the underlying halite. The most dominant factor in the removal of salt by solution appears to have been tectonic movement and consequent faulting, probably of relatively minor dimensions but of major importance. Evidence which indicates the tilting of the evaporite basin to the north and northwest is shown by the changing pattern of the basin during succeeding eras of potash deposition. The potash minerals of most importance economically are sylvite and carnallite. Reserve calculations indicate that 6.4 billion tons of recoverable high grade potash in K2O equivalent exist in the basin. The Devonian salt basin, which contains the Saskatchewan potash deposits, extends from just east of the foothills in Alberta, north as far as the Peace River area, across Saskatchewan and into Manitoba as far east as Range 10 west of the First Meridian and south into Montana and North Dakota (Fig. 1). The basin is closed everywhere except to the northwest. The known potash deposits are confined almost entirely to the Province of Saskatchewan, with the exception of a small area in western Manitoba bordering the Saskatchewan boundary. The following discussion will concern only the Saskatchewan part of the basin. The evaporite series in the basin is defined as the Prairie Evaporite Formation of the Elk Point Group, of Middle Devonian age. Recent work done by potassium-argon dating methods has indicated an Upper Middle Devonian (Givetian) age of from 285 to 347 million years for the potash. The Elk Point Group consists in ascending order of the Ashern, Winnipegosis, and Prairie Evaporite Formations. The Ashern formation, with an average thickness of 30 ft, sometimes called the Third Red Bed, consists of dolomitic shales and shaly dolomites. The Winnipegosis, is a reef-type dolomite, usually with good porosity, and in many cases oil-staining, although to date no production has been obtained. The thickness varies from 50 to 250 ft. The Prairie Evaporite formation, varying from 0 to 600 ft in thickness, consists of halite with interbedded anhydrite and shale, with considerable amounts of potassium salts in the upper part of the formation. The potassium salts are chiefly chlorides, although very minor occurrences of sulfates have been re- ported. The anhydrite beds do not appear to be continuous, although generally one or two bands of anhydrite underlie the lowest potash zone and are used as marker horizons. The shale occurs as seams interbedded with the salts, as large irregular inclusions in the salts and as very fine particles in intimate mixture with the salts. The Prairie Evaporite Formation is overlain by the Second Red Bed member, the Dawson Bay Formation and the First Red Bed Member of the Manitoba Group, listed in ascending order. The Red Beds are shales which vary in color from red to green, maroon, grey, grey-black, and reddish purples. They serve as marker horizons for coring the potash. The Second Red Bed averages 14 ft in thickness, the First Red Bed 35 ft. The Dawson Bay Formation, which everywhere overlies the First Red Bed and the Prairie Evaporite Formation in the area under discussion, is a reef type of carbonate, in some places limestone, in others limestone and dolomite, with vugular to pinpoint porosity averaging 130 ft in thickness. In some parts of the area, it has a salt section near the top of the formation, usually with interbedded shales and limestones. In other parts of the area, it is waterbearing and the salt is absent. Detailed mapping has indicated that the areas in which the Dawson Bay is water-bearing are areas which have been disturbed by faulting. Where the Dawson Bay is salt-bearing, the porosity has been plugged by salt. The total thickness of the salt varies from between 600 to 700 ft in the center of the basin to zero at the northern edge of the basin (Fig. 2).* The salt-free area in the center of the Province is believed to have resulted from removal of salt by solution. Evidence from several wells suggests that salt removal has been a continuing process from the time of deposition to the present day. One well drilled between the Quill Lakes for potash information encountered

Jan 1, 1961