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By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.' If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The

By Richard P. Rothwell

The communication which I hare to lay before my fellow-members of the Institute, is no elaborate paper, nor the statement of any great discovery; it is simply the record of convenient methods of conducting topographical survey?, and of keeping the notes of the same; methods that have grown out of practical experience, and have saved me many a day's labor by facilitating office and field work, and at the same time secured a greater degree of accuracy than is obtained by the methods now in general use. I assume it as granted that no topographical map is worthy of the name, except it represent the elevations and depressions of the surface by means of horizontal or contour lines. In the Ordnance Survey of Great Britain, the contour lines are traced for every fifty feet vertical height, I believe, by running out the line with level and compass through all its meanderings on the surface; this, of course, is a very tedious, though accurate process, but " in the woods," where many of our surveys have to be made, it would be practically impossible. Some time ago, I made an extensive and quite elaborate topographical survey and contour map of the southern portion of the Cahaba coal-field, in Alabama, the object of the survey being to

By B. G. Hurd

A liquid-Freon permeameter suitable for making routine permeability determinations on small plug samples is described. The instrument is characterized by simplicity of design and ease of operation, and can be assembled inexpensively from stock items of laboratory equipment. It combines the unique advantages of both liquid and gas permeam-eters while eliminating many undesirable features of both general classes of instruments. Precision and accuracy of the specific Freon permeability measurements compare favorably with results of conventional liquid and gas permeameters. INTRODUCTION The liquid-Freon permeameter described in this paper was designed and built for special investigations of the properties of petroleum reservoir rocks. However, its unique advantages over conventional gas and liquid permeameters make it eminently suitable for routine use in the core analysis of small plug samples. In general, gas permeameters are very popular because of their simplicity of design and ease of operation. However, apparent gas permeabilities are normally higher than true specific permeabilities unless special corrections for gas-slippage are applied. Since these corrections require two or more measurements at different internal gas pressures, much of the time advantage of the specific gas permeability measurements is lost. Liquid permeability measurements, on the other hand, require no slip correction, but liquid saturation of the sample is time-consuming and difficult to insure. Often, too, the saturating liquid must be extracted or dried from the plug before it can be used for another experiment. The liquid-Freon permeameter described herein retains the inherent accuracy of the liquid permeameter, while affording the speed and ease of operation of the gas permeameter. Freon-12 (dichlorodifluoromethane) is a haloge-nated hydrocarbon, immiscible in the liquid phase with water. It may be considered as an oil phase in laboratory fluid-flow studies. Like butane and propane, it is a gas at normal room temperatures and atmospheric pressure but can be liquefied at moderate pressures. Complete liquid saturation of a plug sample with any of these fluids can be easily achieved by condensing vapors in the sample and operating the permeameter at a pressure above the vapor pressure of the liquid. Freon-12 is superior to butane or propane for permeability measurements only in that it is relatively nontoxic and completely incombustible, and thus presents no fire or explosion hazard. Freon-12 is believed to be completely nonreactive with most petroleum-reservoir rock samples. It volatilizes immediately from a plug on depressurizing to leave a clean, dry sample suitable for subsequent experiments. Thus, the inherent risk of changing physical properties of rock samples by cleaning and drying operations between permeability measurement and subsequent experiments is eliminated. DESCRIPTION OF THE PERMEAMETER The design of the liquid Freon-permeameter is shown schematically in Fig. 1. Regulated nitrogen pressure caps are used both as a driving pressure

By J. M. Campbell, T. S. Buxton

The most widely used methods of predicting the volumetric properties of gas are based on the principle of corresponding states, which asserts that the compressibility factor is a universal function of reduced temperature and pressure. Previous studies have shown that the acentric factor, as proposed by Pitzer, l is an important addition to reduced pressure and reduced temperature as factors affecting the compressibility factor. Results of this study indicate that, if the pseudocritical temperature and pressure used to determine the reduced conditions are adequately predicted, characterization of natural gas-carbon dioxide mixtures with the acentric factor will allow reliable determination of the compressibility factor. Comparisons of predicted and experimental compressibility factors have shown that the pseudo-critical constant rules of Stewart, Burkhardt and Voo 2 are satisfactory for hydrocarbon mixtures. However, these rules fail to predict the pseduo-critical constants for hydrocarbon-carbon dioxide mixtures. Based on graphically determined pseudocritical temperatures for binary hydrocarbon-carbon dioxide mixtures, a correlation which gives the required correction to the Stewart, Burkhardt and Voo rules was prepared and a compressibility factor prediction technique was proposed. To test the proposed technique, compressibility factors for live mixtures of methane, carbon dioxide and either ethne or propane were experimentally determined at 100, 130 and 160F and pressures up to 7,026 psia. The predicted and experimental compressibility factors for these live mixtures had an average absolute deviation of 0.55 percent. INTRODUCTION Two-parameter generalized correlations based on the principle of corresponding states (PCS) are presently available for reliably predicting the compressibility factor of lean natural gas, i.e., natural gas with low concentrations of hydrocarbons heavier than methane. When these same correlations are used for mixtures of natural gas and carbon dioxide, large deviations between actual and predicted compressibility factors are observed. This study was undertaken to provide a means for accurately predicting the compressibility factor for such mixtures. In the past, two avenues of approach have been employed to extend the applicability of the PCS. The first has been to introduce additional parameters. The second has been to develop combination rules for predicting pseudocritical constants which do not suffer from the limitations of the commonly used molal average constants. In this study, both of these approaches have been considered and employed to arrive at a method for predicting the compressibility factor of mixtures of hydrocarbons and carbon dioxide. SELECTION OF A THIRD PARAMETER Failure of the original PCS to predict the compressibility factor for all pure gases, regardless of their mass, shape or polar moment, has led to the introduction of additional parameters into the PCS. Parameters have been introduced to correct for quantum deviations,3-5 non-spherical or globular shapes6-9 and for polar moments.8-12 In addition to these parameters which are based on some microscopic property and intended to correct for some specific cause of deviation, more general parameters based on some bulk property have also been introduced.1913-16 To use additional parameters to correct for each of the possible causes of deviation among the individual constituents of a gas mixture would require a rather complex form of the PCS. To maintain the PCS in as simple a form as possible, it is more desirable to have a single third parameter which is based on some bulk property influenced by several of the factors causing deviations. The third parameter selected for use in this study is a factor originally proposed by Pitzer.9

By G. W. Doepel, W. P. Sibley

A three-dimensional, multilayer, mathematical model has been developed for predicting performance by mis-c.ible displacement. Areal and vertical coverage, total gas-oil ratio, propane-oil ratio and oil-recovery factor for the multilayer system are computed as functions of hydrocarbon pore volumes of solvent injected. The technique has been programed for use on the IBM-7090 digital computer and was used in calculating perfortnance for continuous miscible displacement of a five-spot, 50-layer .system. Results reported are based on the use of published laboratory data for a single, uniform five-spot layer. However, the technique is sufficiently generalized to calculate performance of any system of layers of any pattern configuration and mobility ratio, provided data are available to describe perfortilance of a single layer. The technique has also been adapted for predicting oil recovery resulting from various gas-driven slug sizes. The results presented for both continuous and slug-type injection show, that permeability variation has 0 significant effect on oil recovery but that solvent composition, within the range studied, has a lesser effect on oil recovery. INTRODUCTION Experience from many of the miscible-phase displacement projects currently in operation indicates that the injected solvent flows preferentially through the more permeable zones in the reservoir. This preferential solvent flow in the high-permeability streaks results in a reduction of vertical coverage (C,) and an attendant decrease in oil recovery. The multilayer technique presented in this paper uses areal coverage (C.,) data for a single layer from the literature and from laboratory measurements of displacement efficiency (herein referred to as microscopic coverage, C,,) to calculate areal coverage (C,) and vertical coverage (C,) for the multilayer system. Oil recovery for the multilayer system is obtained as the product of (Ca) (Cm) (Cv). It is assumed that C, in a single layer is 100 per cent; therefore, (C,) (Cm) is a measure of oil recovery from that layer. Data presented in the literature for a single layer generally deal only with areal coverage and/or microscopic coverage —but seldom specifically with oil recovery. Nevertheless, this technique is flexible in that either Ca and C,, of an individual layer or a direct measurement of oil recovery for the layer may be used. In developing this technique, the problem arose concerning a method of determining the relative amounts of solvent that will enter each layer during any increment of solvent injected. To solve the problem, a dimensionless equation was derived for expressing solvent injected into each layer as a fraction of total injection. A finite-difference method was applied in integrating the equation to determine oil recovery for the system of layers as a function of pore volumes injected. The technique subsequently was programed for solution on a digital computer. The method was applied to predict performance of a deep California reservoir under continuous miscible displacement and has been extended for calculating oil recovery as a function of slug size for gas-driven slug injection. The technique may be applied to any petroleum reservoir that can be adequately represented as a layered system, by considering permeability variation,1-3 permeability range and average permeability. Each layer is then assigned its appropriate permeability, porosity and hydrocarbon saturation. RESERVOIR VOLUME CONTACTED BY SOLVENT It has been recognized for some time that high microscopic coverage (C,) can be obtained by injecting a miscible agent, such as propane, into an oil reservoir. These high values of C,,, have been demonstrated in the laboratory and are normally between 80 and 100 per cent, depending on solvent and reservoir oil composition as well as on reservoir temperature and pressure. In miscible-phase displacement, because there is no interface between solvent and oil, effective permeability to solvent is the same as that to oil. (This assumes that oil saturation has not changed and that water is immobile.) Consequently, mobility ratio (M) simply reduces to that of viscosity ratio . Perrine4 and Habermann5 have shown that large

By John S. Alexander

DURING the past few years the block coal of Indiana has been talked about and written upon to such an extent, that almost every one at all interested in such subjects, has been made acquainted with the area and geographical position of the field, the quality and peculiar properties of the coal, the thickness of the veins, the manner of mining, etc. The writer, therefore, taking for granted that, to those present all this is familiar ground, desires more especially to call attention to the position this coal takes in the market, and at those points of consumption where it is brought in direct competition with rival fuels. Chicago, thus far, has been the chief consumer of Indiana block coal, the distance from the mines at Brazil, via Terre Haute and the

By V. Carlson, J. A. Rowe, E. O. Bennett

This report concerns the microbial flora found throughout the surface facilities of six water-injection systems in Texas and Oklahoma. Each system is described in detail and water quality data are presented when available. Pseudomonads and sulfate-reducers (Desulfovibrio) were the predominate organisms found in the systems. The genera Sphaerotilus, Bacillus, Achromobacter, Minococcus, Clostridium, Flavobacteriurn, and Sarcina were also isolated in significant numbers. Molds, iron bacteria, sulfur bacteria and soil bacteria were found less frequently in the systems. It is concluded that a complex microbiological flora exists in oilfield water-injection systems. A tendency for waters to deteriorate in passage through solid bed filters is also noted. INTRODUCTION The injection of water into a subsurface formation is often accompanied by numerous problems, the origin and nature of which are only partially understood. During the past few years, investigators have indicated that bacteria are involved in some of these problems even though very little specific information is available concerning this matter. It is surprising that investigators working on microbiological problems in water injection have never made a complete study of the flora of these systems. The logical course to pursue is that of identifying the microbial flora and then examining each organism individually and in combination with others to determine if they produce a particular problem. The objective of the present investigation is to identify the microbial flora in water-injection systems. In addition. the quality of the water in most of the systems was determined and some observations made on the extent to which passage through surface-handling facilities affects water quality. The information derived from this study can serve as a foundation for additional basic investigations. EXPERIMENTAL PROCEDURE The microbial flora of six water-injection systems were studied at 50 sampling points. These systems are experiencing problems which may be attributable to micro-organisms, and two were being treated with antimicrobial agents at the time of this study. The samples were obtained by inoculating 1.0 ml of the water onto the different media at the sampling point. The media used for primary isolation included nutrient agar, Strokes agar, M-10-E medium and semi-solid thioglycollate medium. The cultures were returned to the laboratory, incubated at 30°C until growth occured; then, pure cultures were obtained from individual colonies. The pure cultures were identified according to standardbacteriologica1 procedures. Those organisms not fitting identification criteria exactly, even though exhibiting close similarities to known species, are listed as unidentified organisms. Membrane filters were used to make water-quality tests at intervals before and after collection of the microbiological samples. The filter discs were 47 mm in diameter with a 0.45-micron particle-size retention, and the tests were done under closed conditions at 20) psi. Membrane flow rates are plotted as increasing filtrate volumes, and the total solids contents arcs given when available. An effort was made to sample at each place in a system where a change in environment occurred. In this manner, the effect of passage through filters, tanks, hay sections, etc., on the microbial flora and water quality could be observed. RESULTS SYSTEM A This waterflood system (Fig. 1) is about four years old and daily pumps approx&ately 110,000 bbl of oil-free sour water from a 3,700-ft deep reef. The

By P. B. Baxendell, R. Thomas

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

By R. J. S. Brown, B. W. Ganison

A new logging method has been developed, based on measurement of the nuclear magnetism of formation fluids. The nuclear magnetism log (NML) is the only log that responds solely to formation fluids. It operates equally well in both oil-base and water-base muds and in empty holes, and can be used in all kinds of formations except strongly magnetic ones. Two separate NML measurements can be made, one of which provides a continuous formation fluid curve. This fluid curve is called the free fluid log (FFL) and is believed to indicate a minimum effective porosity in most formations. The FFL not only delineates fluid-containing zones, but provides an excellent correlation curve that can be obtained under conditions where conventional correlation logs are ineffective. Preliminary tests indicate that the second kind of NML measurement may help distinguish oil and water zones and provide information concerning permeability and wettability. (The FFL itself appears to provide some information on permeability.) The second kind of NML measurement requires stopping the logging tool for a short time opposite a zone of interest and taking more extensive NML data that can be displayed as nuclear magnetic relaxation curves. In some instances, oil and water saturations for the region immediately adjacent to the borehole can be read from these relaxation curves. INTRODUCTION In 1946, Bloch, Hansen and Packard and Purcell, Torrey and Pound3 independently announced the successful demonstration of the phenomenon of nuclear magnetic resonance. During the past 13 years, there have been many applications of nuclear magnetic resonance, including applications to the study of chemical structure and to the measurement of magnetic field strengths. Preliminary experiments on the feasibility of using nuclear magnetism measurements in well logging were made independently by California Research Corp. and Varian Assoc., the Varian work being sponsored by the Byron Jackson Tools, Inc. Since then a cooperative research program on nuclear magnetism logging has been carried out by the Byron Jackson Div. and Research Center of Borg-Warner Corp., and California Research Corp., subsidiary of Standard Oil Co. of California. The use of nuclear magnetism in well logging is of special interest because it offers a way of making direct measurements on the hydrogen in the formation fluids and not on the rock matrix. Within the past 1 1/2 years, successful measurements have been made with a research model logging tool in wells in California, Tex as, Utah, Louisiana and Wyoming. NUCLEAR MAGNETISM SIGNALS Polarization, Relaxation and Precession Many atomic nuclei possess magnetic moments and spins; that is, they are similar in some respects to bar-magnet and gyroscope combinations. Molecules and their nuclei are subject to thermal motion, which has a scrambling effect, tending to leave as many nuclear spins oriented in any one direction as in any other. However, if a magnetic field is applied, the magnetic nuclei tend to align in the direction of the field. The scrambling and aligning forces compete with each other, with the result that a few more spins are oriented parallel to the field than in other directions. This gives a net magnetization, or polarization, which is directly proportional to the strength of the applied magnetic field (aligning influence) and inversely proportional to the absolute temperature (scrambling influence). When the magnetic field in, or temperature of, a liquid sample containing protons is changed, the new equilibrium value of proton polarization is not established immediately but requires an amount of time which depends on the nature of the hydrogen-containing materials. The process of approaching the equilibrium value of polarization is called relaxation.'.' Polarization is a vector quantity, and the components parallel to and perpendicular to the magnetic field must be considered separately. Relaxation of the component parallel to the field is called "thermal relaxation", or "longitudinal relaxation", and the corresponding time for this component of non-equilibrium polarization to decay by a factor of e (natural log base) is denoted T. The relaxation of the perpendicular component is called "transverse relaxation", and the corresponding relaxation time is denoted T,. The potential energy of a magnet in a uniform field depends on the angle the magnet makes with the field; therefore, a change of the component of net polarization parallel to the magnetic field involves an exchange of energy between the spin system and the thermal motion of the molecules, leading to the term thermal relaxation for the relaxation of this component. Suppose we subject a sample to a strong magnetic field at right angles to the earth's field for a time greater than TI. A polarization, thus, is established at right an-

By Andrew A. Blair

The increased importance and value of chemical analysis in connection with metallurgical operations is largely, if not entirely, due to the increased accuracy of the analytical methods used for the quantitative determination of the foreign elements always associated with the metal operated upon. This applies especially in the working of iron and steel, and to the determination of the amounts of such elements as phosphorus, carbon, and silicon. The influence of greater or smaller amounts of these elements upon the physical properties of iron and steel will be better understood when the proper experiments shall have been made upon samples whose chemical composition is known with almost absolute certainty. From the present standpoint of analytical chemistry, it is easy to see that at least one reason for the failure of many attempts to solve this problem, is the inaccuracy of the analytical methods used. Even at the present time the frequent want of agreement (over and above the unavoidable error due to manipulation) between chemists working on the same sample, leads one to think that there is still at least a choice in the methods used. It is true that very frequently a faulty method in the hands of a skilful analyst may be made to give corroborative results

By M. A. El-Aouar

Drilling muds are complex colloidal systems. In an effort to analyze the physical properties that affect their performance at high temperature, an investigation was made of the hydrothermal stability of the monoionic hydrogen, calcium and magnesium forms of montmorillonite and attapulgite. Samples were heated to 400°1F in a simple autoclave and analyzed for cation exchange capacity, c-axis X-ray diffraction spacing and pH factor us sodium hydroxide titration dependence. Out of the six monoionic clay minerals tested, calcium montmorillonite and magnesium attapulgite showed the least base exchange capacities and were relatively unaffected to heat. It is concluded that, of the six clays studied, these two clays were the most suitable forms for use in drilling fluids. INTRODUCTION The drilling of deep wells is dependent upon the drilling mud, and problems frequently arise concerning the effect of mud temperature and prolonged heating. Drilling muds are complex colloidal systems. In an effort to analyze their behavior in deep, hot boreholes, it was thought desirable in this investigation to study suspension of pure, monoionic montmorillonite and attapulgite clays before and after hydrothermal heating. Chemically, clays are hydrated aluminum silicates, such as montmorillonites and attapulgites. The structure of montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. Attapulgite consists of double silica chains running parallel to the c-axis with the chains linked together at their longitudinal edges. The apexes of the tetrahedrons in successive chains point in opposite direc-tions.4,7,10 One of the most important characteristics of clay minerals is their property of sorbing certain anions and cations and retaining them in exchangeable state. The property of exchange capacity is measured in terms of milliequivalents (meq) per 100 gm of clay. The cation-exchange capacities are taken at pH 7 from titration curves which show the relation between pH and milliequivalents of added NaoH.9,11 The following are causes of cation exchange: (1) broken bonds around the edges of the silica alumina units would give rise to unsatisfied charges, which would be balanced by adsorbed cations; (2) substitution within the lattice structure of trivalent aluminum for quadrivalent silicon in the tetrahedral sheet and of ions of lower valence; and (3) the hydrogen of exposed hydroxyls may be replaced by a cation which would be exchangeable. The primary techniques employed to study the effects of hydrothermal treatment were titration curves and X-ray diffraction analyses. Titration curves were useful in characterizing the nature of the clay mineral surface and the stability of the various samples to attack by acid or alkali before and after hydrothermal treatment. X-ray diffraction analyses were used to determine changes in the nature and crystal structure of the minerals present and to determine the cations in exchange positions on the montmorillonite samples. EXPERMENTAL PROCEDURE PREPARATION OF SAMPLES Selected samples of Wyoming bentonite and attapulgite clay from mines along the Georgia and Florida border were purified by centrifugation to remove all particles larger than 2 microns. In preparing magnesium attapulgite, first a 1.00-normal solution of magnesium acetate was prepared. The pH of the solution was adjusted to 7.0 by adding magnesium oxide. One hundred grams of attapulgite clay were mixed in a blender for 30 minutes with the magnesium acetate solution. The attapulgite solution was left overnight, and then filtered in a Buchner funnel. The suspension was leached with further quantity of magnesium acetate solution and then washed with distilled water for 20 days, after which the filtrate was free from magnesium ions. The concentration of magnesium attapulgite in the clay slurry was adjusted and determined quantita-

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

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

By C. E. Murphey

C. E. Murphey, Jr., has presented a relevant, simplified comparison of drill string response when drilling with and without bumper subs. His point that drilling without bumper subs gives conditions further from resonance is valid. Thus, drilling from a floating vessel without bumper subs is undoubtedly feasible, especially when the heave motions of the drilling vessel are small. When these heave motions become large, an evaluation of the magnitude of the change of bit weight is a requirement for a realistic comparison between using and not using bumper subs. As Murphey states, this evaluation should include the effects of damping and presence of drill collars. The analysis would be similar to that presented in our Appendix, but is far beyond the scope of this Reply. ***

By V. J. Driscoll

A method is given for checking pore volume reserve estimates and transient water inflzix factors utilizing early well performance. Principal applications are based on the observation that there is a convenient transient time-range in terms of well spacing in which observed pressure drop will give a good indication of fluid-in-place. Primary quantity determined is a porosity-feet value applicable in the vicinity of an observation well. Checks on porosity or net pay thickness and permeability values also are obtained. These are particularly valuable in improving quality of interpretive factors entering into pore-volume reserve determinations for larger fields. In smaller fields, direct determination of total field reserves and approximate location of boundaries may be made in some cases. Well interference and production data plus a build-up curve on the observation well are needed. The build-up curve may be taken at any time. Field applications are given. The method can be applied with the completion of the second well on a new discovery or to older reservoirs by major changes in withdrawal rates from a local area. Appropriate test length permits results to be obtained with equal accuracy on widely spaced wells. Criteria for optimizing test conditions are given. Provision is made for various boundary and well effects including incomplete observation well build-up. INTRODUCTION Due to low quality data, initial pore volume reserve and water influx estimates may often vary by a factor of two or more from results obtained at a later date. Unfortunately, by conventional methods, more reliable answers from performance usually are not available until after most significant economic decisions have been made. Furthermore, in older reservoirs, uncertainties may still exist as to original oil-in-place, recovery factors and residual oil saturations due to incomplete or inaccurate performance data. This paper outlines situations and appropriate arrangements of basic transient theory whereby well interference data can be utilized to improve the quality of estimates under certain conditions. In addition to production data on offset producers, key information required is a measured pressure drop at an observation well, corrected for any incomplete build-up due to previous production, plus a formation capacity value derived from a conventional pressure build-up plot on the observation well. The method, as outlined, is strictly applicable only to a horizontal single-layered system of uniform rock characteristics containing a homogeneous fluid of low and constant compressibility. However, under the set of test conditions devised, requirements can usually be relaxed so that it should be applicable to most low permeability gas, water and undersaturated oil reservoirs. This is an area where more reliable information is certainly needed. BASIC CONSIDERATIONS A, B, C and F as subscripts or in the text refer to producing Well A, observation Well B, a more remote producing Well C and field boundary F. Combinations such as AB refer to distances and dimensionless times in terms of distances between these points, while single letters refer to distances and dimensionless times in terms of the well-bore or field radius. Equations covering definitions of quantities and complex situations are given in the Appendix. Key equations in practical units are given in Table 2. Transient Pressure Behavior Fig. 1 illustrates pressure drop at Point B with time due to initiation of a constant rate of withdrawal from Point A. This is shown as since a quantitative under-

By H. Matlock

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

By W. E. Coxe

In 1857 the Philadelphia and Reading Railroad Company, whose main line extended from Philadelphia to Pottsville, Pennsylvania, with branches into the coal regions of Schuylliill County, made a contract with the Fairmount Rolling Mill, at Philadelphia, for the rerolling of some four thousand tons of iron rails. The essential features of the agreement were that the old rails should be piled with puddled iron and rolled into flats for the rail pile, which latter was • to be of a section seven inches square, and after being heated, and reduced, by rolling, to a bloom of a section about fire inches by six inches, was to be reheated, before being finished into the rail of the T pattern, four inches high, weighing sixty-four pounds per yard. Great care was exercised in the execution of this contract, and the rails being distributed over all parts of the road, gave general satisfaction by their excellent wear. Five years afterward, the principal proprietor and manager of the Fairmount Rolling Mill was elected President of the Reading Railroad, and very many of the rails made under his supervision were still in use in the tracks of the company, of which he had just assumed the management. His first efforts were, therefore, directed to the procuring of more rails of the same quality wherewith to replace those worn out. Here he encountered some trouble, makers refusing to bid because of the details in the specification, the required reheating being the objectionable feature, for which it was generally intimated they would not be sufficiently remunerated for the increased labor, extra coal consumed, and the changes necessary from the established methods of working. Most of the new rails were, therefore, bought, and the old rails rerolled without regard to any particulars as to the manner of piling, heating, etc., each manufacturer furnishing what he deemed the best article possible for the money. As a consequence, rails of all imaginable grades were placed in the tracks, some giving out in six

By P. T. Bail, J. E. Bobek

In reservoirs containing soft shales interbedded with oil-producing sands, it is possible to have water movement from the shales into the sands during reservoir depletion. This paper presents the results of scaled flow-model tests performed to investigate the efficiency of oil displacement by this vertical influx of water into oil-producing sands. In these model tests, the effects of rate of influx and rock wettability were considered. Oil recoveries by shale-wafer influx and by water flooding were cornpared after 0.4 hydrocarbon volume of water entered the producing sand. This comparison was made for water-wet and oil-wet systems. In water-wet sand, shale-water influx produces slightly less oil than conventional water flooding; in oil-wet sand, shale-water influx produces about one-half as much oil as conventional water flooding. In another type of comparison, it was found that shale-water influx followed by water flooding recovers less oil than water flooding alone. This is true for both water-wet and oil-wet sands. A comparison of tests run at different rates of shale-water influx shows that oil recovery is insensitive to rate in water-wet sand; in oil-wet sand, oil recovery decreases with decreasing rate of influx. INTRODUCTION Localized subsidence of the earth's surface has accompanied the depletion of some oil reservoirs, particularly in California,1, 2 along the Texas Gulf Coast,3 4 and in the Bolivar Coastal fields of Venezuela. Subsidence occurs when fluid withdrawals reduce the pressure in the reservoir. The reasons for subsidence accompanying a reduction in reservoir pressure are not known with certainty.10° However, there is considerable evidence that compaction of soft shale beds adjacent to producing oil sands can be a major cause of this subsi-dence.3, 6, 10-12 When the shales compact, a limited amount of water moves from the shales into the producing sands. A schematic illustration of this oil-producing mechanism is shown in Fig. 1. As the pressure in the sand declines due to oil production, a predominantly vertical pressure gradient develops at the sand-shale boundary. This causes water to move from the shale into the sand as indicated by the solid arrows. This paper reports the results of scaled flow-model tests to investigate the efficiency of oil displacement by the vertical influx of shale water into producing sands. The model tests were not performed with the aim of duplicating the recovery behavior of any specific reservoir. The primary purpose of the tests was to obtain a better understanding of oil displacement by shale-water influx. A knowledge of the oil- and water-production characteristics of even a simplified reservoir system should be of value to engineers estimating the performance of reservoirs where shale-water influx is occurring in conjunction with other production mechanisms. The following limitations and assumptions apply to the model work. 1. The sand of the prototype reservoir is homogeneous and horizontal. 2. The shale-water influx is uniformly distributed along the top and bottom of the sand member being studied. 3. No effects of edge-water drive or dissolved-gas drive that might accompany shale-water influx are considered. PROTOTYPE RESERVOIRS Scaled-model tests were performed to study oil displacement from three prototype reservoir sections. The reservoir sections modeled consist of single sand layers out of a sequence of -sand and -shale layers, as illustrated in Fig. 1. Each prototype represents a homogeneous, high-permeability, unconsolidated sand layer. In the field, the prototype is oriented in such a manner that one end is at the radius of drainage of a producing well and the other end is pointed toward the producing well (Fig. 2). The sand and fluid properties and the dimensions of the three prototypes are given in Table 1. The capillary pressure relationships for the three prototypes are presented in Figs. 3, 4 and 5. The oil-water per-

By M. R. Annis, P. H. Monaghan

The control of mud properties affords two practical means of tnitigating pipe sticking caused by differential pressure: (I) teducing weight and, therefore, differential pressure; and (2) reducing the friction berween the pipe and mud cake. This paper describes investigation of the second of these—the friction between the pipe and the mud cake. Friction between a steel plate and a mud cake, held in contact by a differential pressure, was measured in the laboratory while maintaining a constant area of contact. Experiments were performed to determine how this friction varied with changes in mud composition and with changes in experimental conditions such as the differential pressure, time of contact of plate and mud cake, and filter-cake thickness. It was found that the apparent coefficient of friction, or the "sticking" coeficient, was not a constant; instead, it increased with increased time of contact between plate and mud cake, and with increased barite content of the Mud. The sticking coeficient varied from about 0.05 to 0.2 afer 20 , and eventually reached values of 0.1 to 0.3 after two Hours. Quehracho or ferrochrome lignosulfonate reduced the sticking coefficient at short .set times but did not reduce the maximum value. Carboxy-~t~etlz~lcellulose had no effect on the sticking coeficient. Emulsification of oil in the mud reduced the sticking coefficient. Some oils reduced the sticking coefficient to about one-third of its Value in the oil- free base mud, while other oils reduced it only slightly. Addition of certain surfactants with the oils further reduced the sticking coefficient. Spotting a clean fluid over the stuck plate caused a reduction in sticking coefficient only if the differential presslrrr was reduced, either temporarily or- permanently. INTRODUCTION Often during drilling operations the drill string becomes stuck and cannot be raised, lowered, or rotated. This condition can be brought about by a number of causes, such as sloughing of the hole wall, settling of large particles carried by the mud, accumulation of mud filter cake during long stoppage of circulation and, finally, sticking by pressure of the mud column holding the pipe against the filter cake on the hole wall. This paper is concerned with the last-mentioned phenomenon. Helmick 2nd Longley' in 1957 suggested that a pressure differential from the wellbore to a permeable formation covered with mud cake could hold the drill pipe against the borehole wall with great force. This situation occurs when a portion of the drill string rests against the wall of the borehole, imbedding itself in the filter cake. The area of the drill pipe in contact with filter cake is then sealed from the full hydrostatic pressure of the mud column. The pressure difference between the mud-column pressure and the formation pressure acts on the area of drill pipe in contact with the filter cake to hold the drill pipe against the wall of the borehole. Helmick and Longley also presented laboratory cxperiments which showed that the force required to move steel across a mud cake increased with increasing differential pressure and with the time the stcel and mud cake had been In cuntact. Their data indicated that replacing the bulk mud with oil reduced the force required for movement. Field evidence was rcported that spotting oil over the stuck interval sometimes freed the pipe. Outmans- in 1958 presented a theoretical paper which described the sticking mechanism and explained the increase of sticking force with time with equations derived from consolidation theory. Since publication of these papers, there has been interest in the differential pressure sticking of drill strings, and several mud additives to reduce sticking or special equipment to free stuck pipe have been proposed."" Haden and Welch" have recently reported laboratory evidence showing that the composition of the filter cake influences the force necessary to move steel on the filter cake. There seems no doubt that differential pressure sticking is a real phenomenon and that its severity depends on the magnitude of the pressure differential across the mud cake, the area of contact and the friction between pipe and mud cake. The mud weight required to control a well is determined by the highest formation pressure in the well: hence, the magnitude of the differential pressure opposite normal or subnormal pressure formations cannot bc reduced. The area of contact may be minimized in several ways (control of filter-cake thickness, use of stabilizers and spirally grooved drill collars), but there arc practical limitations which prevent reduction of contact area from becoming a complete solution of the problem. However. the mud composition might bc altered to reduce the friction between pipe and mud cake. This paper presents quantitative measurements of the friction between steel and mud filter cake and shows how the friction varies with mud composition for given experimental conditions.

By T. Sterry Hunt

I HAVE already referred to this interesting locality in the opening address, but at the request of some of the members of the Institute, brought before them specimens of the ore and the accompanying rock. The ore, which is cassiterite, is also met with elsewhere in Maine, at Paris and Hebron, but it there occurs associated with orthoclase, quartz, tourmaline, and beryl, in concretionary granite veins, which cut the micaceous gneisses of the White Mountain series. At Winslow the veins traverse an impure gray micaceous limestone, which is found in many parts of this region, and is subordinate to the same gneissic series. The veins, which are seldom more than an inch or two in thickness, are abundant through a considerable breadth of the rock, and are interlaminated with it, occupying places between the sedimentary layers, which are distinctly marked by different shades of color. Occasionally, however, they cut across the stratification for a little distance, showing that the disrupting action was not always confined to tearing the layers apart. The vein-stone consists of purple fluor-spar, and silvery white mica with quartz. In this gangue the cassiterite, nearly black in color, is disseminated in small crystalline masses, sometimes one-half an inch in diameter, and is associated with a little mispickel. I have only seen the veins as exposed at a single point, but was informed that similar veins holding the ore are met with at a distance of several thousand feet