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Abstract A mathematical procedure is given for calculating proppant concentration and final fracture shape for proppant concentration and final fracture shape for a fracture generated by injection of a viscous gel in which the propping material does not settle. To prevent bridging in the fracture, a decreasing pad prevent bridging in the fracture, a decreasing pad volume is present ahead of the proppant slurry. If combined with a criterion for proppant admittance - expressing the minimum width required for nonbridging particle transport - the developed procedure will result in a realistic design of fracturing treatments. Introduction Hydraulic fracturing is a well known technique for improving the productivity of wells by creating a highly conductive path in the reservoir. This path is made by fracturing the formation through the injection of fluid into a well at pressures above the breakdown pressure. To keep the fracture open after the treatment, propping material is injected with the fracturing fluid. Settling of the proppant can be reduced or even prevented by using viscous oil- and water-based gels as fracturing fluids.From theoretical considerations it follows that the cross-section of a propagating hydraulic fracture is approximately elliptical. The dimensions of the ellipse are determined by the injection rate, the injected volume of fracturing fluid, and fracturing-fluid properties-taking into account the volume of fluid loss to the permeable formation. The fluid loss depends partly on the fluid potential gradients at the fracture walls, resulting in a time-dependent fluid-loss coefficient, which is proportional to the reciprocal of the square root of the exposure time.Since the propping material can cause early screenout, a relatively large sand-free pad of fracturing fluid is injected to initiate the fracture. This pad volume moves ahead of the fluid (gel) containing the propping material. Owing to spurt and filtration losses - highest at the fracture tip but decreasing gradually toward the well - the pad length in the fracture will decrease. The proppant-laden fracturing fluid is also subject to fluid loss, which causes the proppant concentration to increase with distance from the well. The propped fracture width obtained after the fracturing treatment depends on the balance between pad volume and proppant concentration in the fracture. A treatment design should therefore aim at optimization of pad volume, fracturing-fluid volume, and proppant concentration. A design program should deliver practical pumping schedules, which generate fractures of required penetration and conductivity. penetration and conductivity. The present study is a new step toward a more realistic design of fracturing treatments. Differential equations describing the proppant distribution in fractures created by very viscous fluids (no settling) are derived and solved. DEFINITION OF THE MATHEMATICAL MODEL The derivation of the differential equations describing the proppant distribution is based on the following model premises.1. Vertical fractures are of rectilinear shape.2. Two symmetric fracture wings move diametrically from the well.3. Fracture dimensions follow the relations established by Geertsma and de Klerk.4. Gel and proppant move with the same velocity in a piston-like manner.5. Rheological properties of the gel prevent settling of the proppant.6. Fluid-loss is proportional to the square root of the exposure time.7. A decreasing proppant-free pad moves ahead of the proppant suspension.Based on these conditions, a set of differential equations subject to the boundary conditions has been derived (see Appendix A). In Appendix B the applied finite-difference scheme, and in Appendix C the solution procedure are discussed. To describe radial fractures, a simple coordinate transformation has been given in Appendix D. SPEJ P. 531

Synopsis The attenuation of ultrasonic shear waves with frequencies between 2.5 MHz and 25 MHz has been measured in two single crystals of superconducting aluminium for different polarization directions. At the transition temperature a steep although continuous drop of the attenuation was observed. The remaining part of the attenuation fits quite well into the BCS-theory. No anisotropy has been found for the zero-temperature energy gap, but the shapes of the attenuation-versus-temperature curves are strongly orientation-dependent. Some measurements have also been performed at small magnetic fields.

Abstract Water drive in a homogeneous porous medium with a uniform permeability distribution has been extensively studied in the past, both theoretically and experimentally. In this paper equations are derived for a two-dimensional water drive in a porous system with either a continuously or a porous system with either a continuously or a discontinuously varying permeability distribution perpendicular to the layer. The influence of perpendicular to the layer. The influence of capillary forces bas not been taken into account. A necessary condition for the validity of the equations is that the water should underrun the oil. It is shown that the permeability distribution has much influence on the oil recovery. A large difference in recovery was apparent from a comparison of three systems, in which the oil production decreased as follows: (1) permeability increasing in an upward direction perpendicular to the layer, (2) homogeneous, uniform permeability throughout, (3) permeability increasing in a downward direction perpendicular to the layer. Introduction The recovery from a homogeneous, two-dimensional system in response to a normal water drive can be calculated with the help of theories developed by Beckers. He describes segregated flow of oil and water in which the water underruns the oil due to gravity and viscous forces. In his approach it is impossible to include capillarity, which means that the system does not describe a transition zone. However, we have a great deal of scaled experimental evidence which shows that moderate initial transition zones disappear during the displacement process where gravity and/or viscous tonguing effects occur. The experiments then show a sharp interface, and a transition zone is only found in the top of the water tongue. Neglect of this small zone affects breakthrough-time calculations, but on the other hand, gives the advantage of being able to treat the problem with the end-point permeabilities only. Although not immediately recognizable, there is a form of crossflow involved in this concept. It can be found from the material balance if the layer is divided into two sections parallel to the bedding plane. The theory describes experiments with a maximum initial transition zone of about one-third of the layer thickness. There are no restrictions on the mobility ratio. The production curve predicts too early a breakthrough, but shortly thereafter very satisfactory agreement is found. For many practical cases, these theories can be reduced to the simplified formulation given by Dietz. Experimental verification shows that his theory describes horizontal scaled-model experiments satisfactorily for mobility ratios larger than 6. Although gravity forces are completely neglected in the theory but not in the experiments, only the viscous forces are now responsible for tongue forming. Neglect of gravity delays breakthrough in comparison with predictions from the Beckers theory, but generally gives a somewhat better though not correct prediction of the moment of breakthrough. These findings have encouraged us to apply the same principles to inhomogeneous systems. To delay the theoretical breakthrough, gravity forces parallel to the bedding plane have been included, parallel to the bedding plane have been included, which results in a in a better fit with the over-all production curve for tilted layers. production curve for tilted layers. The equations derived in this paper can be applied to systems with either a continuous or a discontinuous permeability distribution perpendicular to the layer They are therefore applicable to a great number of inhomogeneous systems. Areal extension can be effected with sweep efficiency factors or by applying stream-tube models.

Abstract Experiments on oil displacement from homogeneous porous media have shown that the component porous media have shown that the component oil flow across the layer is often negligibly small compared with that parallel to it. This result is applied in the inspectional analysis of the equations governing the macroscopic displacement processes. It is shown that in rectangular homogeneous models the dimensionless groups l/h and a can usually be neglected. This finding has been proved experimentally in rectangular models of various dimensions, two extremes of which are described in this paper. The work has been extended to curved models. An additional requirement is that the angles of dip must be small. Comparative experiments have been carried out in three-dimensional models of various geometrical configurations. The results of both studies indicate a greater flexibility in the use of models than has previously been assumed. Introduction The production behavior of petroleum reservoirs can to a large extent be investigated with the help of scaled models, although the great number of parameters to be scaled in such processes precludes parameters to be scaled in such processes precludes complete simulation. However, not all parameters have an equally important influence on the process; and it is therefore necessary to select the most important ones and investigate which parameters can possibly be neglected. To date, oil reservoirs have almost always been represented by models of similar geometry. In other words, the characteristic length, width and height are scaled down by the same factor. For many reservoirs, however, the length-height ratio is extremely large, and laboratory models become inconveniently long or very thin. In such cases it would be desirable to make the model too thick relatively. It will be demonstrated that this is in a number of cases a justifiable solution.

D. van der Horst, Albert Herrmann, An historical atlas of China. New edition by Norton Ginsburg. Djambatan N.V., Amsterdam 1966. 88 pp. - A.F.P. Hulsewé, F.S. Drake, Symposium of historical, archaeological and linguistic studies on Southern China, South-East Asia and the Hongkong region. Proceedings of a meeting held in September 1961 as part of the Golden Jubilee Congress of the University of Hongkong. Hongkong, Hongkong University Press, 1967. X + 370 pp. - D.R. Jonker, Liu Shih-Shun, One hundred and one Chinese poems. With English translations and preface. UNESCO Collection of Representative Works, Chinese Series; Hong Kong University Press, 1967. XXXIX + 173 pp. - M.A.P. Meilink-Roelofsz, A. Das Gupta, Malabar in Asian trade 1740-1800. Cambridge South Asian Studies. Cambridge U.P. 1967. XII, 204 blz. Met krt. - C.R. Hooijer, Per Sorensen, Ban-Kao, Neolithic settlements with cemeteries in the Kanchanaburi Province. 140 pp., 140 plates, 4 maps, figs. The Thai-Danish Prehistoric Expedition 1960-62, Archaeological Excavations in Thailand, Vol. II. Munksgaard, Copenhagen, 1967. - C.R. Hooijer, H.R. van Heekeren, Sai-Yok, Stone-age settlements in the Kanchanaburi Province. 129 pp., 33 plates, 47 figs. The Thai-Danish Prehistoric Expedition 1960-1962, Archaeological Excavations in Thailand, Vol. I. Munksgaard, Copenhagen, 1967., Eigil Knuth (eds.) - Th. G. Th. Pigeaud, C. Hooykaas, Bagus Umbara, Prince of Koripan. The story of a prince of Bali and a princess of Java, illustrated on palm leaves by a Balines artist. With Balinese text and English translation by Dr C. Hooykaas, Reader in Old Javanese, University of London. Published by the Trustees of the British Museum, London, 1968. 55 pp., 9 illustrations, 31 x 25 cm. - H.J. de Graaf, Soemarsaid Moertono, State and statecraft in old Java: A study of the late Mataram period 16th to 19th century. Monograph series Modern Indonesia Project. Southeast Asia Program Department of Asian Studies. Cornell University Ithaca New York 1968. - M.A.P. Meilink-Roelofsz, John Bastin, Sir Thomas Stamford Raffles. With an account of the Raffles-Minto manuscript collection presented to the India Office Library on 17 July 1969 by the Malaysia-Singapore Commercial Association. The Ocean Steamship Company Limited, Liverpool 1969. 33 pp. - C. Fasseur, W.F. Wertheim, Ketters en kwezels. Regenten en rebellen. Laverman N.V., Drachten, 1968. 212 blz., A.H. Wertheim-Gijse Weenink (eds.) - S. Kooijman, Tropical Man. Continuation of International Archives of Ethnography. Yearbook of the Anthropology Department of the Royal Tropical Institute, Amsterdam, Vol. 2; Leiden, E.J. Brill, 1968. Vol. I: 247 pp.

Abstract The theoretical analysis of the acid-fracturing process for turbulent-flow conditions has been process for turbulent-flow conditions has been reconsidered taking fluid losses into account. For a simple fracture model and an idealized acidizing process, the acid concentration in the fracture process, the acid concentration in the fracture during acid injection and the fracture width have been determined as functions of time and place for three loss conditions: (1) no fluid loss, (2) fluid loss proportional to time, and (3) fluid loss proportional to the square root of time. proportional to the square root of time. From the results of the analysis, it is concluded that even under the unfavorable conditions of turbulent flow in the fracture and fluid loss, acid penetration is, in general, not a limiting factor in penetration is, in general, not a limiting factor in the application of the acid-fracturing process. However, it will not be possible to predict the productivity increase resulting from a given productivity increase resulting from a given treatment until more experimental data on the conductivity of etched fractures and on certain aspects of the reaction kinetics have been gathered. Introduction Acid-fracturing treatments are frequently applied to improve well productivity in limestone formations. In this process, hydrochloric acid is injected into a hydraulically induced fracture, which extends diametrically from the wellbore into the formation. During injection, the limestone faces of the fracture are dissolved. As a result, acid is consumed and its concentration decreases in the direction of flow. The width of the fracture increases, and the fracture faces may become irregularly etched as a result of the natural anisotropies of the formation. The etching pattern produced may contribute to an improvement in fracture conductivity after the fracture is allowed to close. The extent of this etching into the fracture and its final fluid conductivity determine the increase in productivity. Barron et al. have presented an empirical formulation of the acid-fracturing process for laminar flow conditions without fluid loss. When a theoretical description given by Prins et al. concerning the heat-transfer in laminar flow between parallel plates, is applied to the acid-fracturing parallel plates, is applied to the acid-fracturing process, the acid concentration in a fracture for process, the acid concentration in a fracture for steady-state laminar flow can be exactly described, provided that the fracture width is constant and no provided that the fracture width is constant and no fluid loss occurs. A comparison of the acid concentrations calculated from the empirical reaction-rate data of Barron with those theoretically derived according to Prins shows that these values are of the same order of magnitude and can be made equal for acceptable values of the diffusion rate only in the range of low velocities. Judging from the experimental set-up of Barron, we believe that for higher velocities the entrance transition length for fully developed laminar flow should be longer. For this reason, no agreement in the higher velocity ranges can be expected. This view is supported by Williams et al., who compared theoretically derived reaction rates in the heterogeneous calcium-carbonate /hydrochloric-acid system with those of Barron et al., who also conclude that entry effects may be responsible for the discrepancies in the higher velocity range. Nierode and Williams determined a kinetic model for the heterogeneous reaction of hydrochloric acid with limestone. The reaction order and rate constant used in their model were obtained from experiments. On the basis of this model, they derived an acid-fracturing design for laminar flow conditions including fluid loss. In the study described below, the acid-fracturing process has been reconsidered for turbulent-flow process has been reconsidered for turbulent-flow conditions in which both fluid loss and change in fracture width have been taken into account. We feel that the study provides a more realistic description of the process for both a vertical and horizontal fracture and that it may be used as a basis for designing acid-fracturing treatments.

H.J. de Graaf, D.G.E. Hall, Historians of South East Asia. Edited by D.G.E. Hall, Professor Emeritus of the History of S.E. Asia, London University. Historical Writing on the Peoples of Asia (II). Oxford University Press, London 1961. 355 pp. text. - H.R. van Heekeren, Irmgard Sellnow, Grundprinzipien einer Periodisierung der Urgeschichte. Deutsche Akadamie der Wissenschaften zu Berlin. Berlijn 1961. 497 blz., tabellen, geb. - F.D.K. Bosch, Alastair Lamb, Miscellaneous papers on early Hindu and Buddhist settlements in Northern Malaya and Southern Thailand. 90 pp., 23 figs., 117 pls.; Museums Dept., Federation of Malaya, Kuala Lumpur, 1961. - G.D. van Wengen, Moebirman, Wajang Purwa (Le jeu d’ombres d’Indonésie). 81 pp., 24 p. ills. Editions Ichtiar. Djakarta 1960. - F. Sierksma, Norbert Mylius, Antlitz und Geheimnis der überseeischen Maske. Eine Einführung in das Maskenwesen der Übersee. Wien 1961. 53 Seiten, 30 Bilder. - F. Sierksma, History of religions. An international journal for comparative historical studies. Vol. 1, nr. 2, Winter 1962. The University of Chicago Press. - H.C. van Renselaar, F. Sierksma, “Een nieuwe hemel en een nieuwe aarde”. Uitgeverij Mouton en Co, ‘s-Gravenhage 1962; 302 pp. - J. van Baal, Annali Lateranensi (Publicazione del Pontificio Museo Missionario Etnologico). Vol. XXIV (1960).

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Netherland Section of the Society of Petroleum Engineers, P. O. Box 228, The Hague, the Netherlands. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract From theoretical considerations if follows that the production improvement factor (PIF) for dry oil or gas production due to natural and/or hydraulically induced vertical fractures in bottom water reservoir showing water coning is identical with the PIF obtainable with the same fracture configuration in a reservoir without bottom water. This is generally derived for a single, symmetrical fracture of arbitrary shape. It has been found that the highest PIF is obtained for a fracture with a PIF is obtained for a fracture with a technically-optimised tapered cross section. Results of calculated examples are discussed. Introduction In oil reservoirs with bottom water the height of a steady-state water cone depends on the potential gradient of the fluid moving along the interface: the greater the gradient (production rate), the higher is the cone. A decrease of the potential gradient, and thus a suppression of the cone, can be achieved by means of a fracture that effectively reduces the resistance to flow. Alternatively, if the cone is allowed to reach the same height, a higher production rate would be achieved. Hydraulically-induced vertical fractures would thus permit higher critical rates (maximum water-free oil production-rates), and make it possible to reduce the number of wells to be drilled for a required off-take. The shape of vertical fractures can be better controlled nowadays. This prompted us to investigate the problem of steady-state fluid flow in the presence of vertical fractures in reservoirs with presence of vertical fractures in reservoirs with bottom water, in order to derive the production improvement factors (PIF) for fractures of various prescribed practicable shapes. The PIF is prescribed practicable shapes. The PIF is defined as the ratio between the critical production rates with and without a fracture. The following considerations are generally valid for the movement of a fluid in the presence of a second non-flowing fluid of different density. hence, the results are equally applicable to the case of oil production over bottom water, respectively from under a gas cap, as to the case of gas production over bottom water. production over bottom water.

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Critical gas production rates of interfering wells over bottom water have been calculated for three different well patterns. The calculations are based on the generalized Girinskii potential, which enables one to account for stratification and real gas flow, assuming Darcy's law to hold. This analysis is applicable when the well may be considered as fully perforated. PVT data are used to establish empirical analytic relationships with respect to pressure. This makes it possible to calculate the generalized Girinskii potential for practical cases. A computer program has been developed which calculates critical rates for clusters of interfering wells in stratified horizontal formations of constant thickness. The program forms an Appendix to this paper. Introduction Many gas reservoirs contain bottom water. This imposes a restriction on the gas production from individual wells because above a certain critical rate, which may be different for each well, these wells cut water. The critical rate is defined as the steady-state gas production rate under a drawdown just small enough to prevent water production from bottom water. This critical rate is associated with the phenomenon of upconing bottom water. The form of the steady-state cone depends essentially on the perforation at the well and the reservoir parameters such as stratification. The majority of the investigations concerned with the determination of critical rates are based on steady-state conditions and segregated flow of the fluids. Many of them, as here, deal with the case of fully perforated wells. Lehner gives in the introduction to this paper a survey of the work published to date on the steady-state coning problem for compressible flow in stratified layers. The truly three-dimensional problem of free-surface flow in a stratified. problem of free-surface flow in a stratified. formation had already been treated by Girinskii. Girinskii, however, in his considerations applied the so-called 'Dupuit assumptions'.

An improved counter for lightning flashes to earth has been developed and tested. Results indicate that this counter registers significantly less cloud flash activity than other counters available; the improvement being due to a particular choice of peak response frequency for the counter's input circuit.