Verification of the OOC Mud and Produced Water Discharge Model using lab-scale plume behaviour experiments
Abstract This paper describes comparisons of predictions by the Offshore Operators Committee (OOC) Mud and Produced Water Discharge Model with published data on experimental laboratory-scale observations of plume behavior in flumes, towing tanks, and wind tunnels. The ability of the OOC Model to predict the plume characteristics observed in numerous individual tests of plume behavior covering a wide range of discharge conditions was examined. Data are provided summarizing the predictive ability of the model for all tests. The dimensionless parameters describing the physical characteristics of the plumes were within the range expected for typical Gulf of Mexico produced water and drilling fluid discharges for most of the comparisons. The model was in good to excellent agreement with measurements of plume behavior under most discharge conditions. The model was less accurate for those experimental cases where extreme plume bending occurred. It is believed that turbulence caused by the discharge pipe itself influenced the behavior of these extreme-bending plumes. The predicted density of solids accumulation on the bottom of a towing tank, a lab-scale analogy of the seabed accumulation of drilling solids, was within a factor of two of experimental observations. Excluding the three simulations of extreme bending plumes, the model showed no systematic trend towards either under- or over-estimation of any parameter examined. This suggests that experimental errors or biases may have contributed to observed differences between predictions and observations. The results of the validation testing described in this report increases confidence in the use of OOC Model predictions as an alternative to the difficult and expensive process of performing field measurements for every practical discharge situation.
TURBULENT DENSE PLUMES IN A LAMINAR CROSS FLOW
Experiment of turbulent dense plumes in a cross flow was performed to verify an entrapment theory introduced earlier by CHU and GOLDBERG [1] in the study of buoyant forcedplumes in a cross flow. The theory, involves only one unknown parameter - the entrainment coefficient, is based on a mechanistic model which describes the formation of the circulation of the vortex pair in the plume. In comparing the theory with the experiment, the entrainment coefficient for dense plume was found to be a constant, approximately equal to 0.5. The same constant was obtained by CHU and GOLDBERG for momentum jets and buoyant plumes.
Medieval Modal Theories and Modal Logic Handbook of the History of Logic. Volume 2: Mediaeval and Renaissance Logic
1The translation of the Categories is edited by L. Minio-Paluello in Aristoteles Latinus 1.1-5 (Bruges-Paris: Descl~e de Brouwer, 1961) and the translation of the De interpretatione by L. Minio-Paluello in Aristoteles Latinus II.1-2 (Bruges-Paris: Descl~e de Brouwer, 1965). The translation of Porphyry's Isagoge is edited by L. Minio-Paluello and B.G. Dod in Aristoteles Latinus 1.6-7 (Bruges-Paris: Descl~e de Brouwer, 1966). Boethius's commentary on Aristotle's Categories is found in Patrologia Latina (ed. J.-P. Migne), 64, 159-294, De syllogismis categoricis in Patrologia Latina 64, 793-832, In Ciceronis Topica in Patrologia Latina 64, 1039-1169; an English translation with notes and an introduction by E. Stump, and De differentiis topicis in Patrologia Latina 64, 1174-1216; an English translation with notes and essays by E. Stump, Boethius's De topicis differentiis (Ithaca and London: Cornell University Press, 1978), Boethius's In Ciceronis Topica (Ithaca and London: Cornell University Press, 1988). Boethius's two commentaries on De interpretatione are edited by C. Meiser (Leipzig: Teubner, 1877-1880), his two commentaries on Porphyry's Isagoge by S. Brandt, Corpus Scriptorum Ecclesiasticorum Latinorum 48 (Leipzig: G. Freytag, Vienna: F.Tempsky, 1906), De hypotheticis syllogismis by L. Obertello (Brescia: Paideia, 1969) and De divisione by J. Magee, with a translation and commentary (Leiden: Brill, 1998). Some other ancient works were also used, such as Apuleius's Peri hermeneias (ed. C. Moreschini in Opera III (Stuttgart: Teubner, 1991), Augustine's Dialectica, trans, with notes by B.D. Jackson from the text edited by J. Pinborg, Synthese Historical Library 16 (Dordrecht: Reidel, 1975), and pseudo-Augustinean De decern categoriis, ed. L. Minio-Paluello, in Aristoteles Latinus 1.1-5, 133-75. For the sources of eleventh and twelfth century logic, see J. Marenbon, 'Medieval Latin Commentaries and Glosses on Aristotelian Logical Texts, Before c. 1150 AD' in Ch. Burnett (ed.), Glosses and Commentaries on Aristotelian Logical Tezts (Warburg Institute Surveys and Texts 23), (London: Warburg Institute, 1993), 77-127, republished and revised in J. Marenbon, Aristotelian Logic, Platonism, and the Contezt of Early Medieval Philosophy in the West, Variorum Collected Studies Series (Aldershot: Ashgate, 2000). 2Analytica priora, ed. L. Minio-Paluello, Aristoteles Latinus III.l-4 (Bruges-Paris: Descl~e de Brouwer, 1962), Analytica posteriora, ed. L. Minio-Paluello and B.G. Dod, Aristoteles Latinns IV.l-4 (Bruges-Paris: Descl~e de Brouwer, 1968), Topica, ed. L. Minio-Paluello and B.G.