a b s t r a c tA conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called "reduction." While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory's laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker "local" form of reduction, which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows a certain liberalized construal of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist's" limit-based notion of reduction.

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As with all numerical simulations, the reliability of the output can be no better than the validity of the input. But here is an example of how simulation with meager data can be justified for the range of performance possibilities that it does show. possibilities that it does show. Introduction The Kaybob South field is located approximately 160 miles northwest of Edmonton, Alta., Canada (see Fig. 1). The Beaverhill Lake ‘A’ pool was discovered in 1961 on the southwestern side of the Beaverhill Lake basin. This basin is the scene of sizable oil accumulations such as Swan Hills, Judy Creek, Virginia Hills and Kaybob, but Kaybob South is the first instance of substantial sour gas production. The Kaybob South Beaverhill Lake ‘A’ pool is, in fact, one of the largest gas reservoirs in Canada. The reservoir is at a depth of 10,500 ft and is totally underlaid by water. It currently encompasses some 57,000 acres, has an elongated shape, and extends on trend with the regional strike for about 32 miles. The pool's initial gas in place may be as much as 4,000 Bcf. Because of the possibility of significant retrograde liquid losses upon depletion, it was essential to choose a method of exploiting the pool early in its development. Reservoir simulation to design the cycling project for Unit No. 1 was carried out in three phases. The first phase, involving a reservoir volume of 363 Bcf, produced the basic injection pattern and investigated produced the basic injection pattern and investigated the effects of production rate. The second phase updated pattern studies and included several voidage replacement ratios. The final simulation in Nov., 1968, confirmed the suitability of the scheme with a revised reservoir interpretation and included a study of specialized problems. This paper presents the results as applied to the latest reservoir data. Development History Gas was discovered in the Beaverhill Lake formation in 1961. The follow-up exploratory well revealed the Beaverhill Lake to be water bearing. Over the next 5 years, with mediocre success, four additional wells were drilled to the Beaverhill Lake. Significant Beaverhill Lake stepouts were made in early 1967 with the drilling of two more wells, and the estimate of initial gas in place expanded from 363 to 782 Bcf. A lull in exploration followed, during which the initial planning of a depletion mechanism was formulated. It was apparent that the pool was large enough to support a cycling scheme, and that pressure maintenance would result in a notable increase in recovery of LPG, condensate and sulfur. The planning and designing of the cycling project began in 1967 without full delineation of the reservoir limits. At the start of 1968, three wildcat wells were completed and the proved limit of the pool was extended some 10 miles to the southeast. Subsequent drilling at a brisk pace through 1968 revealed that the pool existed over a distance of 32 miles. The reservoir thickened and broadened to the southeast so much that the cycling scheme under development was hopelessly inadequate for efficient economic depletion of the entire pool. However, the design remained applicable to the earlier pool area. P. 481

The MER (maximum efficient rate) is defined in terms of well known physicalconcepts, and an analytical solution correctly describing them is presented.The differences of opinion regarding its definition and application as an engineering concept are briefly reviewed. The relationship of the basic theoryof water-drive reservoirs and the evolvement of the MER from theseconsiderations is discussed. The primary objective of the study is to reviewprevious work and to present a new analytical technique which is based on theapplication of two different (but acceptable) methods of solution to a partialwater-drive reservoir. The widely divergent results indicate that care must beexercised in choosing a calculation method, and that the acceptability ofresults is dependent upon the accuracy with which the analytical methodcorrectly describes the physical behaviour of the reservoir fluids. The "Fluid Inventory" method, which is a computerized technique adopted as one of theexamples used in this paper, is reviewed in detail and is shown to be the mostacceptable of the investigated methods. This technique, as well as all other MER calculations, results in solutions that require reconciliation withindividual well phenomena and as such they cannot be applied in discriminately. Introduction Historical Review The term MER (maximum efficient rate), as it is currently understood by theoil industry and regulatory bodies, has undergone considerable evolution in thepast 20 years and even today there exists a controversy as to its ramificationsand final utilization. In 1947, Kraus (1) reviewed in detail the history of the MER concept and its useful engineering application as known at that time.Initially, the engineering usefulness of the MER was reflected in devising means of controlling excessive production from prolific oil pools in Texas, Oklahoma and California. It has been believed that prorationing of oilproduction and the resultant decrease in rates in many of the big pools wouldhave a favourable effect on their expected ultimate recoveries. After passingthrough a considerable number of API technical committee reviews, the industryfinally conceived an idea that there must exist an optimum rate for eachreservoir (i.e., a single and unique production rate), which would by itselfinsure optimum conservation of energy and thus result in maximum ultimaterecovery.