Published in Petroleum Transactions, AIME, Volume 207, 1956, pages 256–261. Abstract The bottom water drive analysis presented by Muskat has been extended to include fields with wider well spacings. Curves are presented from which volumetric sweepout, water-oil ratio, and rate relations may be calculated. The effects of non-unity ratios on sweepout efficiency and productivity decline have been studied by an approximate method. Also, the effect of gravity on volumetric sweepout has been approximated for a particular geometry. Introduction The purpose of this paper is to report work done in applying the analysis of bottom water drive reservoirs given by Muskat to a larger class of reservoirs, to extend this analysis to include the effects of gravity and non-unity mobility ratios in an approximate manner, and to investigate the rate of decline of productive capacity. The bottom water drive type reservoir is one where the oil is underlain by a water zone of sufficient thickness that water movement is essentially vertical. This system is defined in more detail in the appendix and a one well element is shown diagrammatically in Fig. 1. Muskat obtained solutions to the equations describing the volumetric displacement efficiency of idealized bottom water drive systems by assuming that gravity effects due to differences in density between oil and water were negligible and that the mobilities of oil and water were the same. If either of these assumptions is not made, the complexity of the system makes an analytical solution well nigh impossible at the present stage of mathematical development. Coles and Stade developed an approximation to consider these factors. The authors have refined approximations, starting with the same basic assumption, which should give a somewhat quantitative picture of bottom water drive performance when mobilities are not equal and the effects of gravity are not negligible. The results of these approximate calculations can then be used to obtain the decline in well productivity as the field is depleted.

A significant quantity of oil is left in reservoirs after conventional oil recovery techniques have been applied. In West Virginia and Pennsylvania alone, this oil has been estimated at over 4.5 billion barrels (0.72 billion m3). Conventional recovery methods are already being used when applicable. But a new recovery method is needed for use in reservoirs that have been abandoned. One alternative method for recovery of the residual oil is known as "oil recovery from underground drill sites". This recovery technology is a combination of proven methods and equipment from the petroleum, mining, and civil construction industries. Underground oil recovery can be an economically viable method of producing oil. This has been shown in producing fields, field tests, and feasibility studies. Faced with decreasing domestic oil production, the petroleum industry should give serious consideration to the use of oil recovery from underground drill sites as a safe, practical, and environmentally sensitive alternative method of producing oil from many reservoirs.

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A significant quantity of oil is left in reservoirs after conventional oil recovery techniques have been applied. In Wesr Virginia and Pennsylvania alone, this oil has been esrimared ar over 4.5 billion barrels (0.72 billion m3). Conventional recovery methods are already being used when applicable. But a new recovery method is needed for use in reservoirs that have been abandoned. One alternarive method for recovery of the residual oil is known as "oil recoveryfrom underground drill sites." ntis recovery technology is a combination of proven merhods and equipment from the perroleum, mining, and civil construction industries.Underground oil recovery can be an economically viable method of producing oil. This has been shown in producing fields, field rests, and feasibility studies. Faced with decreasing domestic oil producrion, rhe petroleum industry should give serious consideration to the use of oil recoveryfrom underground drill sites as a safe, pracrical, and environmentally sensirive alternative method of producing oil from many reservoirs.