Published in PetroleumTransactions, AIME, Volume 207, 1956, pages 118–127. Abstract The dimensionless groups, to which the variables that govern the displacement of oil from reservoirs by liquids can be combined, are derived. Three types of displacement are considered, viz. cold-water drive, hot-water drive and solvent injection. The derivation of the dimensionless groups is carried out by means of the relevant basic equations (inspectional analysis). The resulting sets of groups are afterwards completed by means of dimensional analysis. The form of the groups is given in such a way that they can be adapted to suit the various boundary conditions that are encountered in practice. The physical meaning of the groups is discussed. They have all been brought together on a chart, from which their mutual relation and their correspondence to related dimensionless groups in common use in other engineering sciences can be read off. The limitations of dimensionally scaled model experiments as a useful tool for studying liquid flow in porous media, as occurring in oil reservoirs, are discussed. " The use of models to study fluid mechanics has an appeal for everyone endowed with natural curiosity. What active boy has not played with ship and airplane models, or crude models of dam and drainage systems? Even in the most advanced technical engineering, such models play a fundamental and indispensable role. " And yet in few departments of the physical sciences is there a wider gap between theory and practice, between scientific knowledge and the state of art, than in the use of models to study hydrodynamic phenomena." Garrett Birkhoff Introduction Laboratory displacement experiments are extensively used to investigate, directly or indirectly, the production behavior of petroleum reservoirs. Such experiments are representative of the reservoirs as a whole, if they are carried out with models that are "properly scaled."

Published in Petroleum Transactions, AIME, Volume 204, 1955, pages 35–42. Abstract This paper reports the results of a series of model displacement experiments carried out for measuring the efficiency of the water-drive process. This series forms a continuation and extension of that described by Engelberts and Klinkenberg. Detailed information has been obtained on the influence of the oil/water viscosity ratio. The results are represented in the form of a diagram from which both the oil recovery and the water/oil ratio can be easily read off as a function of the total production (oil plus water) for all values of the viscosity ratio M between 1 and 500. These results are viewed in the light of the two existing theories on water flooding, viz. that of Buckley and Leverett and that of Dietz. It is shown that if the Buckley-Leverett theory applies, the relation between the relative permeability ratio and saturation, which plays a major role in this theory, can be calculated with a high degree of accuracy from the results of the model experiments. Dietz's theory is found to be in agreement with the experimental results in a certain range of circumstances. A discussion of the physical background of the BuckleyLeverett and Dietz theories makes it clear why the latter fails to agree with some of the experimental results. Introduction For an economical exploitation of oil fields both a rational control of natural (primary) recovery processes and a proper application of artificial (secondary) recovery methods are essential. These require detailed information upon the dependence of the relevant flow processes on the variables by which they are governed. Three methods are available for obtaining this information:(statistical) analysis of actual field data;appropriately scaled model experiments; andmathematical analysis of the physical problem. If sufficient data were available, the first method would, in principle, be the most reliable one, although it has the drawback that the basic relationships between the variables involved are to a large extent obscured by the natural inhomogeneities of most reservoirs.

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