Relative Productivity of Perforated Casing-1

Abstract

Abstract An electrolytic model study has been made of the relative productivity ofperforated casing. The results show that the relative productivity is roughlyone-half to two-thirds of that predicted from point-sink calculations. Thisdiscrepancy can be satisfactorily explained on the basis of casinginterference. The relative productivity was found to be insensitive to spatialarrangement of the perforations. Introduction The relative productivity of wells with perforated casing has been treatedmathematically by Muskat. In his treatment the perforations are represented bysmall spheres, thus enabling him to approximate the flow by that to pointsinks. By neglecting interference between the flow into the various spheresrepresenting the perforations, one may deduce the approximate formula (Equation1). Fig. 1 is a comparison of values calculated from equation (1) with Muskat'svalues. It will be observed that the approximate values are in error by lessthan 2' per cent. The disturbing effect of the casing on the flow lines is not explicitly takeninto account by Muskat, but he reasons that interference between the flowpatterns from the various point sinks will result in a negligible flow in theregion within the well radius, and that no appreciable error will result fromnot explicitly excluding flow from this region. This line of reasoning is opento question, however, as the flow impedance, in the immediate vicinity of thewell, of a hemispherical cavity in contact with an opening in the casing istwice that of a spherical sink in a continuous sand layer. There will be adifference, moveover, between the flow into a hemispherical cavity and thatinto a circular hole in the casing. This latter difference can best beappreciated by comparing the flow from a semi-infinite medium into ahemispherical cavity at the edge of the medium with the flow out of a circularopening of the same radius as the hemisphere and which is also on the edge ofthe medium. T.P. 2851