How To Diagnose a Thief Zone

Abstract

Calhoun presented a classical method for determining the time required for tracer-tagged liquids to flow from injection wells to producing wells. This method can also be used for evaluating the permeability of the most conductive layer of the formation. This layer may turn out to be a "thief" zone that ought to be closed by subsequent remedial action. Calhoun's method of analysis unfortunately is time consuming because it involves either a graphical integration or an approximation using a summation of terms. A simpler method was therefore developed that achieves the same purpose with much greater speed and with sufficient accuracy. The method is based on a model of two radial-flow regimes illustrated in Fig. 1. Radial flow emanates from the injection well, which acts as a "source," and converges in the producing well, which acts as a "sink" . A unit mobility ratio for the displacing and displaced phases and a piston-like advance of the tracer-laden liquid are assumed. The derivation of the equations starts with the familiar radial-flow and material-balance relationships, which are modified so that they apply to the highest-permeability layer of the formation. Thus,(1)0.00707 k1h1 (p/2) qf = ln(d/2rw)(2)2 2 Wif = 0.1781 (r1 - rw) h1 (1-Sor), where Subscript 1 refers to the high-permeability layer or "thief" zone and(3)f = k1h1/total kh of formation, q = injection rate for well, B/D, Wi = cumulative injection in well, bbl, ri = radius of tracer front in high-permeability layer Eqs. 1 and 2 are combined through the relationship Wi = qt and the resulting equation is solved for t', the time required for the flood front to travel half way from the injection well to the producing well. The desired time, t, for first arrival of tracer-tagged liquid at the producing well is then set equal to 2 t'. P. 839