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The Buckley–Leverett displacement mechanism has been used to predict the performance of waterflood. With Buckley–Leverett method, oil recovery from waterflood is calculated and required water injection volume to achieve that oil recovery is estimated. This method does provide a very useful tool in waterflood design. Our experience in oil industry and a thorough literature review indicates that Buckley–Leverett method was used to analyze waterflood project directly without any adjustment based on the real reservoir and production situations. By doing so, errors are introduced into the analysis. Buckley–Leverett method assumed that displacement occurs in a linear system. This is true for some waterflood scenarios while for others it is not. For some waterflood scenarios, a radial system is more appropriate than a linear system. In this study, we investigated the fractional flow in a radial system and derived the solutions to predict the performance of water displacing oil in radial system. With this radial displacement model, design and prediction of waterflood can be achieved by Buckley–Leverett method and our model, whichever fits the waterflood pattern. Considering the fact that many waterflood scenarios follow radial displacement, our model is an important supplement to Buckley–Leverett method.

Fractional flow in radial flow systems: a study for peripheral waterflood