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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 6273492, 9 pages
Research Article

Analytical Model of Waterflood Sweep Efficiency in Vertical Heterogeneous Reservoirs under Constant Pressure

1School of Earth and Space Sciences, Peking University, Beijing 100871, China
2Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, China

Received 20 June 2016; Revised 27 September 2016; Accepted 25 October 2016

Academic Editor: Jian Guo Zhou

Copyright © 2016 Lisha Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An analytical model has been developed for quantitative evaluation of vertical sweep efficiency based on heterogeneous multilayer reservoirs. By applying the Buckley-Leverett displacement mechanism, a theoretical relationship is deduced to describe dynamic changes of the front of water injection, water saturation of producing well, and swept volume during waterflooding under the condition of constant pressure, which substitutes for the condition of constant rate in the traditional way. Then, this method of calculating sweep efficiency is applied from single layer to multilayers, which can be used to accurately calculate the sweep efficiency of heterogeneous reservoirs and evaluate the degree of waterflooding in multilayer reservoirs. In the case study, the water frontal position, water cut, volumetric sweep efficiency, and oil recovery are compared between commingled injection and zonal injection by applying the derived equations. The results are verified by numerical simulators, respectively. It is shown that zonal injection works better than commingled injection in respect of sweep efficiency and oil recovery and has a longer period of water free production.