Predicting oil recovery using percolation theory

P.R. King (1), S.V. Buldyrev (2), N.V. Dokholyan (2,3), S. Havlin (4), G. Paul (2), H.E. Stanley (2),

(1) Department of Earth Science & Engineering, Imperial College, London SW7 2BP, UK
(2) Center for Polymer Studies, Boston University, Boston, MA 02215, USA
(3) Department of Chemistry, Harvard University, Cambridge MA 02138, USA
(4) Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel

Hydrocarbon reservoirs are large, geologically complex entities with heterogeneities on all length scales from millimetres to kilometres. Modern mathematical models of reservoir geology can be very detailed with up to 20 million gridblocks. This is a much higher level of detail than can be resolved by numerical flow simulation required to predict oil recovery rates. In order to span this difference in scales a variety of methods of upscaling have been used. In this paper we describe how percolation theory can be used to estimate the large scale flow rates in hydrocarbon reservoirs. We use a scaling theory to predict the probability distribution of time to breakthrough of an injected fluid (typically water). This breakthrough time is extremely important as it influences the economic recovery rates from oil fields. The scaling law predicts the entire probability distribution semi-analytically something that would be extremely computationally time consuming by conventional Monte Carlo and flow simulation approaches. We also demonstrate the validity of this approach on a real field example.