A Fractal Wormhole Model for Cold Heavy Oil Production

Abstract Wormholes are believed to be generated during the process of cold production and are responsible for enhanced production rates. Understanding the wormhole patterns generated inside the reservoir formation is critical to improve the recovery efficiency and to model the fluid flow behaviour in the cold production process. In this paper, we have proposed that the wormhole growth can be described by the Diffusion-Limited Aggregation (DLA) model, which naturally relates to a broad variety of branchinggrowth patterns through the physics of the processes. The physical processes that were described using fractal models include the following: the growth of a drainage network; the formation of cavities; the dissolution of porous materials; and, the growth of random dendrites in the thin films. The DLA model has important implications in petroleum geology and engineering. Based on the experimental results published in the literature, which were specifically designed to investigate the wormhole dynamics by a Computed-Tomography X-Ray scanner, the wormhole diameter distribution along the wormhole path has been analyzed using the Area Version of Gaussian Function. Then, the material balance method has been applied to the sand production data to determine the possible range of the wormhole structure around the wellbore, assuming that the sand particles are solely produced along the paths of wormholes. Finally, a numerical method has been developed to analyze the field sand production data. The studies have shown that the fractal wormhole model can be used to diagnose the characteristics of the wormhole structures, and that it can be applied to optimize well placement in cold heavy oil production. The model will greatly enhance the analyses of the inflow performance and the pressure response of wells in wormholed reservoirs. Results acquired from this study can also be implemented in field scale numerical simulations for the cold flow process. Introduction Cold production is a non-thermal process in which sand is aggressively produced to reach a higher oil production rate. In the cold flow process, sand and oil are produced together under primary conditions and oil production rates can typically increase by a factor of 10 or more(1–5). For example, primary oil production rates of 8 – 12 m3/d are roughly 10 times greater than those calculated for the radial flow in the Celtic field using Darcy's law(2). The unusual sand production in cold production was observed in several oil fields. Records have indicated that the production of about 708 m3 of sand in the first four months, and in nearly all the wells in S.E. Pauls Valley Field, Oklahoma, produced 10 – 50% sand initially, declining a few months later to 0.1 – 2%, regardless of completion method(5). The cumulative gross fluid production of about 9,000 m3 with an associated sand production of 200 m3 within a period of 1,000 days was observed in the Lindbergh and Frog Lake Fields, Alberta(1).

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