High permeability channels (wormholes) are believed to be generated, starting from the wellbore and propagating into the reservoir, during the initial phase of cold production. The development of wormholes drastically enhances oil production. Understanding the wormhole development pattern, therefore, is critical to the modelling of the fluid flow behaviour and recovery rates in the cold production process. We propose that the wormhole growth can be described by the probabilistic active walker (PAW) model, which is a generalisation of the classical random walk model. This simple description may lead to an improved understanding of: the mechanisms involved in cold production, the fluid flow in the area where wormholes are formed (the wormhole zone) and field production data. Previous experimental and theoretical studies indicate that the wormhole diameter may be a function of distance from the wellbore. We assume that this function follows a power law, slowly decreasing with increasing radial distance. We calculated the mobility of a slurry of sand and oil through the wormhole network. This mobility was used to calculate oil and sand production rates. Furthermore, we related the maximum size of the wormhole zone and its expansion rate to the sand production data in a typical cold production operation. This relationship can be useful in determining well spacing. This wormhole network model can also be useful as a tool for analysing field data and for the development of field scale numerical simulations of the cold production process.

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