Modelling of Sand Transport Through Wormholes
Authors: Tremblay B. 
Published: March 2010

Abstract
One of the key mechanisms in the cold production (CHOPS) process is the development of high permeability channels (wormholes), which increase the access to the reservoir. In order to model the growth of wormholes in the field, it is necessary to predict the flow of sand along the wormholes. The laminar flow of sand and oil through an open channel within a wormhole was modelled using an analytical Bingham Mohr-Coulomb model. This model was tested by comparing its predictions to oil and sand flow rate measurements obtained in pipe flow experiments reported in the literature. The model for sand transport was used in developing a field wormhole growth model.

Introduction
In Western Canada, well operators have observed that encouraging sand production along with the oil, in primary recovery, can lead to the economical production of heavy oil from thin reservoirs. Field tests and laboratory experiments suggest that the enhanced recovery associated with massive sand production can best be explained by the development of high permeability channels (wormholes), which access the reservoir(1).
The existing cold production models can be essentially divided into three groups.Equivalent Permeability Models: In these models, the production of sand was thought to lead to the development of a radial higher permeability (dilated) zone which would start at the vertical well and grow into the formation(2–5). The earlier models assumed that the permeability of the dilated zone was constant(2). Denbina et al.(3) concluded that both a dynamically enhanced absolute permeability of the formation with sand production and a suppressed gas relative permeability were required to history match the oil production from typical cold production wells. Kumar and Pooladi-Darvish(4) went further in this approach by also history matching the sand production from a typical cold production well. Wang and Chen(5) developed a cold production model which also takes into account the sand transport within wormholes. They history matched the cumulative oil and sand for a typical cold production well.Wormhole Network (Fractal) Models: In this category of models, the enhanced permeability zone caused by sand production is assumed to be caused by a fractal network of wormholes(6–9). The number and density of the wormhole network was assumed to be large enough such that on a larger scale, the region from which sand is produced can be assumed to be uniform. This required that the wormholes be small and that significant branching occur. Reasonable history matches of the oil and sand production rates were obtained for a set of cold production wells(8). Tan et al.(6) also matched the temperature in producing wells during steam injection. The wormhole network was modelled using the Diffusion Limited Aggregation (DLA) fractal geostatistical approach. A semi-analytical cold production model based on a fractal distribution of wormholes was also developed by Liu and Zhao(9).Linear Channel Models: Loughead and Saltuklaroglu(10) interpreted the pressure build-up tests in cold production wells as indicative of linear flow through a high permeability channel.