Quantification of Sand Production by Use of a Pressure-Gradient-Based Sand Failure Criterion

Abstract A pressure-gradient-based sand failure criterion has been proposed and validated to quantitatively determine the sand production and then characterize the corresponding wormhole growth and its propagations during cold heavy oil production with sand (CHOPS) processes. The new sand failure criterion was firstly developed at a pore-scale by analyzing the mechanical balance around a throat. To simplify the mechanical analysis, a pseudo-interaction force between a failed throat and the rest was proposed to comprehensively and implicitly represent the potential contribution of cementation and geomechanical stresses to fluidization of sand particles. As such, the mechanical balance was mathematically expressed by use of the pressure gradient, the pseudo-interaction force, and the friction caused by the mobilization of sand particles. Then, the sand failure criterion at the pore-scale was achieved and further extended to a grid-scale since the pressure gradient, a key factor dominating the sand production, is constant at either a pore-scale or a grid-scale within wormholes. With the bottomhole pressure as input constraints, the newly proposed sand failure criterion has been validated by history matching production profiles (i.e., cumulative oil production, cumulative gas production, and cumulative sand production) and wormhole propagations of laboratory sand production experiments in the literature. The new sand failure criterion has also been successfully applied to quantify the sand production and then characterize the wormhole propagations of a CHOPS well in the Cold Lake field, Canada. Good agreements have been found from history matching both the experimental measurements and field observations, confirming that the newly proposed sand failure criterion can be used to reproduce the multiphase flow under CHOPS conditions. It is found that both the sand failure and slurry flow contribute to the continuously observed sand production. According to the experimental measurements, the history-matched pressure distribution indicates that the wormhole propagation greatly depends on the magnitude of the breakdown pressure gradient. It is shown from the generated wormhole propagations that continuous sand production may cause heterogeneity no matter whether the original formation is homogeneous or heterogeneous. In addition, the newly proposed sand failure criterion is convenient to be incorporated with any numerical reservoir simulator and thus to be useful for field cases since only a few parameters are required to be inversely determined.

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