Sand production is often observed during the development of weakly consolidated reservoirs. In this paper the physico-mathematical models of the main processes associated with sand production are presented. These models are combined into a single process that allows calculating the dynamics of skin-factor of the well, estimate the risk of well plugging with sand and estimate the concentration of the solids in the flow at the wellhead. Model can also be used for the optimization of the filter.
Coupled model consists of three parts: geomechanical module for estimating the amount of solid particles flowing out of the formation, module for calculating the filter efficiency, and module for solids transport in the well. To evaluate the geomechanical failure of the formation the radial semi-analytical model was used that considers plastic deformations of the weakly consolidated rocks. Pressure drop in the filter was calculated with the one-dimentional suspension model with multiple solid particle sizes. The evaluation of solids transport the was based on the one dimentional model of the multiphase flow. One-way coupling was used to combine these modules. Information about concentration of solid particles in the flow is passed from geomechanical module to the filter module and then to the well transport module.
Presented coupled model covers most significant processes affecting the oil production from weakly consolidated reservoirs. In the course of the work, the dynamics of the near-wellbore area failure was modeled and the dependence of the concentration of solid impurities in the inflow was calculated over time. This data is used as input parameter for the filter model. Calculation of the filter allows estimating the pressure drop across the filter and well's skin factor. The model takes into account the particle size distribution of reservoir particles, which allows it to be used for the optimization problem of filter selection. The constructed model of sand transport along the well allows calculating the risk of sand blockages formation and find the fluid production rate that is sufficient of carrying solids to the welltop. Further development of the model will allow taking into account the erosion of submersible equipment, estimate the turnaround time and calculate the multiphase flow in the near-wellbore area.