Mathematical modelling of fines migration in geothermal reservoirs

• Governing equations for slow fines drift during migration and straining.
• Analytical model for slow fines migration with mobilisation and size exclusion.
• Good agreement between the laboratory coreflood and modelling data.
• Determination of fines particle distribution from the maximum retention function.
• Successfully matched laboratory data providing an input for the reservoir simulator.

Laboratory-based mathematical modelling of fines migration allows predicting well productivity reduction during the geothermal reservoir exploitation. The analytical model for one-dimensional flow with ionic strength alteration has been derived. Good adjustment of the permeability and breakthrough concentration data from coreflood test by the analytical model has been achieved, and the tuned model coefficients fall in the common ranges. The obtained maximum retention function of multi-sized fines allows calculating their size distribution. During the temperature rise, weakening of electrostatic attraction on fines attached to rock surface overwhelms the reduction of detaching drag force due to water viscosity decrease. It leads to increased fines detachment and more severe permeability decline at elevated temperatures, typical for geothermal fields.

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