A method for controlling computerized operations related to a wellbore comprises drilling the wellbore in a subsurface formation with a drill string including a drill bit. The method comprises acquiring a plurality of drilling parameters while drilling the wellbore. The method comprises determining, based on the plurality of drilling parameters, solids properties for solids forming a cutting plug up hole of the drill bit. The method comprises determining a length of the cutting plug based on the solids properties. The method comprises determining a cutting plug friction force based on the cutting plug length and a pressure differential across the cutting plug. The method comprises performing a drilling operation based on the cutting plug friction force.