A system includes a processor. The processor estimates a pattern of a flow of a mixture of drilling fluid and cuttings in an annulus of a wellbore. The flow is estimated as a stationary bed flow, a dispersed flow, or a transitional flow relative to the stationary bed and dispersed flows. The processor estimates parameters based on the estimated pattern of the flow, and determines a plurality of dimensionless parameters including a first dimensionless parameter corresponding to an effect of turbulence on the flow and a second dimensionless parameter corresponding to an effect of gravity on the flow, based on the estimated parameters. The processor characterizes the pattern of the flow as the stationary bed flow, the dispersed flow, or the transitional flow, based on the dimensionless parameters, and models the flow based on the estimated pattern if it is determined that the characterized pattern matches the estimated pattern.